%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV422-1.100 : TPTP v9.0.0. Released v3.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 : Sat Jun 21 05:33:13 AM UTC 2025
% Result : Unsatisfiable 0.60s 0.79s
% Output : Proof 2.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV422-1.100 : TPTP v9.0.0. Released v3.5.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 09:50:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.60/0.79 % SZS status Unsatisfiable
% 0.60/0.79 % SZS output start Proof
% 0.60/0.79 tff(always25_type, type, (
% 0.60/0.79 always25: $i > $o)).
% 0.60/0.79 tff(s44_type, type, (
% 0.60/0.79 s44: $i)).
% 0.60/0.79 tff(m_main_v_state2_type, type, (
% 0.60/0.79 m_main_v_state2: ( $i * $i ) > $o)).
% 0.60/0.79 tff(c_c2_type, type, (
% 0.60/0.79 c_c2: $i)).
% 0.60/0.79 tff(node9_type, type, (
% 0.60/0.79 node9: $i > $o)).
% 0.60/0.79 tff(s43_type, type, (
% 0.60/0.79 s43: $i)).
% 0.60/0.79 tff(c_n2_type, type, (
% 0.60/0.79 c_n2: $i)).
% 0.60/0.79 tff(node13_type, type, (
% 0.60/0.79 node13: ( $i * $i ) > $o)).
% 0.60/0.79 tff(s42_type, type, (
% 0.60/0.79 s42: $i)).
% 0.60/0.79 tff(node12_type, type, (
% 0.60/0.79 node12: $i > $o)).
% 0.60/0.79 tff(m_main_v_turn_type, type, (
% 0.60/0.79 m_main_v_turn: ( $i * $i ) > $o)).
% 0.60/0.79 tff(c_2_type, type, (
% 0.60/0.79 c_2: $i)).
% 0.60/0.79 tff(c_1_type, type, (
% 0.60/0.79 c_1: $i)).
% 0.60/0.79 tff(m_main_v_state1_type, type, (
% 0.60/0.79 m_main_v_state1: ( $i * $i ) > $o)).
% 0.60/0.79 tff(c_t1_type, type, (
% 0.60/0.79 c_t1: $i)).
% 0.60/0.79 tff(s41_type, type, (
% 0.60/0.79 s41: $i)).
% 0.60/0.79 tff(node6_type, type, (
% 0.60/0.79 node6: ( $i * $i ) > $o)).
% 0.60/0.79 tff(s40_type, type, (
% 0.60/0.79 s40: $i)).
% 0.60/0.79 tff(node1_type, type, (
% 0.60/0.79 node1: $i > $o)).
% 0.60/0.79 tff(c_n1_type, type, (
% 0.60/0.79 c_n1: $i)).
% 0.60/0.79 tff(s39_type, type, (
% 0.60/0.79 s39: $i)).
% 0.60/0.79 tff(node5_type, type, (
% 0.60/0.79 node5: $i > $o)).
% 0.60/0.79 tff(s38_type, type, (
% 0.60/0.79 s38: $i)).
% 0.60/0.79 tff(c_c1_type, type, (
% 0.60/0.79 c_c1: $i)).
% 0.60/0.79 tff(node3_type, type, (
% 0.60/0.79 node3: $i > $o)).
% 0.60/0.79 tff(s37_type, type, (
% 0.60/0.79 s37: $i)).
% 0.60/0.79 tff(s36_type, type, (
% 0.60/0.79 s36: $i)).
% 0.60/0.79 tff(c_t2_type, type, (
% 0.60/0.79 c_t2: $i)).
% 0.60/0.79 tff(s35_type, type, (
% 0.60/0.79 s35: $i)).
% 0.60/0.79 tff(s34_type, type, (
% 0.60/0.79 s34: $i)).
% 0.60/0.79 tff(s33_type, type, (
% 0.60/0.79 s33: $i)).
% 0.60/0.79 tff(s32_type, type, (
% 0.60/0.79 s32: $i)).
% 0.60/0.79 tff(s31_type, type, (
% 0.60/0.79 s31: $i)).
% 0.60/0.79 tff(s30_type, type, (
% 0.60/0.79 s30: $i)).
% 0.60/0.79 tff(s29_type, type, (
% 0.60/0.79 s29: $i)).
% 0.60/0.79 tff(s28_type, type, (
% 0.60/0.79 s28: $i)).
% 0.60/0.79 tff(s27_type, type, (
% 0.60/0.79 s27: $i)).
% 0.60/0.79 tff(s26_type, type, (
% 0.60/0.79 s26: $i)).
% 0.60/0.79 tff(s25_type, type, (
% 0.60/0.79 s25: $i)).
% 0.60/0.79 tff(s24_type, type, (
% 0.60/0.79 s24: $i)).
% 0.60/0.79 tff(s23_type, type, (
% 0.60/0.79 s23: $i)).
% 0.60/0.79 tff(s22_type, type, (
% 0.60/0.79 s22: $i)).
% 0.60/0.79 tff(s21_type, type, (
% 0.60/0.79 s21: $i)).
% 0.60/0.79 tff(s20_type, type, (
% 0.60/0.79 s20: $i)).
% 0.60/0.79 tff(s19_type, type, (
% 0.60/0.79 s19: $i)).
% 0.60/0.79 tff(s18_type, type, (
% 0.60/0.79 s18: $i)).
% 0.60/0.79 tff(s17_type, type, (
% 0.60/0.79 s17: $i)).
% 0.60/0.79 tff(s16_type, type, (
% 0.60/0.79 s16: $i)).
% 0.60/0.79 tff(s15_type, type, (
% 0.60/0.79 s15: $i)).
% 0.60/0.79 tff(s14_type, type, (
% 0.60/0.79 s14: $i)).
% 0.60/0.79 tff(s13_type, type, (
% 0.60/0.79 s13: $i)).
% 0.60/0.79 tff(s12_type, type, (
% 0.60/0.79 s12: $i)).
% 0.60/0.79 tff(s11_type, type, (
% 0.60/0.79 s11: $i)).
% 0.60/0.79 tff(s10_type, type, (
% 0.60/0.79 s10: $i)).
% 0.60/0.79 tff(s9_type, type, (
% 0.60/0.79 s9: $i)).
% 0.60/0.79 tff(s8_type, type, (
% 0.60/0.79 s8: $i)).
% 0.60/0.79 tff(s7_type, type, (
% 0.60/0.79 s7: $i)).
% 0.60/0.79 tff(s6_type, type, (
% 0.60/0.79 s6: $i)).
% 0.60/0.79 tff(s5_type, type, (
% 0.60/0.79 s5: $i)).
% 0.60/0.79 tff(s4_type, type, (
% 0.60/0.79 s4: $i)).
% 0.60/0.79 tff(s3_type, type, (
% 0.60/0.79 s3: $i)).
% 0.60/0.79 tff(s2_type, type, (
% 0.60/0.79 s2: $i)).
% 0.60/0.79 tff(s1_type, type, (
% 0.60/0.79 s1: $i)).
% 0.60/0.79 tff(node8_type, type, (
% 0.60/0.79 node8: $i > $o)).
% 0.60/0.79 tff(s0_type, type, (
% 0.60/0.79 s0: $i)).
% 0.60/0.79 tff(node14_type, type, (
% 0.60/0.79 node14: ( $i * $i ) > $o)).
% 0.60/0.79 tff(trans_type, type, (
% 0.60/0.79 trans: ( $i * $i ) > $o)).
% 0.60/0.79 tff(succ_type, type, (
% 0.60/0.79 succ: ( $i * $i ) > $o)).
% 0.60/0.79 tff(node17_type, type, (
% 0.60/0.79 node17: ( $i * $i ) > $o)).
% 0.60/0.79 tff(node15_type, type, (
% 0.60/0.79 node15: $i > $o)).
% 0.60/0.79 tff(node16_type, type, (
% 0.60/0.79 node16: $i > $o)).
% 0.60/0.79 tff(node18_type, type, (
% 0.60/0.79 node18: ( $i * $i ) > $o)).
% 0.60/0.79 tff(node11_type, type, (
% 0.60/0.79 node11: $i > $o)).
% 0.60/0.79 tff(node7_type, type, (
% 0.60/0.79 node7: ( $i * $i ) > $o)).
% 0.60/0.79 tff(node10_type, type, (
% 0.60/0.79 node10: $i > $o)).
% 0.60/0.79 tff(node4_type, type, (
% 0.60/0.79 node4: $i > $o)).
% 0.60/0.79 tff(node2_type, type, (
% 0.60/0.79 node2: $i > $o)).
% 0.60/0.79 tff(s99_type, type, (
% 0.60/0.79 s99: $i)).
% 0.60/0.79 tff(xuntil28_type, type, (
% 0.60/0.79 xuntil28: $i > $o)).
% 0.60/0.79 tff(node26_type, type, (
% 0.60/0.79 node26: $i > $o)).
% 0.60/0.79 tff(until27_type, type, (
% 0.60/0.79 until27: $i > $o)).
% 0.60/0.79 tff(s98_type, type, (
% 0.60/0.79 s98: $i)).
% 0.60/0.79 tff(s97_type, type, (
% 0.60/0.79 s97: $i)).
% 0.60/0.79 tff(s96_type, type, (
% 0.60/0.79 s96: $i)).
% 0.60/0.79 tff(s95_type, type, (
% 0.60/0.79 s95: $i)).
% 0.60/0.79 tff(s94_type, type, (
% 0.60/0.79 s94: $i)).
% 0.60/0.79 tff(s93_type, type, (
% 0.60/0.79 s93: $i)).
% 0.60/0.79 tff(s92_type, type, (
% 0.60/0.79 s92: $i)).
% 0.60/0.79 tff(s91_type, type, (
% 0.60/0.79 s91: $i)).
% 0.60/0.79 tff(s90_type, type, (
% 0.60/0.79 s90: $i)).
% 0.60/0.79 tff(s89_type, type, (
% 0.60/0.79 s89: $i)).
% 0.60/0.79 tff(s88_type, type, (
% 0.60/0.79 s88: $i)).
% 0.60/0.79 tff(s87_type, type, (
% 0.60/0.79 s87: $i)).
% 0.60/0.79 tff(s86_type, type, (
% 0.60/0.79 s86: $i)).
% 0.60/0.79 tff(s85_type, type, (
% 0.60/0.79 s85: $i)).
% 0.60/0.79 tff(s84_type, type, (
% 0.60/0.79 s84: $i)).
% 0.60/0.79 tff(s83_type, type, (
% 0.60/0.79 s83: $i)).
% 0.60/0.79 tff(s82_type, type, (
% 0.60/0.79 s82: $i)).
% 0.60/0.79 tff(s81_type, type, (
% 0.60/0.79 s81: $i)).
% 0.60/0.79 tff(s80_type, type, (
% 0.60/0.79 s80: $i)).
% 0.60/0.79 tff(s79_type, type, (
% 0.60/0.80 s79: $i)).
% 0.60/0.80 tff(s78_type, type, (
% 0.60/0.80 s78: $i)).
% 0.60/0.80 tff(s77_type, type, (
% 0.60/0.80 s77: $i)).
% 0.60/0.80 tff(s76_type, type, (
% 0.60/0.80 s76: $i)).
% 0.60/0.80 tff(s75_type, type, (
% 0.60/0.80 s75: $i)).
% 0.60/0.80 tff(s74_type, type, (
% 0.60/0.80 s74: $i)).
% 0.60/0.80 tff(s73_type, type, (
% 0.60/0.80 s73: $i)).
% 0.60/0.80 tff(s72_type, type, (
% 0.60/0.80 s72: $i)).
% 0.60/0.80 tff(s71_type, type, (
% 0.60/0.80 s71: $i)).
% 0.60/0.80 tff(s70_type, type, (
% 0.60/0.80 s70: $i)).
% 0.60/0.80 tff(s69_type, type, (
% 0.60/0.80 s69: $i)).
% 0.60/0.80 tff(s68_type, type, (
% 0.60/0.80 s68: $i)).
% 0.60/0.80 tff(s67_type, type, (
% 0.60/0.80 s67: $i)).
% 0.60/0.80 tff(s66_type, type, (
% 0.60/0.80 s66: $i)).
% 0.60/0.80 tff(s65_type, type, (
% 0.60/0.80 s65: $i)).
% 0.60/0.80 tff(s64_type, type, (
% 0.60/0.80 s64: $i)).
% 0.60/0.80 tff(s63_type, type, (
% 0.60/0.80 s63: $i)).
% 0.60/0.80 tff(s62_type, type, (
% 0.60/0.80 s62: $i)).
% 0.60/0.80 tff(s61_type, type, (
% 0.60/0.80 s61: $i)).
% 0.60/0.80 tff(s60_type, type, (
% 0.60/0.80 s60: $i)).
% 0.60/0.80 tff(s59_type, type, (
% 0.60/0.80 s59: $i)).
% 0.60/0.80 tff(s58_type, type, (
% 0.60/0.80 s58: $i)).
% 0.60/0.80 tff(s57_type, type, (
% 0.60/0.80 s57: $i)).
% 0.60/0.80 tff(s56_type, type, (
% 0.60/0.80 s56: $i)).
% 0.60/0.80 tff(s55_type, type, (
% 0.60/0.80 s55: $i)).
% 0.60/0.80 tff(s54_type, type, (
% 0.60/0.80 s54: $i)).
% 0.60/0.80 tff(s53_type, type, (
% 0.60/0.80 s53: $i)).
% 0.60/0.80 tff(s52_type, type, (
% 0.60/0.80 s52: $i)).
% 0.60/0.80 tff(s51_type, type, (
% 0.60/0.80 s51: $i)).
% 0.60/0.80 tff(s50_type, type, (
% 0.60/0.80 s50: $i)).
% 0.60/0.80 tff(s49_type, type, (
% 0.60/0.80 s49: $i)).
% 0.60/0.80 tff(s48_type, type, (
% 0.60/0.80 s48: $i)).
% 0.60/0.80 tff(s47_type, type, (
% 0.60/0.80 s47: $i)).
% 0.60/0.80 tff(s46_type, type, (
% 0.60/0.80 s46: $i)).
% 0.60/0.80 tff(s45_type, type, (
% 0.60/0.80 s45: $i)).
% 0.60/0.80 tff(until2p29_type, type, (
% 0.60/0.80 until2p29: $i > $o)).
% 0.60/0.80 tff(xuntil2p30_type, type, (
% 0.60/0.80 xuntil2p30: $i > $o)).
% 0.60/0.80 tff(last_type, type, (
% 0.60/0.80 last: $i > $o)).
% 0.60/0.80 tff(loop_type, type, (
% 0.60/0.80 loop: $o)).
% 0.60/0.80 tff(1,plain,
% 0.60/0.80 (m_main_v_state1(s0, c_n1) <=> m_main_v_state1(s0, c_n1)),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(2,axiom,(m_main_v_state1(s0, c_n1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_11')).
% 0.60/0.80 tff(3,plain,
% 0.60/0.80 (m_main_v_state1(s0, c_n1)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.60/0.80 tff(4,plain,
% 0.60/0.80 (^[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))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(5,plain,
% 0.60/0.80 (![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)))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[4])).
% 0.60/0.80 tff(6,plain,
% 0.60/0.80 (![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)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(7,axiom,(![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_2')).
% 0.60/0.80 tff(8,plain,
% 0.60/0.80 (![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.60/0.80 tff(9,plain,(
% 0.60/0.80 ![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))),
% 0.60/0.80 inference(skolemize,[status(sab)],[8])).
% 0.60/0.80 tff(10,plain,
% 0.60/0.80 (![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.60/0.80 tff(11,plain,
% 0.60/0.80 (((~![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)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(12,plain,
% 0.60/0.80 ((~![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)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(13,plain,
% 0.60/0.80 ((~![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))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.60/0.80 tff(14,plain,
% 0.60/0.80 (~m_main_v_state1(s0, c_t1)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[13, 10, 3])).
% 0.60/0.80 tff(15,plain,
% 0.60/0.80 (^[X: $i] : refl((m_main_v_state1(X, c_t1) | (~node8(X))) <=> (m_main_v_state1(X, c_t1) | (~node8(X))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(16,plain,
% 0.60/0.80 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X))) <=> ![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X)))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[15])).
% 0.60/0.80 tff(17,plain,
% 0.60/0.80 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X))) <=> ![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(18,axiom,(![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_36')).
% 0.60/0.80 tff(19,plain,
% 0.60/0.80 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.60/0.80 tff(20,plain,(
% 0.60/0.80 ![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X)))),
% 0.60/0.80 inference(skolemize,[status(sab)],[19])).
% 0.60/0.80 tff(21,plain,
% 0.60/0.80 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.60/0.80 tff(22,plain,
% 0.60/0.80 (((~![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)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(23,plain,
% 0.60/0.80 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X)))) | (m_main_v_state1(s0, c_t1) | (~node8(s0)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(24,plain,
% 0.60/0.80 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X)))) | m_main_v_state1(s0, c_t1) | (~node8(s0))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.60/0.80 tff(25,plain,
% 0.60/0.80 (~node8(s0)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[24, 21, 14])).
% 0.60/0.80 tff(26,plain,
% 0.60/0.80 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | trans(X, Y)) <=> ((~succ(X, Y)) | trans(X, Y)))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(27,plain,
% 0.60/0.80 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[26])).
% 0.60/0.80 tff(28,plain,
% 0.60/0.80 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(29,axiom,(![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound101')).
% 0.60/0.80 tff(30,plain,
% 0.60/0.80 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.60/0.80 tff(31,plain,(
% 0.60/0.80 ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 0.60/0.80 inference(skolemize,[status(sab)],[30])).
% 0.60/0.80 tff(32,plain,
% 0.60/0.80 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.60/0.80 tff(33,plain,
% 0.60/0.80 (succ(s0, s1) <=> succ(s0, s1)),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(34,axiom,(succ(s0, s1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound1')).
% 0.60/0.80 tff(35,plain,
% 0.60/0.80 (succ(s0, s1)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.60/0.80 tff(36,plain,
% 0.60/0.80 (((~![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))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(37,plain,
% 0.60/0.80 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s0, s1)) | trans(s0, s1))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(38,plain,
% 0.60/0.80 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s0, s1)) | trans(s0, s1)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.60/0.80 tff(39,plain,
% 0.60/0.80 (trans(s0, s1)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[38, 35, 32])).
% 0.60/0.80 tff(40,plain,
% 0.60/0.80 (^[Y: $i, X: $i] : refl(((~trans(X, Y)) | node14(X, Y)) <=> ((~trans(X, Y)) | node14(X, Y)))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(41,plain,
% 0.60/0.80 (![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y)) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[40])).
% 0.60/0.80 tff(42,plain,
% 0.60/0.80 (![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y)) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(43,axiom,(![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_55')).
% 0.60/0.80 tff(44,plain,
% 0.60/0.80 (![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.60/0.80 tff(45,plain,(
% 0.60/0.80 ![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))),
% 0.60/0.80 inference(skolemize,[status(sab)],[44])).
% 0.60/0.80 tff(46,plain,
% 0.60/0.80 (![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.60/0.80 tff(47,plain,
% 0.60/0.80 (((~![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))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(48,plain,
% 0.60/0.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s0, s1)) | node14(s0, s1))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(49,plain,
% 0.60/0.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s0, s1)) | node14(s0, s1)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.60/0.80 tff(50,plain,
% 0.60/0.80 (node14(s0, s1)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[49, 46, 39])).
% 0.60/0.80 tff(51,plain,
% 0.60/0.80 (^[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)))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(52,plain,
% 0.60/0.80 (![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))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[51])).
% 0.60/0.80 tff(53,plain,
% 0.60/0.80 (![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))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(54,plain,
% 0.60/0.80 (^[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))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(55,plain,
% 0.60/0.80 (![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))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[54])).
% 0.60/0.80 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/sandbox/benchmark/theBenchmark.p','m_main_49')).
% 0.60/0.80 tff(57,plain,
% 0.60/0.80 (![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))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.60/0.80 tff(58,plain,
% 0.60/0.80 (![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))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.60/0.80 tff(59,plain,(
% 0.60/0.80 ![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))),
% 0.60/0.80 inference(skolemize,[status(sab)],[58])).
% 0.60/0.80 tff(60,plain,
% 0.60/0.80 (![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))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.60/0.80 tff(61,plain,
% 0.60/0.80 (m_main_v_state2(s0, c_n2) <=> m_main_v_state2(s0, c_n2)),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(62,axiom,(m_main_v_state2(s0, c_n2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_12')).
% 0.60/0.80 tff(63,plain,
% 0.60/0.80 (m_main_v_state2(s0, c_n2)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.60/0.80 tff(64,plain,
% 0.60/0.80 (((~![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)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(65,plain,
% 0.60/0.80 (((~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)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(66,plain,
% 0.60/0.80 (((~![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))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[65])).
% 0.60/0.80 tff(67,plain,
% 0.60/0.80 (((~![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)))),
% 0.60/0.80 inference(transitivity,[status(thm)],[66, 64])).
% 0.60/0.80 tff(68,plain,
% 0.60/0.80 ((~![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))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(69,plain,
% 0.60/0.80 ((~![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))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.60/0.80 tff(70,plain,
% 0.60/0.80 (m_main_v_state2(s1, c_t2)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[69, 3, 63, 60, 50, 25])).
% 0.60/0.80 tff(71,plain,
% 0.60/0.80 (^[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))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(72,plain,
% 0.60/0.80 (![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)))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[71])).
% 0.60/0.80 tff(73,plain,
% 0.60/0.80 (![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)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(74,axiom,(![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_6')).
% 0.60/0.80 tff(75,plain,
% 0.60/0.80 (![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.60/0.80 tff(76,plain,(
% 0.60/0.80 ![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))),
% 0.60/0.80 inference(skolemize,[status(sab)],[75])).
% 0.60/0.80 tff(77,plain,
% 0.60/0.80 (![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.60/0.80 tff(78,plain,
% 0.60/0.80 (((~![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)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(79,plain,
% 0.60/0.80 ((~![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)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(80,plain,
% 0.60/0.80 ((~![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))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.60/0.80 tff(81,plain,
% 0.60/0.80 (~m_main_v_state2(s1, c_n2)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[80, 77, 70])).
% 0.60/0.80 tff(82,plain,
% 0.60/0.80 (^[X: $i] : refl((m_main_v_state2(X, c_n2) | (~node9(X))) <=> (m_main_v_state2(X, c_n2) | (~node9(X))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(83,plain,
% 0.60/0.80 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[82])).
% 0.60/0.80 tff(84,plain,
% 0.60/0.80 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(85,axiom,(![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_37')).
% 0.60/0.80 tff(86,plain,
% 0.60/0.80 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.60/0.80 tff(87,plain,(
% 0.60/0.80 ![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))),
% 0.60/0.80 inference(skolemize,[status(sab)],[86])).
% 0.60/0.80 tff(88,plain,
% 0.60/0.80 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.60/0.80 tff(89,plain,
% 0.60/0.80 (((~![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)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(90,plain,
% 0.60/0.80 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s1, c_n2) | (~node9(s1)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(91,plain,
% 0.60/0.80 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s1, c_n2) | (~node9(s1))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.60/0.80 tff(92,plain,
% 0.60/0.80 (~node9(s1)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[91, 88, 81])).
% 0.60/0.80 tff(93,plain,
% 0.60/0.80 (((~![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)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(94,plain,
% 0.60/0.80 ((~![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)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(95,plain,
% 0.60/0.80 ((~![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))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.60/0.80 tff(96,plain,
% 0.60/0.80 (~m_main_v_state2(s0, c_t2)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[95, 77, 63])).
% 0.60/0.80 tff(97,plain,
% 0.60/0.80 (^[X: $i] : refl((m_main_v_state2(X, c_t2) | (~node15(X))) <=> (m_main_v_state2(X, c_t2) | (~node15(X))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(98,plain,
% 0.60/0.80 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X))) <=> ![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[97])).
% 0.60/0.80 tff(99,plain,
% 0.60/0.80 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X))) <=> ![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(100,axiom,(![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_57')).
% 0.60/0.80 tff(101,plain,
% 0.60/0.80 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.60/0.80 tff(102,plain,(
% 0.60/0.80 ![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))),
% 0.60/0.80 inference(skolemize,[status(sab)],[101])).
% 0.60/0.80 tff(103,plain,
% 0.60/0.80 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.60/0.80 tff(104,plain,
% 0.60/0.80 (((~![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)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(105,plain,
% 0.60/0.80 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s0, c_t2) | (~node15(s0)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(106,plain,
% 0.60/0.80 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s0, c_t2) | (~node15(s0))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.60/0.80 tff(107,plain,
% 0.60/0.80 (~node15(s0)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[106, 103, 96])).
% 0.60/0.80 tff(108,plain,
% 0.60/0.80 (^[X: $i] : refl((m_main_v_state1(X, c_t1) | (~node16(X))) <=> (m_main_v_state1(X, c_t1) | (~node16(X))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(109,plain,
% 0.60/0.80 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X))) <=> ![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X)))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[108])).
% 0.60/0.80 tff(110,plain,
% 0.60/0.80 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X))) <=> ![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(111,axiom,(![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_59')).
% 0.60/0.80 tff(112,plain,
% 0.60/0.80 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.60/0.80 tff(113,plain,(
% 0.60/0.80 ![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X)))),
% 0.60/0.80 inference(skolemize,[status(sab)],[112])).
% 0.60/0.80 tff(114,plain,
% 0.60/0.80 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.60/0.80 tff(115,plain,
% 0.60/0.80 (((~![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)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(116,plain,
% 0.60/0.80 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X)))) | (m_main_v_state1(s0, c_t1) | (~node16(s0)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(117,plain,
% 0.60/0.80 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X)))) | m_main_v_state1(s0, c_t1) | (~node16(s0))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.60/0.80 tff(118,plain,
% 0.60/0.80 (~node16(s0)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[117, 114, 14])).
% 0.60/0.80 tff(119,plain,
% 0.60/0.80 (^[Y: $i, X: $i] : refl(((~trans(X, Y)) | node18(X, Y)) <=> ((~trans(X, Y)) | node18(X, Y)))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(120,plain,
% 0.60/0.80 (![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y)) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[119])).
% 0.60/0.80 tff(121,plain,
% 0.60/0.80 (![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y)) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(122,axiom,(![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_65')).
% 0.60/0.80 tff(123,plain,
% 0.60/0.80 (![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.60/0.80 tff(124,plain,(
% 0.60/0.80 ![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))),
% 0.60/0.80 inference(skolemize,[status(sab)],[123])).
% 0.60/0.80 tff(125,plain,
% 0.60/0.80 (![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.60/0.80 tff(126,plain,
% 0.60/0.80 (((~![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))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(127,plain,
% 0.60/0.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s0, s1)) | node18(s0, s1))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(128,plain,
% 0.60/0.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s0, s1)) | node18(s0, s1)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.60/0.80 tff(129,plain,
% 0.60/0.80 (node18(s0, s1)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[128, 125, 39])).
% 0.60/0.80 tff(130,plain,
% 0.60/0.80 (^[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))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(131,plain,
% 0.60/0.80 (![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)))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[130])).
% 0.60/0.80 tff(132,plain,
% 0.60/0.80 (![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)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(133,plain,
% 0.60/0.80 (^[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)))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(134,plain,
% 0.60/0.80 (![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)))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[133])).
% 0.60/0.80 tff(135,axiom,(![Y: $i, X: $i] : (((node15(X) | node16(X)) | node17(X, Y)) | (~node18(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_64')).
% 0.60/0.80 tff(136,plain,
% 0.60/0.80 (![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.60/0.80 tff(137,plain,
% 0.60/0.80 (![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.60/0.80 tff(138,plain,(
% 0.60/0.80 ![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))),
% 0.60/0.80 inference(skolemize,[status(sab)],[137])).
% 0.60/0.80 tff(139,plain,
% 0.60/0.80 (![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[138, 131])).
% 0.60/0.80 tff(140,plain,
% 0.60/0.80 (((~![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)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(141,plain,
% 0.60/0.81 ((node15(s0) | node16(s0) | node17(s0, s1) | (~node18(s0, s1))) <=> (node16(s0) | node15(s0) | node17(s0, s1) | (~node18(s0, s1)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(142,plain,
% 0.60/0.81 (((~![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))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[141])).
% 0.60/0.81 tff(143,plain,
% 0.60/0.81 (((~![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)))),
% 0.60/0.81 inference(transitivity,[status(thm)],[142, 140])).
% 0.60/0.81 tff(144,plain,
% 0.60/0.81 ((~![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))) | (node15(s0) | node16(s0) | node17(s0, s1) | (~node18(s0, s1)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(145,plain,
% 0.60/0.81 ((~![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))) | node16(s0) | node15(s0) | node17(s0, s1) | (~node18(s0, s1))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.60/0.81 tff(146,plain,
% 0.60/0.81 (node17(s0, s1)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[145, 139, 129, 118, 107])).
% 0.60/0.81 tff(147,plain,
% 0.60/0.81 (m_main_v_turn(s0, c_1) <=> m_main_v_turn(s0, c_1)),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(148,axiom,(m_main_v_turn(s0, c_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_13')).
% 0.60/0.81 tff(149,plain,
% 0.60/0.81 (m_main_v_turn(s0, c_1)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.60/0.81 tff(150,plain,
% 0.60/0.81 (^[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))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(151,plain,
% 0.60/0.81 (![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)))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[150])).
% 0.60/0.81 tff(152,plain,
% 0.60/0.81 (![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)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(153,axiom,(![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_10')).
% 0.60/0.81 tff(154,plain,
% 0.60/0.81 (![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.60/0.81 tff(155,plain,(
% 0.60/0.81 ![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))),
% 0.60/0.81 inference(skolemize,[status(sab)],[154])).
% 0.60/0.81 tff(156,plain,
% 0.60/0.81 (![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.60/0.81 tff(157,plain,
% 0.60/0.81 (((~![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)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(158,plain,
% 0.60/0.81 ((~![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)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(159,plain,
% 0.60/0.81 ((~![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))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.60/0.81 tff(160,plain,
% 0.60/0.81 (~m_main_v_turn(s0, c_2)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[159, 156, 149])).
% 0.60/0.81 tff(161,plain,
% 0.60/0.81 (^[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))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(162,plain,
% 0.60/0.81 (![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)))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[161])).
% 0.60/0.81 tff(163,plain,
% 0.60/0.81 (![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)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(164,plain,
% 0.60/0.81 (^[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))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(165,plain,
% 0.60/0.81 (![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)))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[164])).
% 0.60/0.81 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/sandbox/benchmark/theBenchmark.p','m_main_61')).
% 0.60/0.81 tff(167,plain,
% 0.60/0.81 (![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.60/0.81 tff(168,plain,
% 0.60/0.81 (![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[167, 163])).
% 0.60/0.81 tff(169,plain,(
% 0.60/0.81 ![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))),
% 0.60/0.81 inference(skolemize,[status(sab)],[168])).
% 0.60/0.81 tff(170,plain,
% 0.60/0.81 (![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[169, 162])).
% 0.60/0.81 tff(171,plain,
% 0.60/0.81 (((~![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)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(172,plain,
% 0.60/0.81 (((~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)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(173,plain,
% 0.60/0.81 (((~![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))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[172])).
% 0.60/0.81 tff(174,plain,
% 0.60/0.81 (((~![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)))),
% 0.60/0.81 inference(transitivity,[status(thm)],[173, 171])).
% 0.60/0.81 tff(175,plain,
% 0.60/0.81 ((~![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)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(176,plain,
% 0.60/0.81 ((~![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))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.60/0.81 tff(177,plain,
% 0.60/0.81 (~m_main_v_turn(s1, c_2)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[176, 170, 160, 146])).
% 0.60/0.81 tff(178,plain,
% 0.60/0.81 (^[X: $i] : refl((m_main_v_turn(X, c_2) | (~node12(X))) <=> (m_main_v_turn(X, c_2) | (~node12(X))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(179,plain,
% 0.60/0.81 (![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X))) <=> ![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[178])).
% 0.60/0.81 tff(180,plain,
% 0.60/0.81 (![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X))) <=> ![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(181,axiom,(![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_45')).
% 0.60/0.81 tff(182,plain,
% 0.60/0.81 (![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.60/0.81 tff(183,plain,(
% 0.60/0.81 ![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))),
% 0.60/0.81 inference(skolemize,[status(sab)],[182])).
% 0.60/0.81 tff(184,plain,
% 0.60/0.81 (![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[183, 179])).
% 0.60/0.81 tff(185,plain,
% 0.60/0.81 (((~![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)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(186,plain,
% 0.65/0.81 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s1, c_2) | (~node12(s1)))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(187,plain,
% 0.65/0.81 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s1, c_2) | (~node12(s1))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.65/0.81 tff(188,plain,
% 0.65/0.81 (~node12(s1)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[187, 184, 177])).
% 0.65/0.81 tff(189,plain,
% 0.65/0.81 (^[X: $i] : refl((m_main_v_state2(X, c_t2) | (~node1(X))) <=> (m_main_v_state2(X, c_t2) | (~node1(X))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(190,plain,
% 0.65/0.81 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X))) <=> ![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[189])).
% 0.65/0.81 tff(191,plain,
% 0.65/0.81 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X))) <=> ![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(192,axiom,(![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_15')).
% 0.65/0.81 tff(193,plain,
% 0.65/0.81 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.65/0.81 tff(194,plain,(
% 0.65/0.81 ![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))),
% 0.65/0.81 inference(skolemize,[status(sab)],[193])).
% 0.65/0.81 tff(195,plain,
% 0.65/0.81 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[194, 190])).
% 0.65/0.81 tff(196,plain,
% 0.65/0.81 (((~![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)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(197,plain,
% 0.65/0.81 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s0, c_t2) | (~node1(s0)))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(198,plain,
% 0.65/0.81 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s0, c_t2) | (~node1(s0))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.65/0.81 tff(199,plain,
% 0.65/0.81 (~node1(s0)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[198, 195, 96])).
% 0.65/0.81 tff(200,plain,
% 0.65/0.81 (^[Y: $i, X: $i] : refl(((~trans(X, Y)) | node7(X, Y)) <=> ((~trans(X, Y)) | node7(X, Y)))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(201,plain,
% 0.65/0.81 (![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y)) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[200])).
% 0.65/0.81 tff(202,plain,
% 0.65/0.81 (![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y)) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(203,axiom,(![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_34')).
% 0.65/0.81 tff(204,plain,
% 0.65/0.81 (![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.65/0.81 tff(205,plain,(
% 0.65/0.81 ![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))),
% 0.65/0.81 inference(skolemize,[status(sab)],[204])).
% 0.65/0.81 tff(206,plain,
% 0.65/0.81 (![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[205, 201])).
% 0.65/0.81 tff(207,plain,
% 0.65/0.81 (((~![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))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(208,plain,
% 0.65/0.81 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s0, s1)) | node7(s0, s1))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(209,plain,
% 0.65/0.81 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s0, s1)) | node7(s0, s1)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.65/0.81 tff(210,plain,
% 0.65/0.81 (node7(s0, s1)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[209, 206, 39])).
% 0.65/0.81 tff(211,plain,
% 0.65/0.81 (^[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)))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(212,plain,
% 0.65/0.81 (![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))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[211])).
% 0.65/0.81 tff(213,plain,
% 0.65/0.81 (![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))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(214,plain,
% 0.65/0.81 (^[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))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(215,plain,
% 0.65/0.81 (![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))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[214])).
% 0.65/0.81 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/sandbox/benchmark/theBenchmark.p','m_main_28')).
% 0.65/0.81 tff(217,plain,
% 0.65/0.81 (![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))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.65/0.81 tff(218,plain,
% 0.65/0.81 (![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))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[217, 213])).
% 0.65/0.81 tff(219,plain,(
% 0.65/0.81 ![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))),
% 0.65/0.81 inference(skolemize,[status(sab)],[218])).
% 0.65/0.81 tff(220,plain,
% 0.65/0.81 (![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))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[219, 212])).
% 0.65/0.81 tff(221,plain,
% 0.65/0.81 (((~![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)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(222,plain,
% 0.65/0.81 (((~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)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(223,plain,
% 0.65/0.81 (((~![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))))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[222])).
% 0.65/0.81 tff(224,plain,
% 0.65/0.81 (((~![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)))),
% 0.65/0.81 inference(transitivity,[status(thm)],[223, 221])).
% 0.65/0.81 tff(225,plain,
% 0.65/0.81 ((~![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))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(226,plain,
% 0.65/0.81 ((~![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))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.65/0.81 tff(227,plain,
% 0.65/0.81 (m_main_v_state1(s1, c_t1)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[226, 3, 63, 220, 210, 199])).
% 0.65/0.81 tff(228,plain,
% 0.65/0.81 (((~![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)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(229,plain,
% 0.65/0.81 ((~![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)))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(230,plain,
% 0.65/0.81 ((~![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))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.65/0.81 tff(231,plain,
% 0.65/0.81 (~m_main_v_state1(s1, c_n1)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[230, 10, 227])).
% 0.65/0.81 tff(232,plain,
% 0.65/0.81 (^[X: $i] : refl((m_main_v_state1(X, c_n1) | (~node11(X))) <=> (m_main_v_state1(X, c_n1) | (~node11(X))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(233,plain,
% 0.65/0.81 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[232])).
% 0.65/0.81 tff(234,plain,
% 0.65/0.81 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(235,axiom,(![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_42')).
% 0.65/0.81 tff(236,plain,
% 0.65/0.81 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.65/0.81 tff(237,plain,(
% 0.65/0.81 ![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))),
% 0.65/0.81 inference(skolemize,[status(sab)],[236])).
% 0.65/0.81 tff(238,plain,
% 0.65/0.81 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[237, 233])).
% 0.65/0.81 tff(239,plain,
% 0.65/0.81 (((~![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)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(240,plain,
% 0.65/0.81 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s1, c_n1) | (~node11(s1)))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(241,plain,
% 0.65/0.81 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s1, c_n1) | (~node11(s1))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.65/0.81 tff(242,plain,
% 0.65/0.81 (~node11(s1)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[241, 238, 231])).
% 0.65/0.81 tff(243,plain,
% 0.65/0.81 (^[X: $i] : refl((m_main_v_state2(X, c_n2) | (~node10(X))) <=> (m_main_v_state2(X, c_n2) | (~node10(X))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(244,plain,
% 0.65/0.81 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[243])).
% 0.65/0.81 tff(245,plain,
% 0.65/0.81 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(246,axiom,(![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_39')).
% 0.65/0.81 tff(247,plain,
% 0.65/0.81 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.65/0.81 tff(248,plain,(
% 0.65/0.81 ![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))),
% 0.65/0.81 inference(skolemize,[status(sab)],[247])).
% 0.65/0.81 tff(249,plain,
% 0.65/0.81 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[248, 244])).
% 0.65/0.81 tff(250,plain,
% 0.65/0.81 (((~![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)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(251,plain,
% 0.65/0.81 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s1, c_n2) | (~node10(s1)))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(252,plain,
% 0.65/0.81 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s1, c_n2) | (~node10(s1))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.65/0.81 tff(253,plain,
% 0.65/0.81 (~node10(s1)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[252, 249, 81])).
% 0.65/0.81 tff(254,plain,
% 0.65/0.81 (^[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))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(255,plain,
% 0.65/0.81 (![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)))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[254])).
% 0.65/0.81 tff(256,plain,
% 0.65/0.81 (![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)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(257,axiom,(![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_8')).
% 0.65/0.81 tff(258,plain,
% 0.65/0.81 (![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.65/0.81 tff(259,plain,(
% 0.65/0.81 ![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))),
% 0.65/0.81 inference(skolemize,[status(sab)],[258])).
% 0.65/0.81 tff(260,plain,
% 0.65/0.81 (![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[259, 255])).
% 0.65/0.81 tff(261,plain,
% 0.65/0.81 (((~![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)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(262,plain,
% 0.65/0.81 ((~![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)))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(263,plain,
% 0.65/0.81 ((~![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))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.65/0.81 tff(264,plain,
% 0.65/0.81 (~m_main_v_state2(s1, c_c2)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[263, 260, 70])).
% 0.65/0.81 tff(265,plain,
% 0.65/0.81 (^[X: $i] : refl((m_main_v_state2(X, c_n2) | (~node8(X))) <=> (m_main_v_state2(X, c_n2) | (~node8(X))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(266,plain,
% 0.65/0.81 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[265])).
% 0.65/0.81 tff(267,plain,
% 0.65/0.81 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(268,axiom,(![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_35')).
% 0.65/0.81 tff(269,plain,
% 0.65/0.81 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.65/0.81 tff(270,plain,(
% 0.65/0.81 ![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))),
% 0.65/0.81 inference(skolemize,[status(sab)],[269])).
% 0.65/0.81 tff(271,plain,
% 0.65/0.81 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[270, 266])).
% 0.65/0.81 tff(272,plain,
% 0.65/0.81 (((~![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)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(273,plain,
% 0.65/0.81 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s1, c_n2) | (~node8(s1)))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(274,plain,
% 0.65/0.81 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s1, c_n2) | (~node8(s1))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.65/0.81 tff(275,plain,
% 0.65/0.81 (~node8(s1)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[274, 271, 81])).
% 0.65/0.81 tff(276,plain,
% 0.65/0.81 (succ(s1, s2) <=> succ(s1, s2)),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(277,axiom,(succ(s1, s2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound2')).
% 0.65/0.81 tff(278,plain,
% 0.65/0.81 (succ(s1, s2)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.65/0.81 tff(279,plain,
% 0.65/0.81 (((~![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))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(280,plain,
% 0.65/0.82 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s1, s2)) | trans(s1, s2))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(281,plain,
% 0.65/0.82 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s1, s2)) | trans(s1, s2)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.65/0.82 tff(282,plain,
% 0.65/0.82 (trans(s1, s2)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[281, 278, 32])).
% 0.65/0.82 tff(283,plain,
% 0.65/0.82 (((~![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))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(284,plain,
% 0.65/0.82 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s1, s2)) | node14(s1, s2))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(285,plain,
% 0.65/0.82 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s1, s2)) | node14(s1, s2)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[284, 283])).
% 0.65/0.82 tff(286,plain,
% 0.65/0.82 (node14(s1, s2)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[285, 46, 282])).
% 0.65/0.82 tff(287,plain,
% 0.65/0.82 (^[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))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(288,plain,
% 0.65/0.82 (![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)))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[287])).
% 0.65/0.82 tff(289,plain,
% 0.65/0.82 (![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)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(290,plain,
% 0.65/0.82 (^[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)))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(291,plain,
% 0.65/0.82 (![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)))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[290])).
% 0.65/0.82 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/sandbox/benchmark/theBenchmark.p','m_main_54')).
% 0.65/0.82 tff(293,plain,
% 0.65/0.82 (![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)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.65/0.82 tff(294,plain,
% 0.65/0.82 (![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)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[293, 289])).
% 0.65/0.82 tff(295,plain,(
% 0.65/0.82 ![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)))),
% 0.65/0.82 inference(skolemize,[status(sab)],[294])).
% 0.65/0.82 tff(296,plain,
% 0.65/0.82 (![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)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[295, 288])).
% 0.65/0.82 tff(297,plain,
% 0.65/0.82 (((~![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)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(298,plain,
% 0.65/0.82 ((~![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)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(299,plain,
% 0.65/0.82 ((~![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))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.65/0.82 tff(300,plain,
% 0.65/0.82 (m_main_v_state2(s1, c_c2) | node9(s1) | node8(s1) | node10(s1) | node11(s1) | node12(s1) | node13(s1, s2)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[299, 296, 286])).
% 0.65/0.82 tff(301,plain,
% 0.65/0.82 (node13(s1, s2)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[300, 275, 264, 253, 242, 188, 92])).
% 0.65/0.82 tff(302,plain,
% 0.65/0.82 (^[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))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(303,plain,
% 0.65/0.82 (![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)))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[302])).
% 0.65/0.82 tff(304,plain,
% 0.65/0.82 (![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)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(305,plain,
% 0.65/0.82 (^[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))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(306,plain,
% 0.65/0.82 (![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)))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[305])).
% 0.65/0.82 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/sandbox/benchmark/theBenchmark.p','m_main_47')).
% 0.65/0.82 tff(308,plain,
% 0.65/0.82 (![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.65/0.82 tff(309,plain,
% 0.65/0.82 (![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[308, 304])).
% 0.65/0.82 tff(310,plain,(
% 0.65/0.82 ![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))),
% 0.65/0.82 inference(skolemize,[status(sab)],[309])).
% 0.65/0.82 tff(311,plain,
% 0.65/0.82 (![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[310, 303])).
% 0.65/0.82 tff(312,plain,
% 0.65/0.82 (((~![V: $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)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(313,plain,
% 0.65/0.82 (((~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)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(314,plain,
% 0.65/0.82 (((~![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))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[313])).
% 0.65/0.82 tff(315,plain,
% 0.65/0.82 (((~![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)))),
% 0.65/0.82 inference(transitivity,[status(thm)],[314, 312])).
% 0.65/0.82 tff(316,plain,
% 0.65/0.82 ((~![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)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(317,plain,
% 0.65/0.82 ((~![V: $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))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.65/0.82 tff(318,plain,
% 0.65/0.82 (~m_main_v_state2(s2, c_n2)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[317, 311, 81, 301])).
% 0.65/0.82 tff(319,plain,
% 0.65/0.82 (((~![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)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(320,plain,
% 0.65/0.82 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s2, c_n2) | (~node9(s2)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(321,plain,
% 0.65/0.82 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s2, c_n2) | (~node9(s2))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.65/0.82 tff(322,plain,
% 0.65/0.82 (~node9(s2)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[321, 88, 318])).
% 0.65/0.82 tff(323,plain,
% 0.65/0.82 (^[X: $i] : refl((m_main_v_state2(X, c_n2) | (~node16(X))) <=> (m_main_v_state2(X, c_n2) | (~node16(X))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(324,plain,
% 0.65/0.82 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[323])).
% 0.65/0.82 tff(325,plain,
% 0.65/0.82 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(326,axiom,(![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_58')).
% 0.65/0.82 tff(327,plain,
% 0.65/0.82 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[326, 325])).
% 0.65/0.82 tff(328,plain,(
% 0.65/0.82 ![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))),
% 0.65/0.82 inference(skolemize,[status(sab)],[327])).
% 0.65/0.82 tff(329,plain,
% 0.65/0.82 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[328, 324])).
% 0.65/0.82 tff(330,plain,
% 0.65/0.82 (((~![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)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(331,plain,
% 0.65/0.82 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))) | (m_main_v_state2(s1, c_n2) | (~node16(s1)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(332,plain,
% 0.65/0.82 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))) | m_main_v_state2(s1, c_n2) | (~node16(s1))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.65/0.82 tff(333,plain,
% 0.65/0.82 (~node16(s1)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[332, 329, 81])).
% 0.65/0.82 tff(334,plain,
% 0.65/0.82 (^[X: $i] : refl((m_main_v_state1(X, c_n1) | (~node15(X))) <=> (m_main_v_state1(X, c_n1) | (~node15(X))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(335,plain,
% 0.65/0.82 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[334])).
% 0.65/0.82 tff(336,plain,
% 0.65/0.82 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(337,axiom,(![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_56')).
% 0.65/0.82 tff(338,plain,
% 0.65/0.82 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.65/0.82 tff(339,plain,(
% 0.65/0.82 ![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))),
% 0.65/0.82 inference(skolemize,[status(sab)],[338])).
% 0.65/0.82 tff(340,plain,
% 0.65/0.82 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[339, 335])).
% 0.65/0.82 tff(341,plain,
% 0.65/0.82 (((~![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)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(342,plain,
% 0.65/0.82 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))) | (m_main_v_state1(s1, c_n1) | (~node15(s1)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(343,plain,
% 0.65/0.82 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))) | m_main_v_state1(s1, c_n1) | (~node15(s1))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[342, 341])).
% 0.65/0.82 tff(344,plain,
% 0.65/0.82 (~node15(s1)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[343, 340, 231])).
% 0.65/0.82 tff(345,plain,
% 0.65/0.82 (((~![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))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(346,plain,
% 0.65/0.82 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s1, s2)) | node18(s1, s2))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(347,plain,
% 0.65/0.82 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s1, s2)) | node18(s1, s2)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[346, 345])).
% 0.65/0.82 tff(348,plain,
% 0.65/0.82 (node18(s1, s2)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[347, 125, 282])).
% 0.65/0.82 tff(349,plain,
% 0.65/0.82 (((~![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)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(350,plain,
% 0.65/0.82 ((~![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))) | (node15(s1) | node16(s1) | node17(s1, s2) | (~node18(s1, s2)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(351,plain,
% 0.65/0.82 ((~![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))) | node15(s1) | node16(s1) | node17(s1, s2) | (~node18(s1, s2))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[350, 349])).
% 0.65/0.82 tff(352,plain,
% 0.65/0.82 (node15(s1) | node16(s1) | node17(s1, s2)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[351, 139, 348])).
% 0.65/0.82 tff(353,plain,
% 0.65/0.82 (node17(s1, s2)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[352, 344, 333])).
% 0.65/0.82 tff(354,plain,
% 0.65/0.82 (((~![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)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(355,plain,
% 0.65/0.82 (((~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)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(356,plain,
% 0.65/0.82 (((~![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))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[355])).
% 0.65/0.82 tff(357,plain,
% 0.65/0.82 (((~![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)))),
% 0.65/0.82 inference(transitivity,[status(thm)],[356, 354])).
% 0.65/0.82 tff(358,plain,
% 0.65/0.82 ((~![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)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(359,plain,
% 0.65/0.82 ((~![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))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[358, 357])).
% 0.65/0.82 tff(360,plain,
% 0.65/0.82 (~m_main_v_turn(s2, c_2)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[359, 170, 353, 177])).
% 0.65/0.82 tff(361,plain,
% 0.65/0.82 (((~![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)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(362,plain,
% 0.65/0.82 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s2, c_2) | (~node12(s2)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(363,plain,
% 0.65/0.82 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s2, c_2) | (~node12(s2))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[362, 361])).
% 0.65/0.82 tff(364,plain,
% 0.65/0.82 (~node12(s2)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[363, 184, 360])).
% 0.65/0.82 tff(365,plain,
% 0.65/0.82 (^[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)))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(366,plain,
% 0.65/0.82 (![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))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[365])).
% 0.65/0.82 tff(367,plain,
% 0.65/0.82 (![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))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(368,plain,
% 0.65/0.82 (^[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))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(369,plain,
% 0.65/0.82 (![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))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[368])).
% 0.65/0.82 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/sandbox/benchmark/theBenchmark.p','m_main_60')).
% 0.65/0.82 tff(371,plain,
% 0.65/0.82 (![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | (~m_main_v_turn(X, V)) | m_main_v_turn(Y, V))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[370, 369])).
% 0.65/0.82 tff(372,plain,
% 0.65/0.82 (![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | (~m_main_v_turn(X, V)) | m_main_v_turn(Y, V))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[371, 367])).
% 0.65/0.82 tff(373,plain,(
% 0.65/0.82 ![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | (~m_main_v_turn(X, V)) | m_main_v_turn(Y, V))),
% 0.65/0.82 inference(skolemize,[status(sab)],[372])).
% 0.65/0.82 tff(374,plain,
% 0.65/0.82 (![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | (~m_main_v_turn(X, V)) | m_main_v_turn(Y, V))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[373, 366])).
% 0.65/0.82 tff(375,plain,
% 0.65/0.82 (((~![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)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(376,plain,
% 0.65/0.82 (((~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)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(377,plain,
% 0.65/0.82 (((~![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))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[376])).
% 0.65/0.82 tff(378,plain,
% 0.65/0.82 (((~![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)))),
% 0.65/0.82 inference(transitivity,[status(thm)],[377, 375])).
% 0.65/0.82 tff(379,plain,
% 0.65/0.82 ((~![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))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(380,plain,
% 0.65/0.82 ((~![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))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.65/0.82 tff(381,plain,
% 0.65/0.82 (m_main_v_turn(s1, c_1)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[380, 149, 374, 146])).
% 0.65/0.82 tff(382,plain,
% 0.65/0.82 (^[X: $i] : refl((m_main_v_state2(X, c_n2) | (~node4(X))) <=> (m_main_v_state2(X, c_n2) | (~node4(X))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(383,plain,
% 0.65/0.82 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[382])).
% 0.65/0.82 tff(384,plain,
% 0.65/0.82 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(385,axiom,(![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_21')).
% 0.65/0.82 tff(386,plain,
% 0.65/0.82 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[385, 384])).
% 0.65/0.82 tff(387,plain,(
% 0.65/0.82 ![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))),
% 0.65/0.82 inference(skolemize,[status(sab)],[386])).
% 0.65/0.82 tff(388,plain,
% 0.65/0.82 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[387, 383])).
% 0.65/0.82 tff(389,plain,
% 0.65/0.82 (((~![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)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(390,plain,
% 0.65/0.82 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s1, c_n2) | (~node4(s1)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(391,plain,
% 0.65/0.82 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s1, c_n2) | (~node4(s1))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[390, 389])).
% 0.65/0.82 tff(392,plain,
% 0.65/0.82 (~node4(s1)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[391, 388, 81])).
% 0.65/0.82 tff(393,plain,
% 0.65/0.82 (^[X: $i] : refl((m_main_v_state2(X, c_c2) | (~node3(X))) <=> (m_main_v_state2(X, c_c2) | (~node3(X))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(394,plain,
% 0.65/0.82 (![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X))) <=> ![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[393])).
% 0.65/0.82 tff(395,plain,
% 0.65/0.82 (![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X))) <=> ![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(396,axiom,(![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_19')).
% 0.65/0.82 tff(397,plain,
% 0.65/0.82 (![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[396, 395])).
% 0.65/0.82 tff(398,plain,(
% 0.65/0.82 ![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))),
% 0.65/0.82 inference(skolemize,[status(sab)],[397])).
% 0.65/0.82 tff(399,plain,
% 0.65/0.82 (![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[398, 394])).
% 0.65/0.82 tff(400,plain,
% 0.65/0.82 (((~![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)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(401,plain,
% 0.65/0.82 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s1, c_c2) | (~node3(s1)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(402,plain,
% 0.65/0.82 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s1, c_c2) | (~node3(s1))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[401, 400])).
% 0.65/0.82 tff(403,plain,
% 0.65/0.82 (~node3(s1)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[402, 399, 264])).
% 0.65/0.82 tff(404,plain,
% 0.65/0.82 (^[X: $i] : refl((m_main_v_state2(X, c_n2) | (~node2(X))) <=> (m_main_v_state2(X, c_n2) | (~node2(X))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(405,plain,
% 0.65/0.82 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[404])).
% 0.65/0.82 tff(406,plain,
% 0.65/0.82 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(407,axiom,(![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_17')).
% 0.65/0.82 tff(408,plain,
% 0.65/0.82 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.65/0.82 tff(409,plain,(
% 0.65/0.82 ![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))),
% 0.65/0.82 inference(skolemize,[status(sab)],[408])).
% 0.65/0.82 tff(410,plain,
% 0.65/0.82 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[409, 405])).
% 0.65/0.82 tff(411,plain,
% 0.65/0.82 (((~![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)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(412,plain,
% 0.65/0.82 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s1, c_n2) | (~node2(s1)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(413,plain,
% 0.65/0.82 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s1, c_n2) | (~node2(s1))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[412, 411])).
% 0.65/0.82 tff(414,plain,
% 0.65/0.82 (~node2(s1)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[413, 410, 81])).
% 0.65/0.82 tff(415,plain,
% 0.65/0.82 (^[X: $i] : refl((m_main_v_state1(X, c_n1) | (~node1(X))) <=> (m_main_v_state1(X, c_n1) | (~node1(X))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(416,plain,
% 0.65/0.82 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[415])).
% 0.65/0.82 tff(417,plain,
% 0.65/0.82 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(418,axiom,(![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_14')).
% 0.65/0.82 tff(419,plain,
% 0.65/0.82 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[418, 417])).
% 0.65/0.82 tff(420,plain,(
% 0.65/0.82 ![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))),
% 0.65/0.82 inference(skolemize,[status(sab)],[419])).
% 0.65/0.82 tff(421,plain,
% 0.65/0.82 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[420, 416])).
% 0.65/0.82 tff(422,plain,
% 0.65/0.82 (((~![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)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(423,plain,
% 0.65/0.82 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s1, c_n1) | (~node1(s1)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(424,plain,
% 0.65/0.82 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s1, c_n1) | (~node1(s1))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[423, 422])).
% 0.65/0.82 tff(425,plain,
% 0.65/0.82 (~node1(s1)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[424, 421, 231])).
% 0.65/0.82 tff(426,plain,
% 0.65/0.82 (((~![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))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(427,plain,
% 0.65/0.82 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s1, s2)) | node7(s1, s2))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(428,plain,
% 0.65/0.82 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s1, s2)) | node7(s1, s2)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[427, 426])).
% 0.65/0.82 tff(429,plain,
% 0.65/0.82 (node7(s1, s2)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[428, 206, 282])).
% 0.65/0.82 tff(430,plain,
% 0.65/0.82 (^[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)))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(431,plain,
% 0.65/0.82 (![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))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[430])).
% 0.65/0.82 tff(432,plain,
% 0.65/0.82 (![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))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(433,plain,
% 0.65/0.82 (^[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))))),
% 0.65/0.83 inference(bind,[status(th)],[])).
% 0.65/0.83 tff(434,plain,
% 0.65/0.83 (![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))),
% 0.65/0.83 inference(quant_intro,[status(thm)],[433])).
% 0.65/0.83 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/sandbox/benchmark/theBenchmark.p','m_main_31')).
% 0.65/0.83 tff(436,plain,
% 0.65/0.83 (![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))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[435, 434])).
% 0.65/0.83 tff(437,plain,
% 0.65/0.83 (![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))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[436, 432])).
% 0.65/0.83 tff(438,plain,(
% 0.65/0.83 ![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))),
% 0.65/0.83 inference(skolemize,[status(sab)],[437])).
% 0.65/0.83 tff(439,plain,
% 0.65/0.83 (![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))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[438, 431])).
% 0.65/0.83 tff(440,plain,
% 0.65/0.83 (((~![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)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(441,plain,
% 0.65/0.83 (((~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)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(442,plain,
% 0.65/0.83 (((~![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))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[441])).
% 0.65/0.83 tff(443,plain,
% 0.65/0.83 (((~![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)))),
% 0.65/0.83 inference(transitivity,[status(thm)],[442, 440])).
% 0.65/0.83 tff(444,plain,
% 0.65/0.83 ((~![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))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(445,plain,
% 0.65/0.83 ((~![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))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[444, 443])).
% 0.65/0.83 tff(446,plain,
% 0.65/0.83 (m_main_v_state1(s2, c_c1) | node1(s1) | node2(s1) | node3(s1) | node4(s1) | (~m_main_v_turn(s1, c_1))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[445, 439, 429, 70, 227])).
% 0.65/0.83 tff(447,plain,
% 0.65/0.83 (m_main_v_state1(s2, c_c1)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[446, 425, 414, 403, 392, 381])).
% 0.65/0.83 tff(448,plain,
% 0.65/0.83 (^[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))))),
% 0.65/0.83 inference(bind,[status(th)],[])).
% 0.65/0.83 tff(449,plain,
% 0.65/0.83 (![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)))),
% 0.65/0.83 inference(quant_intro,[status(thm)],[448])).
% 0.65/0.83 tff(450,plain,
% 0.65/0.83 (![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)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(451,axiom,(![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_3')).
% 0.65/0.83 tff(452,plain,
% 0.65/0.83 (![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[451, 450])).
% 0.65/0.83 tff(453,plain,(
% 0.65/0.83 ![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))),
% 0.65/0.83 inference(skolemize,[status(sab)],[452])).
% 0.65/0.83 tff(454,plain,
% 0.65/0.83 (![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[453, 449])).
% 0.65/0.83 tff(455,plain,
% 0.65/0.83 (((~![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)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(456,plain,
% 0.65/0.83 ((~![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)))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(457,plain,
% 0.65/0.83 ((~![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))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[456, 455])).
% 0.65/0.83 tff(458,plain,
% 0.65/0.83 (~m_main_v_state1(s2, c_n1)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[457, 454, 447])).
% 0.65/0.83 tff(459,plain,
% 0.65/0.83 (((~![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)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(460,plain,
% 0.65/0.83 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s2, c_n1) | (~node11(s2)))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(461,plain,
% 0.65/0.83 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s2, c_n1) | (~node11(s2))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[460, 459])).
% 0.65/0.83 tff(462,plain,
% 0.65/0.83 (~node11(s2)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[461, 238, 458])).
% 0.65/0.83 tff(463,plain,
% 0.65/0.83 (((~![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)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(464,plain,
% 0.65/0.83 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s2, c_n2) | (~node10(s2)))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(465,plain,
% 0.65/0.83 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s2, c_n2) | (~node10(s2))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[464, 463])).
% 0.65/0.83 tff(466,plain,
% 0.65/0.83 (~node10(s2)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[465, 249, 318])).
% 0.65/0.83 tff(467,plain,
% 0.65/0.83 (((~![V: $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)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(468,plain,
% 0.65/0.83 (((~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)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(469,plain,
% 0.65/0.83 (((~![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))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[468])).
% 0.65/0.83 tff(470,plain,
% 0.65/0.83 (((~![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)))),
% 0.65/0.83 inference(transitivity,[status(thm)],[469, 467])).
% 0.65/0.83 tff(471,plain,
% 0.65/0.83 ((~![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)))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(472,plain,
% 0.65/0.83 ((~![V: $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))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[471, 470])).
% 0.65/0.83 tff(473,plain,
% 0.65/0.83 (~m_main_v_state2(s2, c_c2)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[472, 311, 264, 301])).
% 0.65/0.83 tff(474,plain,
% 0.65/0.83 (((~![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)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(475,plain,
% 0.65/0.83 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s2, c_n2) | (~node8(s2)))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(476,plain,
% 0.65/0.83 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s2, c_n2) | (~node8(s2))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[475, 474])).
% 0.65/0.83 tff(477,plain,
% 0.65/0.83 (~node8(s2)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[476, 271, 318])).
% 0.65/0.83 tff(478,plain,
% 0.65/0.83 (succ(s2, s3) <=> succ(s2, s3)),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(479,axiom,(succ(s2, s3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound3')).
% 0.65/0.83 tff(480,plain,
% 0.65/0.83 (succ(s2, s3)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[479, 478])).
% 0.65/0.83 tff(481,plain,
% 0.65/0.83 (((~![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))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(482,plain,
% 0.65/0.83 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s2, s3)) | trans(s2, s3))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(483,plain,
% 0.65/0.83 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s2, s3)) | trans(s2, s3)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[482, 481])).
% 0.65/0.83 tff(484,plain,
% 0.65/0.83 (trans(s2, s3)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[483, 480, 32])).
% 0.65/0.83 tff(485,plain,
% 0.65/0.83 (((~![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))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(486,plain,
% 0.65/0.83 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s2, s3)) | node14(s2, s3))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(487,plain,
% 0.65/0.83 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s2, s3)) | node14(s2, s3)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[486, 485])).
% 0.65/0.83 tff(488,plain,
% 0.65/0.83 (node14(s2, s3)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[487, 46, 484])).
% 0.65/0.83 tff(489,plain,
% 0.65/0.83 (((~![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)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(490,plain,
% 0.65/0.83 ((~![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)))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(491,plain,
% 0.65/0.83 ((~![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))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[490, 489])).
% 0.65/0.83 tff(492,plain,
% 0.65/0.83 (m_main_v_state2(s2, c_c2) | node9(s2) | node8(s2) | node10(s2) | node11(s2) | node12(s2) | node13(s2, s3)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[491, 296, 488])).
% 0.65/0.83 tff(493,plain,
% 0.65/0.83 (node13(s2, s3)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[492, 477, 473, 466, 462, 364, 322])).
% 0.65/0.83 tff(494,plain,
% 0.65/0.83 (((~![V: $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)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(495,plain,
% 0.65/0.83 (((~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)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(496,plain,
% 0.65/0.83 (((~![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))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[495])).
% 0.65/0.83 tff(497,plain,
% 0.65/0.83 (((~![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)))),
% 0.65/0.83 inference(transitivity,[status(thm)],[496, 494])).
% 0.65/0.83 tff(498,plain,
% 0.65/0.83 ((~![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)))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(499,plain,
% 0.65/0.83 ((~![V: $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))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[498, 497])).
% 0.65/0.83 tff(500,plain,
% 0.65/0.83 (~m_main_v_state2(s3, c_n2)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[499, 311, 318, 493])).
% 0.65/0.83 tff(501,plain,
% 0.65/0.83 (((~![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)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(502,plain,
% 0.65/0.83 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s3, c_n2) | (~node9(s3)))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(503,plain,
% 0.65/0.83 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s3, c_n2) | (~node9(s3))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[502, 501])).
% 0.65/0.83 tff(504,plain,
% 0.65/0.83 (~node9(s3)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[503, 88, 500])).
% 0.65/0.83 tff(505,plain,
% 0.65/0.83 (((~![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)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(506,plain,
% 0.65/0.83 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s3, c_n2) | (~node10(s3)))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(507,plain,
% 0.65/0.83 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s3, c_n2) | (~node10(s3))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[506, 505])).
% 0.65/0.83 tff(508,plain,
% 0.65/0.83 (~node10(s3)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[507, 249, 500])).
% 0.65/0.83 tff(509,plain,
% 0.65/0.83 (^[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)))),
% 0.65/0.83 inference(bind,[status(th)],[])).
% 0.65/0.83 tff(510,plain,
% 0.65/0.83 (![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))),
% 0.65/0.83 inference(quant_intro,[status(thm)],[509])).
% 0.65/0.83 tff(511,plain,
% 0.65/0.83 (![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))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(512,plain,
% 0.65/0.83 (^[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))))),
% 0.65/0.83 inference(bind,[status(th)],[])).
% 0.65/0.83 tff(513,plain,
% 0.65/0.83 (![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))),
% 0.65/0.83 inference(quant_intro,[status(thm)],[512])).
% 0.65/0.83 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/sandbox/benchmark/theBenchmark.p','m_main_46')).
% 0.65/0.83 tff(515,plain,
% 0.65/0.83 (![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[514, 513])).
% 0.65/0.83 tff(516,plain,
% 0.65/0.83 (![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[515, 511])).
% 0.65/0.83 tff(517,plain,(
% 0.65/0.83 ![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))),
% 0.65/0.83 inference(skolemize,[status(sab)],[516])).
% 0.65/0.83 tff(518,plain,
% 0.65/0.83 (![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[517, 510])).
% 0.65/0.83 tff(519,plain,
% 0.65/0.83 (((~![V: $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)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(520,plain,
% 0.65/0.83 (((~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)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(521,plain,
% 0.65/0.83 (((~![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))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[520])).
% 0.65/0.83 tff(522,plain,
% 0.65/0.83 (((~![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)))),
% 0.65/0.83 inference(transitivity,[status(thm)],[521, 519])).
% 0.65/0.83 tff(523,plain,
% 0.65/0.83 ((~![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))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(524,plain,
% 0.65/0.83 ((~![V: $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))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[523, 522])).
% 0.65/0.83 tff(525,plain,
% 0.65/0.83 (m_main_v_state2(s2, c_t2)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[524, 518, 70, 301])).
% 0.65/0.83 tff(526,plain,
% 0.65/0.83 (((~![V: $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)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(527,plain,
% 0.65/0.83 (((~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)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(528,plain,
% 0.65/0.83 (((~![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))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[527])).
% 0.65/0.83 tff(529,plain,
% 0.65/0.83 (((~![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)))),
% 0.65/0.83 inference(transitivity,[status(thm)],[528, 526])).
% 0.65/0.83 tff(530,plain,
% 0.65/0.83 ((~![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))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(531,plain,
% 0.65/0.83 ((~![V: $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))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[530, 529])).
% 0.65/0.83 tff(532,plain,
% 0.65/0.83 (m_main_v_state2(s3, c_t2)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[531, 518, 525, 493])).
% 0.65/0.83 tff(533,plain,
% 0.65/0.83 (^[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))))),
% 0.65/0.83 inference(bind,[status(th)],[])).
% 0.65/0.84 tff(534,plain,
% 0.65/0.84 (![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)))),
% 0.65/0.84 inference(quant_intro,[status(thm)],[533])).
% 0.65/0.84 tff(535,plain,
% 0.65/0.84 (![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)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(536,axiom,(![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_4')).
% 0.65/0.84 tff(537,plain,
% 0.65/0.84 (![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[536, 535])).
% 0.65/0.84 tff(538,plain,(
% 0.65/0.84 ![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))),
% 0.65/0.84 inference(skolemize,[status(sab)],[537])).
% 0.65/0.84 tff(539,plain,
% 0.65/0.84 (![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[538, 534])).
% 0.65/0.84 tff(540,plain,
% 0.65/0.84 (((~![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)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(541,plain,
% 0.65/0.84 ((~![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)))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(542,plain,
% 0.65/0.84 ((~![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))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[541, 540])).
% 0.65/0.84 tff(543,plain,
% 0.65/0.84 (~m_main_v_state1(s2, c_t1)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[542, 539, 447])).
% 0.65/0.84 tff(544,plain,
% 0.65/0.84 (^[X: $i] : refl((m_main_v_state1(X, c_t1) | (~node5(X))) <=> (m_main_v_state1(X, c_t1) | (~node5(X))))),
% 0.65/0.84 inference(bind,[status(th)],[])).
% 0.65/0.84 tff(545,plain,
% 0.65/0.84 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X))) <=> ![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))),
% 0.65/0.84 inference(quant_intro,[status(thm)],[544])).
% 0.65/0.84 tff(546,plain,
% 0.65/0.84 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X))) <=> ![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(547,axiom,(![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_22')).
% 0.65/0.84 tff(548,plain,
% 0.65/0.84 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[547, 546])).
% 0.65/0.84 tff(549,plain,(
% 0.65/0.84 ![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))),
% 0.65/0.84 inference(skolemize,[status(sab)],[548])).
% 0.65/0.84 tff(550,plain,
% 0.65/0.84 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[549, 545])).
% 0.65/0.84 tff(551,plain,
% 0.65/0.84 (((~![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)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(552,plain,
% 0.65/0.84 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s2, c_t1) | (~node5(s2)))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(553,plain,
% 0.65/0.84 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s2, c_t1) | (~node5(s2))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[552, 551])).
% 0.65/0.84 tff(554,plain,
% 0.65/0.84 (~node5(s2)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[553, 550, 543])).
% 0.65/0.84 tff(555,plain,
% 0.65/0.84 (((~![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)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(556,plain,
% 0.65/0.84 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s2, c_n2) | (~node4(s2)))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(557,plain,
% 0.65/0.84 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s2, c_n2) | (~node4(s2))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[556, 555])).
% 0.65/0.84 tff(558,plain,
% 0.65/0.84 (~node4(s2)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[557, 388, 318])).
% 0.65/0.84 tff(559,plain,
% 0.65/0.84 (((~![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)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(560,plain,
% 0.65/0.84 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s2, c_c2) | (~node3(s2)))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(561,plain,
% 0.65/0.84 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s2, c_c2) | (~node3(s2))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[560, 559])).
% 0.65/0.84 tff(562,plain,
% 0.65/0.84 (~node3(s2)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[561, 399, 473])).
% 0.65/0.84 tff(563,plain,
% 0.65/0.84 (((~![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)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(564,plain,
% 0.65/0.84 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s2, c_n2) | (~node2(s2)))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(565,plain,
% 0.65/0.84 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s2, c_n2) | (~node2(s2))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[564, 563])).
% 0.65/0.84 tff(566,plain,
% 0.65/0.84 (~node2(s2)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[565, 410, 318])).
% 0.65/0.84 tff(567,plain,
% 0.65/0.84 (((~![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)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(568,plain,
% 0.65/0.84 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s2, c_n1) | (~node1(s2)))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(569,plain,
% 0.65/0.84 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s2, c_n1) | (~node1(s2))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[568, 567])).
% 0.65/0.84 tff(570,plain,
% 0.65/0.84 (~node1(s2)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[569, 421, 458])).
% 0.65/0.84 tff(571,plain,
% 0.65/0.84 (((~![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))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(572,plain,
% 0.65/0.84 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s2, s3)) | node7(s2, s3))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(573,plain,
% 0.65/0.84 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s2, s3)) | node7(s2, s3)),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[572, 571])).
% 0.65/0.84 tff(574,plain,
% 0.65/0.84 (node7(s2, s3)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[573, 206, 484])).
% 0.65/0.84 tff(575,plain,
% 0.65/0.84 (^[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)))),
% 0.65/0.84 inference(bind,[status(th)],[])).
% 0.65/0.84 tff(576,plain,
% 0.65/0.84 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1)) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))),
% 0.65/0.84 inference(quant_intro,[status(thm)],[575])).
% 0.65/0.84 tff(577,plain,
% 0.65/0.84 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1)) <=> ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(578,plain,
% 0.65/0.84 (^[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))))),
% 0.65/0.84 inference(bind,[status(th)],[])).
% 0.65/0.84 tff(579,plain,
% 0.65/0.84 (![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))),
% 0.65/0.84 inference(quant_intro,[status(thm)],[578])).
% 0.65/0.84 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/sandbox/benchmark/theBenchmark.p','m_main_32')).
% 0.65/0.84 tff(581,plain,
% 0.65/0.84 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[580, 579])).
% 0.65/0.84 tff(582,plain,
% 0.65/0.84 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[581, 577])).
% 0.65/0.84 tff(583,plain,(
% 0.65/0.84 ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))),
% 0.65/0.84 inference(skolemize,[status(sab)],[582])).
% 0.65/0.84 tff(584,plain,
% 0.65/0.84 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[583, 576])).
% 0.65/0.84 tff(585,plain,
% 0.65/0.84 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(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)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(586,plain,
% 0.65/0.84 (((~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)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(587,plain,
% 0.65/0.84 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(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))))),
% 0.65/0.84 inference(monotonicity,[status(thm)],[586])).
% 0.65/0.84 tff(588,plain,
% 0.65/0.84 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(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)))),
% 0.65/0.84 inference(transitivity,[status(thm)],[587, 585])).
% 0.65/0.84 tff(589,plain,
% 0.65/0.84 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s2, c_c1)) | node1(s2) | node2(s2) | node3(s2) | node4(s2) | node5(s2) | (~node7(s2, s3)) | m_main_v_state1(s3, c_n1))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(590,plain,
% 0.65/0.84 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s3, c_n1) | (~m_main_v_state1(s2, c_c1)) | node1(s2) | node2(s2) | node3(s2) | node4(s2) | node5(s2) | (~node7(s2, s3))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[589, 588])).
% 0.65/0.84 tff(591,plain,
% 0.65/0.84 (m_main_v_state1(s3, c_n1) | (~m_main_v_state1(s2, c_c1)) | node1(s2) | node2(s2) | node3(s2) | node4(s2) | node5(s2)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[590, 584, 574])).
% 0.65/0.84 tff(592,plain,
% 0.65/0.84 (m_main_v_state1(s3, c_n1)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[591, 570, 447, 566, 562, 558, 554])).
% 0.65/0.84 tff(593,plain,
% 0.65/0.84 (((~![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)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(594,plain,
% 0.65/0.84 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s3, c_n2) | (~node8(s3)))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(595,plain,
% 0.65/0.84 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s3, c_n2) | (~node8(s3))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[594, 593])).
% 0.65/0.84 tff(596,plain,
% 0.65/0.84 (~node8(s3)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[595, 271, 500])).
% 0.65/0.84 tff(597,plain,
% 0.65/0.84 (succ(s3, s4) <=> succ(s3, s4)),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(598,axiom,(succ(s3, s4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound4')).
% 0.65/0.84 tff(599,plain,
% 0.65/0.84 (succ(s3, s4)),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[598, 597])).
% 0.65/0.84 tff(600,plain,
% 0.65/0.84 (((~![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))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(601,plain,
% 0.65/0.84 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s3, s4)) | trans(s3, s4))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(602,plain,
% 0.65/0.84 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s3, s4)) | trans(s3, s4)),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[601, 600])).
% 0.65/0.84 tff(603,plain,
% 0.65/0.84 (trans(s3, s4)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[602, 599, 32])).
% 0.65/0.84 tff(604,plain,
% 0.65/0.84 (((~![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))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(605,plain,
% 0.65/0.84 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s3, s4)) | node14(s3, s4))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(606,plain,
% 0.65/0.84 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s3, s4)) | node14(s3, s4)),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[605, 604])).
% 0.65/0.84 tff(607,plain,
% 0.65/0.84 (node14(s3, s4)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[606, 46, 603])).
% 0.65/0.84 tff(608,plain,
% 0.65/0.84 (^[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)))),
% 0.65/0.84 inference(bind,[status(th)],[])).
% 0.65/0.84 tff(609,plain,
% 0.65/0.84 (![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))),
% 0.65/0.84 inference(quant_intro,[status(thm)],[608])).
% 0.65/0.84 tff(610,plain,
% 0.65/0.84 (![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))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(611,plain,
% 0.65/0.84 (^[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))))),
% 0.65/0.84 inference(bind,[status(th)],[])).
% 0.65/0.84 tff(612,plain,
% 0.65/0.84 (![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))),
% 0.65/0.84 inference(quant_intro,[status(thm)],[611])).
% 0.65/0.84 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/sandbox/benchmark/theBenchmark.p','m_main_51')).
% 0.65/0.84 tff(614,plain,
% 0.65/0.84 (![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))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[613, 612])).
% 0.65/0.84 tff(615,plain,
% 0.65/0.84 (![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))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[614, 610])).
% 0.65/0.84 tff(616,plain,(
% 0.65/0.84 ![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))),
% 0.65/0.84 inference(skolemize,[status(sab)],[615])).
% 0.65/0.84 tff(617,plain,
% 0.65/0.84 (![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))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[616, 609])).
% 0.65/0.84 tff(618,plain,
% 0.65/0.84 (((~![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))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(619,plain,
% 0.65/0.84 ((~![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))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(620,plain,
% 0.65/0.84 ((~![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)),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[619, 618])).
% 0.65/0.84 tff(621,plain,
% 0.65/0.84 ((~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)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[620, 617, 607])).
% 0.65/0.84 tff(622,plain,
% 0.65/0.84 (m_main_v_state2(s4, c_c2)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[621, 596, 592, 532, 508, 504])).
% 0.65/0.84 tff(623,plain,
% 0.65/0.84 (((~![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)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(624,plain,
% 0.65/0.84 ((~![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)))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(625,plain,
% 0.65/0.84 ((~![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))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[624, 623])).
% 0.65/0.84 tff(626,plain,
% 0.65/0.84 (~m_main_v_state2(s4, c_t2)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[625, 260, 622])).
% 0.65/0.84 tff(627,plain,
% 0.65/0.84 (^[X: $i] : refl((m_main_v_state2(X, c_t2) | (~node12(X))) <=> (m_main_v_state2(X, c_t2) | (~node12(X))))),
% 0.65/0.84 inference(bind,[status(th)],[])).
% 0.65/0.84 tff(628,plain,
% 0.65/0.84 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X))) <=> ![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))),
% 0.65/0.84 inference(quant_intro,[status(thm)],[627])).
% 0.65/0.84 tff(629,plain,
% 0.65/0.84 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X))) <=> ![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(630,axiom,(![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_43')).
% 0.65/0.84 tff(631,plain,
% 0.65/0.84 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[630, 629])).
% 0.65/0.84 tff(632,plain,(
% 0.65/0.84 ![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))),
% 0.65/0.84 inference(skolemize,[status(sab)],[631])).
% 0.65/0.84 tff(633,plain,
% 0.65/0.84 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[632, 628])).
% 0.65/0.84 tff(634,plain,
% 0.65/0.84 (((~![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)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(635,plain,
% 0.65/0.84 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s4, c_t2) | (~node12(s4)))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(636,plain,
% 0.65/0.84 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s4, c_t2) | (~node12(s4))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[635, 634])).
% 0.65/0.84 tff(637,plain,
% 0.65/0.84 (~node12(s4)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[636, 633, 626])).
% 0.65/0.84 tff(638,plain,
% 0.65/0.84 (((~![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))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(639,plain,
% 0.65/0.84 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s3, s4)) | node7(s3, s4))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(640,plain,
% 0.65/0.84 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s3, s4)) | node7(s3, s4)),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[639, 638])).
% 0.65/0.84 tff(641,plain,
% 0.65/0.84 (node7(s3, s4)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[640, 206, 603])).
% 0.65/0.84 tff(642,plain,
% 0.65/0.84 (^[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)))),
% 0.65/0.84 inference(bind,[status(th)],[])).
% 0.65/0.84 tff(643,plain,
% 0.65/0.84 (![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))),
% 0.65/0.84 inference(quant_intro,[status(thm)],[642])).
% 0.65/0.84 tff(644,plain,
% 0.65/0.84 (![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))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(645,plain,
% 0.65/0.84 (^[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))))),
% 0.65/0.84 inference(bind,[status(th)],[])).
% 0.65/0.84 tff(646,plain,
% 0.65/0.84 (![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))),
% 0.65/0.84 inference(quant_intro,[status(thm)],[645])).
% 0.65/0.84 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/sandbox/benchmark/theBenchmark.p','m_main_27')).
% 0.65/0.84 tff(648,plain,
% 0.65/0.84 (![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))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[647, 646])).
% 0.65/0.84 tff(649,plain,
% 0.65/0.84 (![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))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[648, 644])).
% 0.65/0.84 tff(650,plain,(
% 0.65/0.84 ![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))),
% 0.65/0.84 inference(skolemize,[status(sab)],[649])).
% 0.65/0.84 tff(651,plain,
% 0.65/0.84 (![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))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[650, 643])).
% 0.65/0.84 tff(652,plain,
% 0.65/0.84 (((~![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))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(653,plain,
% 0.65/0.84 ((~![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))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(654,plain,
% 0.65/0.84 ((~![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)),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[653, 652])).
% 0.65/0.84 tff(655,plain,
% 0.65/0.84 ((~m_main_v_state1(s3, c_n1)) | (~m_main_v_state2(s3, c_t2)) | m_main_v_state1(s4, c_t1)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[654, 651, 641])).
% 0.65/0.84 tff(656,plain,
% 0.65/0.84 (m_main_v_state1(s4, c_t1)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[655, 532, 592])).
% 0.65/0.84 tff(657,plain,
% 0.65/0.84 (((~![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)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(658,plain,
% 0.65/0.84 ((~![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)))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(659,plain,
% 0.65/0.84 ((~![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))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[658, 657])).
% 0.65/0.84 tff(660,plain,
% 0.65/0.84 (~m_main_v_state1(s4, c_n1)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[659, 10, 656])).
% 0.65/0.84 tff(661,plain,
% 0.65/0.84 (((~![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)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(662,plain,
% 0.65/0.84 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s4, c_n1) | (~node11(s4)))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(663,plain,
% 0.65/0.84 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s4, c_n1) | (~node11(s4))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[662, 661])).
% 0.65/0.84 tff(664,plain,
% 0.65/0.84 (~node11(s4)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[663, 238, 660])).
% 0.65/0.84 tff(665,plain,
% 0.65/0.84 (((~![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)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(666,plain,
% 0.65/0.85 ((~![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)))),
% 0.65/0.85 inference(quant_inst,[status(thm)],[])).
% 0.65/0.85 tff(667,plain,
% 0.65/0.85 ((~![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))),
% 0.65/0.85 inference(modus_ponens,[status(thm)],[666, 665])).
% 0.65/0.85 tff(668,plain,
% 0.65/0.85 (~m_main_v_state1(s4, c_c1)),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[667, 539, 656])).
% 0.65/0.85 tff(669,plain,
% 0.65/0.85 (^[X: $i] : refl((m_main_v_state1(X, c_c1) | (~node10(X))) <=> (m_main_v_state1(X, c_c1) | (~node10(X))))),
% 0.65/0.85 inference(bind,[status(th)],[])).
% 0.65/0.85 tff(670,plain,
% 0.65/0.85 (![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X))) <=> ![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))),
% 0.65/0.85 inference(quant_intro,[status(thm)],[669])).
% 0.65/0.85 tff(671,plain,
% 0.65/0.85 (![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X))) <=> ![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))),
% 0.65/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(672,axiom,(![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_40')).
% 0.69/0.85 tff(673,plain,
% 0.69/0.85 (![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[672, 671])).
% 0.69/0.85 tff(674,plain,(
% 0.69/0.85 ![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))),
% 0.69/0.85 inference(skolemize,[status(sab)],[673])).
% 0.69/0.85 tff(675,plain,
% 0.69/0.85 (![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[674, 670])).
% 0.69/0.85 tff(676,plain,
% 0.69/0.85 (((~![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)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(677,plain,
% 0.69/0.85 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s4, c_c1) | (~node10(s4)))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(678,plain,
% 0.69/0.85 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s4, c_c1) | (~node10(s4))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[677, 676])).
% 0.69/0.85 tff(679,plain,
% 0.69/0.85 (~node10(s4)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[678, 675, 668])).
% 0.69/0.85 tff(680,plain,
% 0.69/0.85 (^[X: $i] : refl((m_main_v_state1(X, c_n1) | (~node9(X))) <=> (m_main_v_state1(X, c_n1) | (~node9(X))))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(681,plain,
% 0.69/0.85 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[680])).
% 0.69/0.85 tff(682,plain,
% 0.69/0.85 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(683,axiom,(![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_38')).
% 0.69/0.85 tff(684,plain,
% 0.69/0.85 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[683, 682])).
% 0.69/0.85 tff(685,plain,(
% 0.69/0.85 ![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))),
% 0.69/0.85 inference(skolemize,[status(sab)],[684])).
% 0.69/0.85 tff(686,plain,
% 0.69/0.85 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[685, 681])).
% 0.69/0.85 tff(687,plain,
% 0.69/0.85 (((~![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)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(688,plain,
% 0.69/0.85 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s4, c_n1) | (~node9(s4)))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(689,plain,
% 0.69/0.85 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s4, c_n1) | (~node9(s4))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[688, 687])).
% 0.69/0.85 tff(690,plain,
% 0.69/0.85 (~node9(s4)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[689, 686, 660])).
% 0.69/0.85 tff(691,plain,
% 0.69/0.85 (^[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))))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(692,plain,
% 0.69/0.85 (![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)))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[691])).
% 0.69/0.85 tff(693,plain,
% 0.69/0.85 (![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)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(694,axiom,(![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_7')).
% 0.69/0.85 tff(695,plain,
% 0.69/0.85 (![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[694, 693])).
% 0.69/0.85 tff(696,plain,(
% 0.69/0.85 ![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))),
% 0.69/0.85 inference(skolemize,[status(sab)],[695])).
% 0.69/0.85 tff(697,plain,
% 0.69/0.85 (![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[696, 692])).
% 0.69/0.85 tff(698,plain,
% 0.69/0.85 (((~![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)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(699,plain,
% 0.69/0.85 ((~![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)))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(700,plain,
% 0.69/0.85 ((~![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))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[699, 698])).
% 0.69/0.85 tff(701,plain,
% 0.69/0.85 (~m_main_v_state2(s4, c_n2)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[700, 697, 622])).
% 0.69/0.85 tff(702,plain,
% 0.69/0.85 (((~![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)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(703,plain,
% 0.69/0.85 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s4, c_n2) | (~node8(s4)))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(704,plain,
% 0.69/0.85 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s4, c_n2) | (~node8(s4))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[703, 702])).
% 0.69/0.85 tff(705,plain,
% 0.69/0.85 (~node8(s4)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[704, 271, 701])).
% 0.69/0.85 tff(706,plain,
% 0.69/0.85 (succ(s4, s5) <=> succ(s4, s5)),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(707,axiom,(succ(s4, s5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound5')).
% 0.69/0.85 tff(708,plain,
% 0.69/0.85 (succ(s4, s5)),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[707, 706])).
% 0.69/0.85 tff(709,plain,
% 0.69/0.85 (((~![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))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(710,plain,
% 0.69/0.85 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s4, s5)) | trans(s4, s5))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(711,plain,
% 0.69/0.85 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s4, s5)) | trans(s4, s5)),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[710, 709])).
% 0.69/0.85 tff(712,plain,
% 0.69/0.85 (trans(s4, s5)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[711, 708, 32])).
% 0.69/0.85 tff(713,plain,
% 0.69/0.85 (((~![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))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(714,plain,
% 0.69/0.85 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s4, s5)) | node14(s4, s5))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(715,plain,
% 0.69/0.85 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s4, s5)) | node14(s4, s5)),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[714, 713])).
% 0.69/0.85 tff(716,plain,
% 0.69/0.85 (node14(s4, s5)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[715, 46, 712])).
% 0.69/0.85 tff(717,plain,
% 0.69/0.85 (^[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)))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(718,plain,
% 0.69/0.85 (![Y: $i, X: $i] : ((~m_main_v_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))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[717])).
% 0.69/0.85 tff(719,plain,
% 0.69/0.85 (![Y: $i, X: $i] : ((~m_main_v_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))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(720,plain,
% 0.69/0.85 (^[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))) | 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))))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(721,plain,
% 0.69/0.85 (![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))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[720])).
% 0.69/0.85 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/sandbox/benchmark/theBenchmark.p','m_main_53')).
% 0.69/0.85 tff(723,plain,
% 0.69/0.85 (![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[722, 721])).
% 0.69/0.85 tff(724,plain,
% 0.69/0.85 (![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[723, 719])).
% 0.69/0.85 tff(725,plain,(
% 0.69/0.85 ![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))),
% 0.69/0.85 inference(skolemize,[status(sab)],[724])).
% 0.69/0.85 tff(726,plain,
% 0.69/0.85 (![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[725, 718])).
% 0.69/0.85 tff(727,plain,
% 0.69/0.85 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | 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)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(728,plain,
% 0.69/0.85 (((~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)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(729,plain,
% 0.69/0.85 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | 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))))),
% 0.69/0.85 inference(monotonicity,[status(thm)],[728])).
% 0.69/0.85 tff(730,plain,
% 0.69/0.85 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | 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)))),
% 0.69/0.85 inference(transitivity,[status(thm)],[729, 727])).
% 0.69/0.85 tff(731,plain,
% 0.69/0.85 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | 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))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(732,plain,
% 0.69/0.85 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | 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))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[731, 730])).
% 0.69/0.85 tff(733,plain,
% 0.69/0.85 (m_main_v_state2(s5, c_n2) | node9(s4) | node8(s4) | node10(s4) | node11(s4) | node12(s4) | (~m_main_v_state2(s4, c_c2))),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[732, 726, 716])).
% 0.69/0.85 tff(734,plain,
% 0.69/0.85 (m_main_v_state2(s5, c_n2)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[733, 705, 622, 690, 679, 664, 637])).
% 0.69/0.85 tff(735,plain,
% 0.69/0.85 (((~![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)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(736,plain,
% 0.69/0.85 ((~![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)))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(737,plain,
% 0.69/0.85 ((~![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))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[736, 735])).
% 0.69/0.85 tff(738,plain,
% 0.69/0.85 (~m_main_v_state2(s5, c_c2)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[737, 697, 734])).
% 0.69/0.85 tff(739,plain,
% 0.69/0.85 (((~![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)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(740,plain,
% 0.69/0.85 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s5, c_c2) | (~node3(s5)))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(741,plain,
% 0.69/0.85 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s5, c_c2) | (~node3(s5))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[740, 739])).
% 0.69/0.85 tff(742,plain,
% 0.69/0.85 (~node3(s5)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[741, 399, 738])).
% 0.69/0.85 tff(743,plain,
% 0.69/0.85 (((~![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)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(744,plain,
% 0.69/0.85 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s4, c_n1) | (~node1(s4)))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(745,plain,
% 0.69/0.85 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s4, c_n1) | (~node1(s4))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[744, 743])).
% 0.69/0.85 tff(746,plain,
% 0.69/0.85 (~node1(s4)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[745, 421, 660])).
% 0.69/0.85 tff(747,plain,
% 0.69/0.85 (((~![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))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(748,plain,
% 0.69/0.85 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s3, s4)) | node18(s3, s4))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(749,plain,
% 0.69/0.85 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s3, s4)) | node18(s3, s4)),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[748, 747])).
% 0.69/0.85 tff(750,plain,
% 0.69/0.85 (node18(s3, s4)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[749, 125, 603])).
% 0.69/0.85 tff(751,plain,
% 0.69/0.85 (^[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)))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(752,plain,
% 0.69/0.85 (![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))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[751])).
% 0.69/0.85 tff(753,plain,
% 0.69/0.85 (![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))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(754,plain,
% 0.69/0.85 (^[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))))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(755,plain,
% 0.69/0.85 (![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))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[754])).
% 0.69/0.85 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/sandbox/benchmark/theBenchmark.p','m_main_62')).
% 0.69/0.85 tff(757,plain,
% 0.69/0.85 (![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))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[756, 755])).
% 0.69/0.85 tff(758,plain,
% 0.69/0.85 (![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))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[757, 753])).
% 0.69/0.85 tff(759,plain,(
% 0.69/0.85 ![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))),
% 0.69/0.85 inference(skolemize,[status(sab)],[758])).
% 0.69/0.85 tff(760,plain,
% 0.69/0.85 (![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))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[759, 752])).
% 0.69/0.85 tff(761,plain,
% 0.69/0.85 (((~![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))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(762,plain,
% 0.69/0.85 ((~![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))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(763,plain,
% 0.69/0.85 ((~![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)),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[762, 761])).
% 0.69/0.85 tff(764,plain,
% 0.69/0.85 ((~m_main_v_state1(s3, c_n1)) | (~m_main_v_state2(s3, c_t2)) | m_main_v_turn(s4, c_2)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[763, 760, 750])).
% 0.69/0.85 tff(765,plain,
% 0.69/0.85 (m_main_v_turn(s4, c_2)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[764, 532, 592])).
% 0.69/0.85 tff(766,plain,
% 0.69/0.85 (((~![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)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(767,plain,
% 0.69/0.85 ((~![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)))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(768,plain,
% 0.69/0.85 ((~![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))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[767, 766])).
% 0.69/0.85 tff(769,plain,
% 0.69/0.85 (~m_main_v_turn(s4, c_1)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[768, 156, 765])).
% 0.69/0.85 tff(770,plain,
% 0.69/0.85 (^[X: $i] : refl((m_main_v_turn(X, c_1) | (~node5(X))) <=> (m_main_v_turn(X, c_1) | (~node5(X))))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(771,plain,
% 0.69/0.85 (![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X))) <=> ![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[770])).
% 0.69/0.85 tff(772,plain,
% 0.69/0.85 (![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X))) <=> ![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(773,axiom,(![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_24')).
% 0.69/0.85 tff(774,plain,
% 0.69/0.85 (![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[773, 772])).
% 0.69/0.85 tff(775,plain,(
% 0.69/0.85 ![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))),
% 0.69/0.85 inference(skolemize,[status(sab)],[774])).
% 0.69/0.85 tff(776,plain,
% 0.69/0.85 (![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[775, 771])).
% 0.69/0.85 tff(777,plain,
% 0.69/0.85 (((~![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)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(778,plain,
% 0.69/0.85 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s4, c_1) | (~node5(s4)))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(779,plain,
% 0.69/0.85 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s4, c_1) | (~node5(s4))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[778, 777])).
% 0.69/0.85 tff(780,plain,
% 0.69/0.85 (~node5(s4)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[779, 776, 769])).
% 0.69/0.85 tff(781,plain,
% 0.69/0.85 (^[X: $i] : refl((m_main_v_state1(X, c_n1) | (~node2(X))) <=> (m_main_v_state1(X, c_n1) | (~node2(X))))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(782,plain,
% 0.69/0.85 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[781])).
% 0.69/0.85 tff(783,plain,
% 0.69/0.85 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(784,axiom,(![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_16')).
% 0.69/0.85 tff(785,plain,
% 0.69/0.85 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[784, 783])).
% 0.69/0.85 tff(786,plain,(
% 0.69/0.85 ![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))),
% 0.69/0.85 inference(skolemize,[status(sab)],[785])).
% 0.69/0.85 tff(787,plain,
% 0.69/0.85 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[786, 782])).
% 0.69/0.85 tff(788,plain,
% 0.69/0.85 (((~![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)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(789,plain,
% 0.69/0.85 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s4, c_n1) | (~node2(s4)))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(790,plain,
% 0.69/0.85 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s4, c_n1) | (~node2(s4))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[789, 788])).
% 0.69/0.85 tff(791,plain,
% 0.69/0.85 (~node2(s4)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[790, 787, 660])).
% 0.69/0.85 tff(792,plain,
% 0.69/0.85 (^[X: $i] : refl((m_main_v_state1(X, c_n1) | (~node3(X))) <=> (m_main_v_state1(X, c_n1) | (~node3(X))))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(793,plain,
% 0.69/0.85 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[792])).
% 0.69/0.85 tff(794,plain,
% 0.69/0.85 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(795,axiom,(![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_18')).
% 0.69/0.85 tff(796,plain,
% 0.69/0.85 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[795, 794])).
% 0.69/0.85 tff(797,plain,(
% 0.69/0.85 ![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))),
% 0.69/0.85 inference(skolemize,[status(sab)],[796])).
% 0.69/0.85 tff(798,plain,
% 0.69/0.85 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[797, 793])).
% 0.69/0.85 tff(799,plain,
% 0.69/0.85 (((~![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)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(800,plain,
% 0.69/0.85 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s4, c_n1) | (~node3(s4)))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(801,plain,
% 0.69/0.85 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s4, c_n1) | (~node3(s4))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[800, 799])).
% 0.69/0.85 tff(802,plain,
% 0.69/0.85 (~node3(s4)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[801, 798, 660])).
% 0.69/0.85 tff(803,plain,
% 0.69/0.85 (((~![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)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(804,plain,
% 0.69/0.85 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s4, c_n2) | (~node4(s4)))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(805,plain,
% 0.69/0.85 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s4, c_n2) | (~node4(s4))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[804, 803])).
% 0.69/0.85 tff(806,plain,
% 0.69/0.85 (~node4(s4)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[805, 388, 701])).
% 0.69/0.85 tff(807,plain,
% 0.69/0.85 (((~![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))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(808,plain,
% 0.69/0.85 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s4, s5)) | node7(s4, s5))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(809,plain,
% 0.69/0.85 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s4, s5)) | node7(s4, s5)),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[808, 807])).
% 0.69/0.85 tff(810,plain,
% 0.69/0.85 (node7(s4, s5)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[809, 206, 712])).
% 0.69/0.85 tff(811,plain,
% 0.69/0.85 (^[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))))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(812,plain,
% 0.69/0.85 (![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)))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[811])).
% 0.69/0.85 tff(813,plain,
% 0.69/0.85 (![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)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(814,plain,
% 0.69/0.85 (^[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)))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(815,plain,
% 0.69/0.86 (![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)))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[814])).
% 0.69/0.86 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/sandbox/benchmark/theBenchmark.p','m_main_33')).
% 0.69/0.86 tff(817,plain,
% 0.69/0.86 (![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)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[816, 815])).
% 0.69/0.86 tff(818,plain,
% 0.69/0.86 (![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)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[817, 813])).
% 0.69/0.86 tff(819,plain,(
% 0.69/0.86 ![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)))),
% 0.69/0.86 inference(skolemize,[status(sab)],[818])).
% 0.69/0.86 tff(820,plain,
% 0.69/0.86 (![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)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[819, 812])).
% 0.69/0.86 tff(821,plain,
% 0.69/0.86 (((~![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)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(822,plain,
% 0.69/0.86 ((~![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)))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(823,plain,
% 0.69/0.86 ((~![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))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[822, 821])).
% 0.69/0.86 tff(824,plain,
% 0.69/0.86 (m_main_v_state1(s4, c_c1) | node1(s4) | node2(s4) | node3(s4) | node4(s4) | node5(s4) | node6(s4, s5)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[823, 820, 810])).
% 0.69/0.86 tff(825,plain,
% 0.69/0.86 (node6(s4, s5)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[824, 806, 668, 802, 791, 780, 746])).
% 0.69/0.86 tff(826,plain,
% 0.69/0.86 (^[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))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(827,plain,
% 0.69/0.86 (![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)))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[826])).
% 0.69/0.86 tff(828,plain,
% 0.69/0.86 (![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)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(829,plain,
% 0.69/0.86 (^[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))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(830,plain,
% 0.69/0.86 (![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)))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[829])).
% 0.69/0.86 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/sandbox/benchmark/theBenchmark.p','m_main_26')).
% 0.69/0.86 tff(832,plain,
% 0.69/0.86 (![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[831, 830])).
% 0.69/0.86 tff(833,plain,
% 0.69/0.86 (![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[832, 828])).
% 0.69/0.86 tff(834,plain,(
% 0.69/0.86 ![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))),
% 0.69/0.86 inference(skolemize,[status(sab)],[833])).
% 0.69/0.86 tff(835,plain,
% 0.69/0.86 (![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[834, 827])).
% 0.69/0.86 tff(836,plain,
% 0.69/0.86 (((~![V: $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)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(837,plain,
% 0.69/0.86 (((~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)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(838,plain,
% 0.69/0.86 (((~![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))))),
% 0.69/0.86 inference(monotonicity,[status(thm)],[837])).
% 0.69/0.86 tff(839,plain,
% 0.69/0.86 (((~![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)))),
% 0.69/0.86 inference(transitivity,[status(thm)],[838, 836])).
% 0.69/0.86 tff(840,plain,
% 0.69/0.86 ((~![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)))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(841,plain,
% 0.69/0.86 ((~![V: $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))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[840, 839])).
% 0.69/0.86 tff(842,plain,
% 0.69/0.86 (~m_main_v_state1(s5, c_n1)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[841, 835, 660, 825])).
% 0.69/0.86 tff(843,plain,
% 0.69/0.86 (((~![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)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(844,plain,
% 0.69/0.86 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s5, c_n1) | (~node2(s5)))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(845,plain,
% 0.69/0.86 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s5, c_n1) | (~node2(s5))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[844, 843])).
% 0.69/0.86 tff(846,plain,
% 0.69/0.86 (~node2(s5)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[845, 787, 842])).
% 0.69/0.86 tff(847,plain,
% 0.69/0.86 (^[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)))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(848,plain,
% 0.69/0.86 (![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))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[847])).
% 0.69/0.86 tff(849,plain,
% 0.69/0.86 (![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))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(850,plain,
% 0.69/0.86 (^[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))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(851,plain,
% 0.69/0.86 (![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))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[850])).
% 0.69/0.86 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/sandbox/benchmark/theBenchmark.p','m_main_25')).
% 0.69/0.86 tff(853,plain,
% 0.69/0.86 (![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[852, 851])).
% 0.69/0.86 tff(854,plain,
% 0.69/0.86 (![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[853, 849])).
% 0.69/0.86 tff(855,plain,(
% 0.69/0.86 ![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))),
% 0.69/0.86 inference(skolemize,[status(sab)],[854])).
% 0.69/0.86 tff(856,plain,
% 0.69/0.86 (![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[855, 848])).
% 0.69/0.86 tff(857,plain,
% 0.69/0.86 (((~![V: $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)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(858,plain,
% 0.69/0.86 (((~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)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(859,plain,
% 0.69/0.86 (((~![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))))),
% 0.69/0.86 inference(monotonicity,[status(thm)],[858])).
% 0.69/0.86 tff(860,plain,
% 0.69/0.86 (((~![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)))),
% 0.69/0.86 inference(transitivity,[status(thm)],[859, 857])).
% 0.69/0.86 tff(861,plain,
% 0.69/0.86 ((~![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))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(862,plain,
% 0.69/0.86 ((~![V: $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))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[861, 860])).
% 0.69/0.86 tff(863,plain,
% 0.69/0.86 (m_main_v_state1(s5, c_t1)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[862, 856, 656, 825])).
% 0.69/0.86 tff(864,plain,
% 0.69/0.86 (((~![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)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(865,plain,
% 0.69/0.86 ((~![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)))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(866,plain,
% 0.69/0.86 ((~![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))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[865, 864])).
% 0.69/0.86 tff(867,plain,
% 0.69/0.86 (~m_main_v_state2(s5, c_t2)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[866, 77, 734])).
% 0.69/0.86 tff(868,plain,
% 0.69/0.86 (((~![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)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(869,plain,
% 0.69/0.86 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s5, c_t2) | (~node1(s5)))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(870,plain,
% 0.69/0.86 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s5, c_t2) | (~node1(s5))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[869, 868])).
% 0.69/0.86 tff(871,plain,
% 0.69/0.86 (~node1(s5)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[870, 195, 867])).
% 0.69/0.86 tff(872,plain,
% 0.69/0.86 (succ(s5, s6) <=> succ(s5, s6)),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(873,axiom,(succ(s5, s6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound6')).
% 0.69/0.86 tff(874,plain,
% 0.69/0.86 (succ(s5, s6)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[873, 872])).
% 0.69/0.86 tff(875,plain,
% 0.69/0.86 (((~![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))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(876,plain,
% 0.69/0.86 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s5, s6)) | trans(s5, s6))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(877,plain,
% 0.69/0.86 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s5, s6)) | trans(s5, s6)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[876, 875])).
% 0.69/0.86 tff(878,plain,
% 0.69/0.86 (trans(s5, s6)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[877, 874, 32])).
% 0.69/0.86 tff(879,plain,
% 0.69/0.86 (((~![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))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(880,plain,
% 0.69/0.86 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s5, s6)) | node7(s5, s6))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(881,plain,
% 0.69/0.86 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s5, s6)) | node7(s5, s6)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[880, 879])).
% 0.69/0.86 tff(882,plain,
% 0.69/0.86 (node7(s5, s6)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[881, 206, 878])).
% 0.69/0.86 tff(883,plain,
% 0.69/0.86 (^[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)))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(884,plain,
% 0.69/0.86 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_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))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[883])).
% 0.69/0.86 tff(885,plain,
% 0.69/0.86 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_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))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(886,plain,
% 0.69/0.86 (^[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))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(887,plain,
% 0.69/0.86 (![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))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[886])).
% 0.69/0.86 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/sandbox/benchmark/theBenchmark.p','m_main_30')).
% 0.69/0.86 tff(889,plain,
% 0.69/0.86 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[888, 887])).
% 0.69/0.86 tff(890,plain,
% 0.69/0.86 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[889, 885])).
% 0.69/0.86 tff(891,plain,(
% 0.69/0.86 ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))),
% 0.69/0.86 inference(skolemize,[status(sab)],[890])).
% 0.69/0.86 tff(892,plain,
% 0.69/0.86 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[891, 884])).
% 0.69/0.86 tff(893,plain,
% 0.69/0.86 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(894,plain,
% 0.69/0.86 (((~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)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(895,plain,
% 0.69/0.86 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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))))),
% 0.69/0.86 inference(monotonicity,[status(thm)],[894])).
% 0.69/0.86 tff(896,plain,
% 0.69/0.86 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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)))),
% 0.69/0.86 inference(transitivity,[status(thm)],[895, 893])).
% 0.69/0.86 tff(897,plain,
% 0.69/0.86 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(898,plain,
% 0.69/0.86 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[897, 896])).
% 0.69/0.86 tff(899,plain,
% 0.69/0.86 ((~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)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[898, 892, 882])).
% 0.69/0.86 tff(900,plain,
% 0.69/0.86 (m_main_v_state1(s6, c_c1)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[899, 871, 734, 863, 846, 742])).
% 0.69/0.86 tff(901,plain,
% 0.69/0.86 (((~![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)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(902,plain,
% 0.69/0.86 ((~![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)))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(903,plain,
% 0.69/0.86 ((~![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))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[902, 901])).
% 0.69/0.86 tff(904,plain,
% 0.69/0.86 (~m_main_v_state1(s6, c_t1)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[903, 539, 900])).
% 0.69/0.86 tff(905,plain,
% 0.69/0.86 (((~![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)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(906,plain,
% 0.69/0.86 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s6, c_t1) | (~node5(s6)))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(907,plain,
% 0.69/0.86 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s6, c_t1) | (~node5(s6))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[906, 905])).
% 0.69/0.86 tff(908,plain,
% 0.69/0.86 (~node5(s6)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[907, 550, 904])).
% 0.69/0.86 tff(909,plain,
% 0.69/0.86 (((~![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))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(910,plain,
% 0.69/0.86 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s5, s6)) | node14(s5, s6))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(911,plain,
% 0.69/0.86 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s5, s6)) | node14(s5, s6)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[910, 909])).
% 0.69/0.86 tff(912,plain,
% 0.69/0.86 (node14(s5, s6)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[911, 46, 878])).
% 0.69/0.86 tff(913,plain,
% 0.69/0.86 (^[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)))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(914,plain,
% 0.69/0.86 (![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))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[913])).
% 0.69/0.86 tff(915,plain,
% 0.69/0.86 (![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))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(916,plain,
% 0.69/0.86 (^[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))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(917,plain,
% 0.69/0.86 (![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))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[916])).
% 0.69/0.86 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/sandbox/benchmark/theBenchmark.p','m_main_48')).
% 0.69/0.86 tff(919,plain,
% 0.69/0.86 (![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))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[918, 917])).
% 0.69/0.87 tff(920,plain,
% 0.69/0.87 (![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))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[919, 915])).
% 0.69/0.87 tff(921,plain,(
% 0.69/0.87 ![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))),
% 0.69/0.87 inference(skolemize,[status(sab)],[920])).
% 0.69/0.87 tff(922,plain,
% 0.69/0.87 (![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))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[921, 914])).
% 0.69/0.87 tff(923,plain,
% 0.69/0.87 (((~![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))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(924,plain,
% 0.69/0.87 ((~![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))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(925,plain,
% 0.69/0.87 ((~![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)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[924, 923])).
% 0.69/0.87 tff(926,plain,
% 0.69/0.87 ((~m_main_v_state1(s5, c_t1)) | (~m_main_v_state2(s5, c_n2)) | m_main_v_state2(s6, c_t2)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[925, 922, 912])).
% 0.69/0.87 tff(927,plain,
% 0.69/0.87 (m_main_v_state2(s6, c_t2)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[926, 863, 734])).
% 0.69/0.87 tff(928,plain,
% 0.69/0.87 (((~![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)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(929,plain,
% 0.69/0.87 ((~![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)))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(930,plain,
% 0.69/0.87 ((~![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))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[929, 928])).
% 0.69/0.87 tff(931,plain,
% 0.69/0.87 (~m_main_v_state2(s6, c_n2)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[930, 77, 927])).
% 0.69/0.87 tff(932,plain,
% 0.69/0.87 (((~![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)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(933,plain,
% 0.69/0.87 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s6, c_n2) | (~node4(s6)))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(934,plain,
% 0.69/0.87 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s6, c_n2) | (~node4(s6))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[933, 932])).
% 0.69/0.87 tff(935,plain,
% 0.69/0.87 (~node4(s6)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[934, 388, 931])).
% 0.69/0.87 tff(936,plain,
% 0.69/0.87 (((~![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)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(937,plain,
% 0.69/0.87 ((~![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)))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(938,plain,
% 0.69/0.87 ((~![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))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[937, 936])).
% 0.69/0.87 tff(939,plain,
% 0.69/0.87 (~m_main_v_state2(s6, c_c2)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[938, 260, 927])).
% 0.69/0.87 tff(940,plain,
% 0.69/0.87 (((~![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)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(941,plain,
% 0.69/0.87 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s6, c_c2) | (~node3(s6)))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(942,plain,
% 0.69/0.87 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s6, c_c2) | (~node3(s6))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[941, 940])).
% 0.69/0.87 tff(943,plain,
% 0.69/0.87 (~node3(s6)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[942, 399, 939])).
% 0.69/0.87 tff(944,plain,
% 0.69/0.87 (((~![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)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(945,plain,
% 0.69/0.87 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s6, c_n2) | (~node2(s6)))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(946,plain,
% 0.69/0.87 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s6, c_n2) | (~node2(s6))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[945, 944])).
% 0.69/0.87 tff(947,plain,
% 0.69/0.87 (~node2(s6)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[946, 410, 931])).
% 0.69/0.87 tff(948,plain,
% 0.69/0.87 (((~![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)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(949,plain,
% 0.69/0.87 ((~![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)))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(950,plain,
% 0.69/0.87 ((~![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))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[949, 948])).
% 0.69/0.87 tff(951,plain,
% 0.69/0.87 (~m_main_v_state1(s6, c_n1)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[950, 454, 900])).
% 0.69/0.87 tff(952,plain,
% 0.69/0.87 (((~![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)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(953,plain,
% 0.69/0.87 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s6, c_n1) | (~node1(s6)))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(954,plain,
% 0.69/0.87 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s6, c_n1) | (~node1(s6))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[953, 952])).
% 0.69/0.87 tff(955,plain,
% 0.69/0.87 (~node1(s6)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[954, 421, 951])).
% 0.69/0.87 tff(956,plain,
% 0.69/0.87 (succ(s6, s7) <=> succ(s6, s7)),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(957,axiom,(succ(s6, s7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound7')).
% 0.69/0.87 tff(958,plain,
% 0.69/0.87 (succ(s6, s7)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[957, 956])).
% 0.69/0.87 tff(959,plain,
% 0.69/0.87 (((~![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))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(960,plain,
% 0.69/0.87 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s6, s7)) | trans(s6, s7))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(961,plain,
% 0.69/0.87 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s6, s7)) | trans(s6, s7)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[960, 959])).
% 0.69/0.87 tff(962,plain,
% 0.69/0.87 (trans(s6, s7)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[961, 958, 32])).
% 0.69/0.87 tff(963,plain,
% 0.69/0.87 (((~![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))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(964,plain,
% 0.69/0.87 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s6, s7)) | node7(s6, s7))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(965,plain,
% 0.69/0.87 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s6, s7)) | node7(s6, s7)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[964, 963])).
% 0.69/0.87 tff(966,plain,
% 0.69/0.87 (node7(s6, s7)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[965, 206, 962])).
% 0.69/0.87 tff(967,plain,
% 0.69/0.87 (((~![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(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)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(968,plain,
% 0.69/0.87 (((~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)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(969,plain,
% 0.69/0.87 (((~![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(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))))),
% 0.69/0.87 inference(monotonicity,[status(thm)],[968])).
% 0.69/0.87 tff(970,plain,
% 0.69/0.87 (((~![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(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)))),
% 0.69/0.87 inference(transitivity,[status(thm)],[969, 967])).
% 0.69/0.87 tff(971,plain,
% 0.69/0.87 ((~![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(s6, c_c1)) | node1(s6) | node2(s6) | node3(s6) | node4(s6) | node5(s6) | (~node7(s6, s7)) | m_main_v_state1(s7, c_n1))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(972,plain,
% 0.69/0.87 ((~![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(s7, c_n1) | (~m_main_v_state1(s6, c_c1)) | node1(s6) | node2(s6) | node3(s6) | node4(s6) | node5(s6) | (~node7(s6, s7))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[971, 970])).
% 0.69/0.87 tff(973,plain,
% 0.69/0.87 (m_main_v_state1(s7, c_n1) | (~m_main_v_state1(s6, c_c1)) | node1(s6) | node2(s6) | node3(s6) | node4(s6) | node5(s6)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[972, 584, 966])).
% 0.69/0.87 tff(974,plain,
% 0.69/0.87 (m_main_v_state1(s7, c_n1)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[973, 955, 900, 947, 943, 935, 908])).
% 0.69/0.87 tff(975,plain,
% 0.69/0.87 (((~![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)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(976,plain,
% 0.69/0.87 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s5, c_t2) | (~node15(s5)))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(977,plain,
% 0.69/0.87 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s5, c_t2) | (~node15(s5))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[976, 975])).
% 0.69/0.87 tff(978,plain,
% 0.69/0.87 (~node15(s5)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[977, 103, 867])).
% 0.69/0.87 tff(979,plain,
% 0.69/0.87 (((~![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))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(980,plain,
% 0.69/0.87 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s5, s6)) | node18(s5, s6))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(981,plain,
% 0.69/0.87 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s5, s6)) | node18(s5, s6)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[980, 979])).
% 0.69/0.87 tff(982,plain,
% 0.69/0.87 (node18(s5, s6)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[981, 125, 878])).
% 0.69/0.87 tff(983,plain,
% 0.69/0.87 (^[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)))),
% 0.69/0.87 inference(bind,[status(th)],[])).
% 0.69/0.87 tff(984,plain,
% 0.69/0.87 (![Y: $i, X: $i] : ((~m_main_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))),
% 0.69/0.87 inference(quant_intro,[status(thm)],[983])).
% 0.69/0.87 tff(985,plain,
% 0.69/0.87 (![Y: $i, X: $i] : ((~m_main_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))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(986,plain,
% 0.69/0.87 (^[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))))),
% 0.69/0.87 inference(bind,[status(th)],[])).
% 0.69/0.87 tff(987,plain,
% 0.69/0.87 (![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))),
% 0.69/0.87 inference(quant_intro,[status(thm)],[986])).
% 0.69/0.87 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/sandbox/benchmark/theBenchmark.p','m_main_63')).
% 0.69/0.87 tff(989,plain,
% 0.69/0.87 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[988, 987])).
% 0.69/0.87 tff(990,plain,
% 0.69/0.87 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[989, 985])).
% 0.69/0.87 tff(991,plain,(
% 0.69/0.87 ![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))),
% 0.69/0.87 inference(skolemize,[status(sab)],[990])).
% 0.69/0.87 tff(992,plain,
% 0.69/0.87 (![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[991, 984])).
% 0.69/0.87 tff(993,plain,
% 0.69/0.87 (((~![Y: $i, X: $i] : ((~m_main_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))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(994,plain,
% 0.69/0.87 (((~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))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(995,plain,
% 0.69/0.87 (((~![Y: $i, X: $i] : ((~m_main_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)))),
% 0.69/0.87 inference(monotonicity,[status(thm)],[994])).
% 0.69/0.87 tff(996,plain,
% 0.69/0.87 (((~![Y: $i, X: $i] : ((~m_main_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))),
% 0.69/0.87 inference(transitivity,[status(thm)],[995, 993])).
% 0.69/0.87 tff(997,plain,
% 0.69/0.87 ((~![Y: $i, X: $i] : ((~m_main_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))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(998,plain,
% 0.69/0.87 ((~![Y: $i, X: $i] : ((~m_main_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)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[997, 996])).
% 0.69/0.87 tff(999,plain,
% 0.69/0.87 (node15(s5) | (~m_main_v_state1(s5, c_t1)) | (~m_main_v_state2(s5, c_n2)) | m_main_v_turn(s6, c_1)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[998, 992, 982])).
% 0.69/0.87 tff(1000,plain,
% 0.69/0.87 (m_main_v_turn(s6, c_1)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[999, 978, 734, 863])).
% 0.69/0.87 tff(1001,plain,
% 0.69/0.87 (((~![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)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(1002,plain,
% 0.69/0.87 ((~![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)))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(1003,plain,
% 0.69/0.87 ((~![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))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[1002, 1001])).
% 0.69/0.87 tff(1004,plain,
% 0.69/0.87 (~m_main_v_turn(s6, c_2)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[1003, 156, 1000])).
% 0.69/0.87 tff(1005,plain,
% 0.69/0.87 (((~![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)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(1006,plain,
% 0.69/0.87 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s6, c_2) | (~node12(s6)))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(1007,plain,
% 0.69/0.87 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s6, c_2) | (~node12(s6))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[1006, 1005])).
% 0.69/0.87 tff(1008,plain,
% 0.69/0.87 (~node12(s6)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[1007, 184, 1004])).
% 0.69/0.87 tff(1009,plain,
% 0.69/0.87 (((~![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)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(1010,plain,
% 0.69/0.87 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s6, c_n2) | (~node8(s6)))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(1011,plain,
% 0.69/0.87 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s6, c_n2) | (~node8(s6))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[1010, 1009])).
% 0.69/0.87 tff(1012,plain,
% 0.69/0.87 (~node8(s6)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[1011, 271, 931])).
% 0.69/0.87 tff(1013,plain,
% 0.69/0.87 (((~![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)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(1014,plain,
% 0.69/0.87 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s6, c_n2) | (~node9(s6)))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(1015,plain,
% 0.69/0.87 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s6, c_n2) | (~node9(s6))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[1014, 1013])).
% 0.69/0.87 tff(1016,plain,
% 0.69/0.87 (~node9(s6)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[1015, 88, 931])).
% 0.69/0.87 tff(1017,plain,
% 0.69/0.87 (((~![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)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(1018,plain,
% 0.69/0.87 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s6, c_n2) | (~node10(s6)))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(1019,plain,
% 0.69/0.87 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s6, c_n2) | (~node10(s6))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[1018, 1017])).
% 0.69/0.87 tff(1020,plain,
% 0.69/0.87 (~node10(s6)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[1019, 249, 931])).
% 0.69/0.87 tff(1021,plain,
% 0.69/0.87 (((~![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)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(1022,plain,
% 0.69/0.87 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s6, c_n1) | (~node11(s6)))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(1023,plain,
% 0.69/0.87 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s6, c_n1) | (~node11(s6))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[1022, 1021])).
% 0.69/0.87 tff(1024,plain,
% 0.69/0.87 (~node11(s6)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[1023, 238, 951])).
% 0.69/0.87 tff(1025,plain,
% 0.69/0.87 (((~![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))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(1026,plain,
% 0.69/0.87 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s6, s7)) | node14(s6, s7))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(1027,plain,
% 0.69/0.87 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s6, s7)) | node14(s6, s7)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[1026, 1025])).
% 0.69/0.87 tff(1028,plain,
% 0.69/0.87 (node14(s6, s7)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[1027, 46, 962])).
% 0.69/0.87 tff(1029,plain,
% 0.69/0.87 (((~![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(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)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(1030,plain,
% 0.69/0.87 ((~![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(s6, c_c2) | node9(s6) | node8(s6) | node10(s6) | node11(s6) | node12(s6) | node13(s6, s7) | (~node14(s6, s7)))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(1031,plain,
% 0.69/0.87 ((~![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(s6, c_c2) | node9(s6) | node8(s6) | node10(s6) | node11(s6) | node12(s6) | node13(s6, s7) | (~node14(s6, s7))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[1030, 1029])).
% 0.69/0.87 tff(1032,plain,
% 0.69/0.87 (m_main_v_state2(s6, c_c2) | node9(s6) | node8(s6) | node10(s6) | node11(s6) | node12(s6) | node13(s6, s7)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[1031, 296, 1028])).
% 0.69/0.87 tff(1033,plain,
% 0.69/0.87 (node13(s6, s7)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[1032, 1024, 939, 1020, 1016, 1012, 1008])).
% 0.69/0.87 tff(1034,plain,
% 0.69/0.87 (((~![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(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)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(1035,plain,
% 0.69/0.87 (((~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)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(1036,plain,
% 0.69/0.87 (((~![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))))),
% 0.69/0.88 inference(monotonicity,[status(thm)],[1035])).
% 0.69/0.88 tff(1037,plain,
% 0.69/0.88 (((~![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)))),
% 0.69/0.88 inference(transitivity,[status(thm)],[1036, 1034])).
% 0.69/0.88 tff(1038,plain,
% 0.69/0.88 ((~![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))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1039,plain,
% 0.69/0.88 ((~![V: $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))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1038, 1037])).
% 0.69/0.88 tff(1040,plain,
% 0.69/0.88 (m_main_v_state2(s7, c_t2)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1039, 518, 927, 1033])).
% 0.69/0.88 tff(1041,plain,
% 0.69/0.88 (succ(s7, s8) <=> succ(s7, s8)),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1042,axiom,(succ(s7, s8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound8')).
% 0.69/0.88 tff(1043,plain,
% 0.69/0.88 (succ(s7, s8)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1042, 1041])).
% 0.69/0.88 tff(1044,plain,
% 0.69/0.88 (((~![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))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1045,plain,
% 0.69/0.88 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s7, s8)) | trans(s7, s8))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1046,plain,
% 0.69/0.88 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s7, s8)) | trans(s7, s8)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1045, 1044])).
% 0.69/0.88 tff(1047,plain,
% 0.69/0.88 (trans(s7, s8)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1046, 1043, 32])).
% 0.69/0.88 tff(1048,plain,
% 0.69/0.88 (((~![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))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1049,plain,
% 0.69/0.88 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s7, s8)) | node7(s7, s8))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1050,plain,
% 0.69/0.88 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s7, s8)) | node7(s7, s8)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1049, 1048])).
% 0.69/0.88 tff(1051,plain,
% 0.69/0.88 (node7(s7, s8)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1050, 206, 1047])).
% 0.69/0.88 tff(1052,plain,
% 0.69/0.88 (((~![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(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))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1053,plain,
% 0.69/0.88 ((~![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(s7, c_n1)) | (~m_main_v_state2(s7, c_t2)) | (~node7(s7, s8)) | m_main_v_state1(s8, c_t1))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1054,plain,
% 0.69/0.88 ((~![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(s7, c_n1)) | (~m_main_v_state2(s7, c_t2)) | (~node7(s7, s8)) | m_main_v_state1(s8, c_t1)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1053, 1052])).
% 0.69/0.88 tff(1055,plain,
% 0.69/0.88 ((~m_main_v_state1(s7, c_n1)) | (~m_main_v_state2(s7, c_t2)) | m_main_v_state1(s8, c_t1)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1054, 651, 1051])).
% 0.69/0.88 tff(1056,plain,
% 0.69/0.88 (m_main_v_state1(s8, c_t1)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1055, 1040, 974])).
% 0.69/0.88 tff(1057,plain,
% 0.69/0.88 (((~![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)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1058,plain,
% 0.69/0.88 ((~![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)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1059,plain,
% 0.69/0.88 ((~![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))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1058, 1057])).
% 0.69/0.88 tff(1060,plain,
% 0.69/0.88 (~m_main_v_state1(s8, c_n1)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1059, 10, 1056])).
% 0.69/0.88 tff(1061,plain,
% 0.69/0.88 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s8, c_n1) | (~node1(s8)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s8, c_n1) | (~node1(s8)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1062,plain,
% 0.69/0.88 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s8, c_n1) | (~node1(s8)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1063,plain,
% 0.69/0.88 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s8, c_n1) | (~node1(s8))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1062, 1061])).
% 0.69/0.88 tff(1064,plain,
% 0.69/0.88 (~node1(s8)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1063, 421, 1060])).
% 0.69/0.88 tff(1065,plain,
% 0.69/0.88 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s7, s8)) | node18(s7, s8))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s7, s8)) | node18(s7, s8))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1066,plain,
% 0.69/0.88 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s7, s8)) | node18(s7, s8))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1067,plain,
% 0.69/0.88 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s7, s8)) | node18(s7, s8)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1066, 1065])).
% 0.69/0.88 tff(1068,plain,
% 0.69/0.88 (node18(s7, s8)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1067, 125, 1047])).
% 0.69/0.88 tff(1069,plain,
% 0.69/0.88 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s7, c_n1)) | (~m_main_v_state2(s7, c_t2)) | (~node18(s7, s8)) | m_main_v_turn(s8, c_2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s7, c_n1)) | (~m_main_v_state2(s7, c_t2)) | (~node18(s7, s8)) | m_main_v_turn(s8, c_2))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1070,plain,
% 0.69/0.88 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s7, c_n1)) | (~m_main_v_state2(s7, c_t2)) | (~node18(s7, s8)) | m_main_v_turn(s8, c_2))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1071,plain,
% 0.69/0.88 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s7, c_n1)) | (~m_main_v_state2(s7, c_t2)) | (~node18(s7, s8)) | m_main_v_turn(s8, c_2)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1070, 1069])).
% 0.69/0.88 tff(1072,plain,
% 0.69/0.88 ((~m_main_v_state1(s7, c_n1)) | (~m_main_v_state2(s7, c_t2)) | m_main_v_turn(s8, c_2)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1071, 760, 1068])).
% 0.69/0.88 tff(1073,plain,
% 0.69/0.88 (m_main_v_turn(s8, c_2)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1072, 1040, 974])).
% 0.69/0.88 tff(1074,plain,
% 0.69/0.88 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s8, c_1)) | (~m_main_v_turn(s8, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s8, c_1)) | (~m_main_v_turn(s8, c_2)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1075,plain,
% 0.69/0.88 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s8, c_1)) | (~m_main_v_turn(s8, c_2)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1076,plain,
% 0.69/0.88 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s8, c_1)) | (~m_main_v_turn(s8, c_2))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1075, 1074])).
% 0.69/0.88 tff(1077,plain,
% 0.69/0.88 (~m_main_v_turn(s8, c_1)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1076, 156, 1073])).
% 0.69/0.88 tff(1078,plain,
% 0.69/0.88 (((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s8, c_1) | (~node5(s8)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s8, c_1) | (~node5(s8)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1079,plain,
% 0.69/0.88 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s8, c_1) | (~node5(s8)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1080,plain,
% 0.69/0.88 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s8, c_1) | (~node5(s8))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1079, 1078])).
% 0.69/0.88 tff(1081,plain,
% 0.69/0.88 (~node5(s8)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1080, 776, 1077])).
% 0.69/0.88 tff(1082,plain,
% 0.69/0.88 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s8, c_n1) | (~node2(s8)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s8, c_n1) | (~node2(s8)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1083,plain,
% 0.69/0.88 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s8, c_n1) | (~node2(s8)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1084,plain,
% 0.69/0.88 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s8, c_n1) | (~node2(s8))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1083, 1082])).
% 0.69/0.88 tff(1085,plain,
% 0.69/0.88 (~node2(s8)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1084, 787, 1060])).
% 0.69/0.88 tff(1086,plain,
% 0.69/0.88 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s8, c_n1) | (~node3(s8)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s8, c_n1) | (~node3(s8)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1087,plain,
% 0.69/0.88 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s8, c_n1) | (~node3(s8)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1088,plain,
% 0.69/0.88 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s8, c_n1) | (~node3(s8))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1087, 1086])).
% 0.69/0.88 tff(1089,plain,
% 0.69/0.88 (~node3(s8)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1088, 798, 1060])).
% 0.69/0.88 tff(1090,plain,
% 0.69/0.88 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s8, c_t1)) | (~m_main_v_state1(s8, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s8, c_t1)) | (~m_main_v_state1(s8, c_c1)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1091,plain,
% 0.69/0.88 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s8, c_t1)) | (~m_main_v_state1(s8, c_c1)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1092,plain,
% 0.69/0.88 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s8, c_t1)) | (~m_main_v_state1(s8, c_c1))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1091, 1090])).
% 0.69/0.88 tff(1093,plain,
% 0.69/0.88 (~m_main_v_state1(s8, c_c1)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1092, 539, 1056])).
% 0.69/0.88 tff(1094,plain,
% 0.69/0.88 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s6, c_n2) | (~m_main_v_state2(s7, c_n2)) | (~node13(s6, s7)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s6, c_n2) | (~m_main_v_state2(s7, c_n2)) | (~node13(s6, s7)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1095,plain,
% 0.69/0.88 (((~node13(s6, s7)) | m_main_v_state2(s6, c_n2) | (~m_main_v_state2(s7, c_n2))) <=> (m_main_v_state2(s6, c_n2) | (~m_main_v_state2(s7, c_n2)) | (~node13(s6, s7)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1096,plain,
% 0.69/0.88 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s6, s7)) | m_main_v_state2(s6, c_n2) | (~m_main_v_state2(s7, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s6, c_n2) | (~m_main_v_state2(s7, c_n2)) | (~node13(s6, s7))))),
% 0.69/0.88 inference(monotonicity,[status(thm)],[1095])).
% 0.69/0.88 tff(1097,plain,
% 0.69/0.88 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s6, s7)) | m_main_v_state2(s6, c_n2) | (~m_main_v_state2(s7, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s6, c_n2) | (~m_main_v_state2(s7, c_n2)) | (~node13(s6, s7)))),
% 0.69/0.88 inference(transitivity,[status(thm)],[1096, 1094])).
% 0.69/0.88 tff(1098,plain,
% 0.69/0.88 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s6, s7)) | m_main_v_state2(s6, c_n2) | (~m_main_v_state2(s7, c_n2)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1099,plain,
% 0.69/0.88 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s6, c_n2) | (~m_main_v_state2(s7, c_n2)) | (~node13(s6, s7))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1098, 1097])).
% 0.69/0.88 tff(1100,plain,
% 0.69/0.88 (~m_main_v_state2(s7, c_n2)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1099, 311, 931, 1033])).
% 0.69/0.88 tff(1101,plain,
% 0.69/0.88 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s7, c_n2) | (~node9(s7)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s7, c_n2) | (~node9(s7)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1102,plain,
% 0.69/0.88 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s7, c_n2) | (~node9(s7)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1103,plain,
% 0.69/0.88 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s7, c_n2) | (~node9(s7))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1102, 1101])).
% 0.69/0.88 tff(1104,plain,
% 0.69/0.88 (~node9(s7)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1103, 88, 1100])).
% 0.69/0.88 tff(1105,plain,
% 0.69/0.88 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s7, c_n2) | (~node10(s7)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s7, c_n2) | (~node10(s7)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1106,plain,
% 0.69/0.88 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s7, c_n2) | (~node10(s7)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1107,plain,
% 0.69/0.88 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s7, c_n2) | (~node10(s7))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1106, 1105])).
% 0.69/0.88 tff(1108,plain,
% 0.69/0.88 (~node10(s7)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1107, 249, 1100])).
% 0.69/0.88 tff(1109,plain,
% 0.69/0.88 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s7, c_n2) | (~node8(s7)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s7, c_n2) | (~node8(s7)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1110,plain,
% 0.69/0.88 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s7, c_n2) | (~node8(s7)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1111,plain,
% 0.69/0.88 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s7, c_n2) | (~node8(s7))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1110, 1109])).
% 0.69/0.88 tff(1112,plain,
% 0.69/0.88 (~node8(s7)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1111, 271, 1100])).
% 0.69/0.88 tff(1113,plain,
% 0.69/0.88 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s7, s8)) | node14(s7, s8))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s7, s8)) | node14(s7, s8))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1114,plain,
% 0.69/0.88 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s7, s8)) | node14(s7, s8))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1115,plain,
% 0.69/0.88 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s7, s8)) | node14(s7, s8)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1114, 1113])).
% 0.69/0.88 tff(1116,plain,
% 0.69/0.88 (node14(s7, s8)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1115, 46, 1047])).
% 0.69/0.88 tff(1117,plain,
% 0.69/0.88 (((~![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(s7, c_n1)) | (~m_main_v_state2(s7, c_t2)) | node9(s7) | node8(s7) | node10(s7) | (~node14(s7, s8)) | m_main_v_state2(s8, c_c2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s7, c_n1)) | (~m_main_v_state2(s7, c_t2)) | node9(s7) | node8(s7) | node10(s7) | (~node14(s7, s8)) | m_main_v_state2(s8, c_c2))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1118,plain,
% 0.69/0.88 ((~![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(s7, c_n1)) | (~m_main_v_state2(s7, c_t2)) | node9(s7) | node8(s7) | node10(s7) | (~node14(s7, s8)) | m_main_v_state2(s8, c_c2))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1119,plain,
% 0.69/0.88 ((~![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(s7, c_n1)) | (~m_main_v_state2(s7, c_t2)) | node9(s7) | node8(s7) | node10(s7) | (~node14(s7, s8)) | m_main_v_state2(s8, c_c2)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1118, 1117])).
% 0.69/0.88 tff(1120,plain,
% 0.69/0.88 ((~m_main_v_state1(s7, c_n1)) | (~m_main_v_state2(s7, c_t2)) | node9(s7) | node8(s7) | node10(s7) | m_main_v_state2(s8, c_c2)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1119, 617, 1116])).
% 0.69/0.88 tff(1121,plain,
% 0.69/0.88 (m_main_v_state2(s8, c_c2)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1120, 1112, 974, 1040, 1108, 1104])).
% 0.69/0.88 tff(1122,plain,
% 0.69/0.88 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s8, c_n2)) | (~m_main_v_state2(s8, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s8, c_n2)) | (~m_main_v_state2(s8, c_c2)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1123,plain,
% 0.69/0.88 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s8, c_n2)) | (~m_main_v_state2(s8, c_c2)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1124,plain,
% 0.69/0.88 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s8, c_n2)) | (~m_main_v_state2(s8, c_c2))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1123, 1122])).
% 0.69/0.88 tff(1125,plain,
% 0.69/0.88 (~m_main_v_state2(s8, c_n2)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1124, 697, 1121])).
% 0.69/0.88 tff(1126,plain,
% 0.69/0.88 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s8, c_n2) | (~node4(s8)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s8, c_n2) | (~node4(s8)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1127,plain,
% 0.69/0.88 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s8, c_n2) | (~node4(s8)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1128,plain,
% 0.69/0.88 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s8, c_n2) | (~node4(s8))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1127, 1126])).
% 0.69/0.88 tff(1129,plain,
% 0.69/0.88 (~node4(s8)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1128, 388, 1125])).
% 0.69/0.88 tff(1130,plain,
% 0.69/0.88 (succ(s8, s9) <=> succ(s8, s9)),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1131,axiom,(succ(s8, s9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound9')).
% 0.69/0.88 tff(1132,plain,
% 0.69/0.88 (succ(s8, s9)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1131, 1130])).
% 0.69/0.88 tff(1133,plain,
% 0.69/0.88 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s8, s9)) | trans(s8, s9))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s8, s9)) | trans(s8, s9))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1134,plain,
% 0.69/0.88 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s8, s9)) | trans(s8, s9))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1135,plain,
% 0.69/0.88 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s8, s9)) | trans(s8, s9)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1134, 1133])).
% 0.69/0.88 tff(1136,plain,
% 0.69/0.88 (trans(s8, s9)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1135, 1132, 32])).
% 0.69/0.88 tff(1137,plain,
% 0.69/0.88 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s8, s9)) | node7(s8, s9))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s8, s9)) | node7(s8, s9))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1138,plain,
% 0.69/0.88 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s8, s9)) | node7(s8, s9))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1139,plain,
% 0.69/0.88 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s8, s9)) | node7(s8, s9)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1138, 1137])).
% 0.69/0.88 tff(1140,plain,
% 0.69/0.88 (node7(s8, s9)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1139, 206, 1136])).
% 0.69/0.88 tff(1141,plain,
% 0.69/0.88 (((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s8, c_c1) | node1(s8) | node2(s8) | node3(s8) | node4(s8) | node5(s8) | node6(s8, s9) | (~node7(s8, s9)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s8, c_c1) | node1(s8) | node2(s8) | node3(s8) | node4(s8) | node5(s8) | node6(s8, s9) | (~node7(s8, s9)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1142,plain,
% 0.69/0.88 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s8, c_c1) | node1(s8) | node2(s8) | node3(s8) | node4(s8) | node5(s8) | node6(s8, s9) | (~node7(s8, s9)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1143,plain,
% 0.69/0.88 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s8, c_c1) | node1(s8) | node2(s8) | node3(s8) | node4(s8) | node5(s8) | node6(s8, s9) | (~node7(s8, s9))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1142, 1141])).
% 0.69/0.88 tff(1144,plain,
% 0.69/0.88 (m_main_v_state1(s8, c_c1) | node1(s8) | node2(s8) | node3(s8) | node4(s8) | node5(s8) | node6(s8, s9)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1143, 820, 1140])).
% 0.69/0.88 tff(1145,plain,
% 0.69/0.88 (node6(s8, s9)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1144, 1129, 1093, 1089, 1085, 1081, 1064])).
% 0.69/0.88 tff(1146,plain,
% 0.69/0.88 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s8, c_t1)) | m_main_v_state1(s9, c_t1) | (~node6(s8, s9)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s8, c_t1)) | m_main_v_state1(s9, c_t1) | (~node6(s8, s9)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1147,plain,
% 0.69/0.88 (((~node6(s8, s9)) | (~m_main_v_state1(s8, c_t1)) | m_main_v_state1(s9, c_t1)) <=> ((~m_main_v_state1(s8, c_t1)) | m_main_v_state1(s9, c_t1) | (~node6(s8, s9)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1148,plain,
% 0.69/0.88 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s8, s9)) | (~m_main_v_state1(s8, c_t1)) | m_main_v_state1(s9, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s8, c_t1)) | m_main_v_state1(s9, c_t1) | (~node6(s8, s9))))),
% 0.69/0.88 inference(monotonicity,[status(thm)],[1147])).
% 0.69/0.88 tff(1149,plain,
% 0.69/0.88 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s8, s9)) | (~m_main_v_state1(s8, c_t1)) | m_main_v_state1(s9, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s8, c_t1)) | m_main_v_state1(s9, c_t1) | (~node6(s8, s9)))),
% 0.69/0.88 inference(transitivity,[status(thm)],[1148, 1146])).
% 0.69/0.88 tff(1150,plain,
% 0.69/0.88 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s8, s9)) | (~m_main_v_state1(s8, c_t1)) | m_main_v_state1(s9, c_t1))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1151,plain,
% 0.69/0.88 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s8, c_t1)) | m_main_v_state1(s9, c_t1) | (~node6(s8, s9))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1150, 1149])).
% 0.69/0.88 tff(1152,plain,
% 0.69/0.88 (m_main_v_state1(s9, c_t1)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1151, 856, 1056, 1145])).
% 0.69/0.88 tff(1153,plain,
% 0.69/0.88 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s8, c_t2)) | (~m_main_v_state2(s8, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s8, c_t2)) | (~m_main_v_state2(s8, c_c2)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1154,plain,
% 0.69/0.88 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s8, c_t2)) | (~m_main_v_state2(s8, c_c2)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1155,plain,
% 0.69/0.88 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s8, c_t2)) | (~m_main_v_state2(s8, c_c2))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1154, 1153])).
% 0.69/0.88 tff(1156,plain,
% 0.69/0.88 (~m_main_v_state2(s8, c_t2)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1155, 260, 1121])).
% 0.69/0.88 tff(1157,plain,
% 0.69/0.88 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s8, c_t2) | (~node12(s8)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s8, c_t2) | (~node12(s8)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1158,plain,
% 0.69/0.88 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s8, c_t2) | (~node12(s8)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1159,plain,
% 0.69/0.88 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s8, c_t2) | (~node12(s8))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1158, 1157])).
% 0.69/0.88 tff(1160,plain,
% 0.69/0.88 (~node12(s8)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1159, 633, 1156])).
% 0.69/0.88 tff(1161,plain,
% 0.69/0.88 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s8, c_n1) | (~node11(s8)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s8, c_n1) | (~node11(s8)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1162,plain,
% 0.69/0.88 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s8, c_n1) | (~node11(s8)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1163,plain,
% 0.69/0.88 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s8, c_n1) | (~node11(s8))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1162, 1161])).
% 0.69/0.88 tff(1164,plain,
% 0.69/0.88 (~node11(s8)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1163, 238, 1060])).
% 0.69/0.88 tff(1165,plain,
% 0.69/0.88 (((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s8, c_c1) | (~node10(s8)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s8, c_c1) | (~node10(s8)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1166,plain,
% 0.69/0.88 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s8, c_c1) | (~node10(s8)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1167,plain,
% 0.69/0.88 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s8, c_c1) | (~node10(s8))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1166, 1165])).
% 0.69/0.88 tff(1168,plain,
% 0.69/0.88 (~node10(s8)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1167, 675, 1093])).
% 0.69/0.88 tff(1169,plain,
% 0.69/0.88 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s8, c_n1) | (~node9(s8)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s8, c_n1) | (~node9(s8)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1170,plain,
% 0.69/0.88 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s8, c_n1) | (~node9(s8)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1171,plain,
% 0.69/0.88 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s8, c_n1) | (~node9(s8))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1170, 1169])).
% 0.69/0.88 tff(1172,plain,
% 0.69/0.88 (~node9(s8)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1171, 686, 1060])).
% 0.69/0.88 tff(1173,plain,
% 0.69/0.88 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s8, c_n2) | (~node8(s8)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s8, c_n2) | (~node8(s8)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1174,plain,
% 0.69/0.88 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s8, c_n2) | (~node8(s8)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1175,plain,
% 0.69/0.88 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s8, c_n2) | (~node8(s8))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1174, 1173])).
% 0.69/0.88 tff(1176,plain,
% 0.69/0.88 (~node8(s8)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1175, 271, 1125])).
% 0.69/0.88 tff(1177,plain,
% 0.69/0.88 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s8, s9)) | node14(s8, s9))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s8, s9)) | node14(s8, s9))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1178,plain,
% 0.69/0.88 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s8, s9)) | node14(s8, s9))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(1179,plain,
% 0.69/0.88 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s8, s9)) | node14(s8, s9)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[1178, 1177])).
% 0.69/0.88 tff(1180,plain,
% 0.69/0.88 (node14(s8, s9)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[1179, 46, 1136])).
% 0.69/0.88 tff(1181,plain,
% 0.69/0.88 (((~![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))) | (m_main_v_state2(s9, c_n2) | node9(s8) | node8(s8) | node10(s8) | node11(s8) | node12(s8) | (~node14(s8, s9)) | (~m_main_v_state2(s8, c_c2)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s9, c_n2) | node9(s8) | node8(s8) | node10(s8) | node11(s8) | node12(s8) | (~node14(s8, s9)) | (~m_main_v_state2(s8, c_c2)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1182,plain,
% 0.69/0.88 (((~m_main_v_state2(s8, c_c2)) | node9(s8) | node8(s8) | node10(s8) | node11(s8) | node12(s8) | (~node14(s8, s9)) | m_main_v_state2(s9, c_n2)) <=> (m_main_v_state2(s9, c_n2) | node9(s8) | node8(s8) | node10(s8) | node11(s8) | node12(s8) | (~node14(s8, s9)) | (~m_main_v_state2(s8, c_c2)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(1183,plain,
% 0.69/0.88 (((~![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))) | ((~m_main_v_state2(s8, c_c2)) | node9(s8) | node8(s8) | node10(s8) | node11(s8) | node12(s8) | (~node14(s8, s9)) | m_main_v_state2(s9, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s9, c_n2) | node9(s8) | node8(s8) | node10(s8) | node11(s8) | node12(s8) | (~node14(s8, s9)) | (~m_main_v_state2(s8, c_c2))))),
% 0.69/0.88 inference(monotonicity,[status(thm)],[1182])).
% 0.69/0.88 tff(1184,plain,
% 0.69/0.88 (((~![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))) | ((~m_main_v_state2(s8, c_c2)) | node9(s8) | node8(s8) | node10(s8) | node11(s8) | node12(s8) | (~node14(s8, s9)) | m_main_v_state2(s9, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s9, c_n2) | node9(s8) | node8(s8) | node10(s8) | node11(s8) | node12(s8) | (~node14(s8, s9)) | (~m_main_v_state2(s8, c_c2)))),
% 0.69/0.89 inference(transitivity,[status(thm)],[1183, 1181])).
% 0.69/0.89 tff(1185,plain,
% 0.69/0.89 ((~![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(s8, c_c2)) | node9(s8) | node8(s8) | node10(s8) | node11(s8) | node12(s8) | (~node14(s8, s9)) | m_main_v_state2(s9, c_n2))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(1186,plain,
% 0.69/0.89 ((~![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(s9, c_n2) | node9(s8) | node8(s8) | node10(s8) | node11(s8) | node12(s8) | (~node14(s8, s9)) | (~m_main_v_state2(s8, c_c2))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[1185, 1184])).
% 0.69/0.89 tff(1187,plain,
% 0.69/0.89 (m_main_v_state2(s9, c_n2) | node9(s8) | node8(s8) | node10(s8) | node11(s8) | node12(s8) | (~m_main_v_state2(s8, c_c2))),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[1186, 726, 1180])).
% 0.69/0.89 tff(1188,plain,
% 0.69/0.89 (m_main_v_state2(s9, c_n2)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[1187, 1176, 1121, 1172, 1168, 1164, 1160])).
% 0.69/0.89 tff(1189,plain,
% 0.69/0.89 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s9, c_n2)) | (~m_main_v_state2(s9, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s9, c_n2)) | (~m_main_v_state2(s9, c_t2)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(1190,plain,
% 0.69/0.89 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s9, c_n2)) | (~m_main_v_state2(s9, c_t2)))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(1191,plain,
% 0.69/0.89 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s9, c_n2)) | (~m_main_v_state2(s9, c_t2))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[1190, 1189])).
% 0.69/0.89 tff(1192,plain,
% 0.69/0.89 (~m_main_v_state2(s9, c_t2)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[1191, 77, 1188])).
% 0.69/0.89 tff(1193,plain,
% 0.69/0.89 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s9, c_t2) | (~node15(s9)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s9, c_t2) | (~node15(s9)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(1194,plain,
% 0.69/0.89 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s9, c_t2) | (~node15(s9)))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(1195,plain,
% 0.69/0.89 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s9, c_t2) | (~node15(s9))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[1194, 1193])).
% 0.69/0.89 tff(1196,plain,
% 0.69/0.89 (~node15(s9)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[1195, 103, 1192])).
% 0.69/0.89 tff(1197,plain,
% 0.69/0.89 (succ(s9, s10) <=> succ(s9, s10)),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(1198,axiom,(succ(s9, s10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound10')).
% 0.69/0.89 tff(1199,plain,
% 0.69/0.89 (succ(s9, s10)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[1198, 1197])).
% 0.69/0.89 tff(1200,plain,
% 0.69/0.89 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s9, s10)) | trans(s9, s10))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s9, s10)) | trans(s9, s10))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(1201,plain,
% 0.69/0.89 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s9, s10)) | trans(s9, s10))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(1202,plain,
% 0.69/0.89 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s9, s10)) | trans(s9, s10)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[1201, 1200])).
% 0.69/0.89 tff(1203,plain,
% 0.69/0.89 (trans(s9, s10)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[1202, 1199, 32])).
% 0.69/0.89 tff(1204,plain,
% 0.69/0.89 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s9, s10)) | node18(s9, s10))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s9, s10)) | node18(s9, s10))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(1205,plain,
% 0.69/0.89 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s9, s10)) | node18(s9, s10))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(1206,plain,
% 0.69/0.89 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s9, s10)) | node18(s9, s10)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[1205, 1204])).
% 0.69/0.89 tff(1207,plain,
% 0.69/0.89 (node18(s9, s10)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[1206, 125, 1203])).
% 0.69/0.89 tff(1208,plain,
% 0.69/0.89 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s9) | (~node18(s9, s10)) | (~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_turn(s10, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s9) | (~node18(s9, s10)) | (~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_turn(s10, c_1))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(1209,plain,
% 0.69/0.89 (((~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | node15(s9) | (~node18(s9, s10)) | m_main_v_turn(s10, c_1)) <=> (node15(s9) | (~node18(s9, s10)) | (~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_turn(s10, c_1))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(1210,plain,
% 0.69/0.89 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | node15(s9) | (~node18(s9, s10)) | m_main_v_turn(s10, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s9) | (~node18(s9, s10)) | (~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_turn(s10, c_1)))),
% 0.69/0.89 inference(monotonicity,[status(thm)],[1209])).
% 0.69/0.89 tff(1211,plain,
% 0.69/0.89 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | node15(s9) | (~node18(s9, s10)) | m_main_v_turn(s10, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s9) | (~node18(s9, s10)) | (~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_turn(s10, c_1))),
% 0.69/0.89 inference(transitivity,[status(thm)],[1210, 1208])).
% 0.69/0.89 tff(1212,plain,
% 0.69/0.89 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | node15(s9) | (~node18(s9, s10)) | m_main_v_turn(s10, c_1))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(1213,plain,
% 0.69/0.89 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s9) | (~node18(s9, s10)) | (~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_turn(s10, c_1)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[1212, 1211])).
% 0.69/0.89 tff(1214,plain,
% 0.69/0.89 (node15(s9) | (~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_turn(s10, c_1)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[1213, 992, 1207])).
% 0.69/0.89 tff(1215,plain,
% 0.69/0.89 (m_main_v_turn(s10, c_1)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[1214, 1196, 1188, 1152])).
% 0.69/0.89 tff(1216,plain,
% 0.69/0.89 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s10, c_1)) | (~m_main_v_turn(s10, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s10, c_1)) | (~m_main_v_turn(s10, c_2)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(1217,plain,
% 0.69/0.89 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s10, c_1)) | (~m_main_v_turn(s10, c_2)))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(1218,plain,
% 0.69/0.89 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s10, c_1)) | (~m_main_v_turn(s10, c_2))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[1217, 1216])).
% 0.69/0.89 tff(1219,plain,
% 0.69/0.89 (~m_main_v_turn(s10, c_2)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[1218, 156, 1215])).
% 0.69/0.89 tff(1220,plain,
% 0.69/0.89 (((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s10, c_2) | (~node12(s10)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s10, c_2) | (~node12(s10)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(1221,plain,
% 0.69/0.89 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s10, c_2) | (~node12(s10)))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(1222,plain,
% 0.69/0.89 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s10, c_2) | (~node12(s10))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[1221, 1220])).
% 0.69/0.89 tff(1223,plain,
% 0.69/0.89 (~node12(s10)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[1222, 184, 1219])).
% 0.69/0.89 tff(1224,plain,
% 0.69/0.89 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s9, s10)) | node14(s9, s10))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s9, s10)) | node14(s9, s10))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(1225,plain,
% 0.69/0.89 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s9, s10)) | node14(s9, s10))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(1226,plain,
% 0.69/0.89 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s9, s10)) | node14(s9, s10)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[1225, 1224])).
% 0.69/0.89 tff(1227,plain,
% 0.69/0.89 (node14(s9, s10)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[1226, 46, 1203])).
% 0.69/0.89 tff(1228,plain,
% 0.69/0.89 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | (~node14(s9, s10)) | m_main_v_state2(s10, c_t2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | (~node14(s9, s10)) | m_main_v_state2(s10, c_t2))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(1229,plain,
% 0.69/0.89 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | (~node14(s9, s10)) | m_main_v_state2(s10, c_t2))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(1230,plain,
% 0.69/0.89 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | (~node14(s9, s10)) | m_main_v_state2(s10, c_t2)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[1229, 1228])).
% 0.69/0.89 tff(1231,plain,
% 0.69/0.89 ((~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_state2(s10, c_t2)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[1230, 922, 1227])).
% 0.69/0.89 tff(1232,plain,
% 0.69/0.89 (m_main_v_state2(s10, c_t2)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[1231, 1152, 1188])).
% 0.69/0.89 tff(1233,plain,
% 0.69/0.89 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s10, c_n2)) | (~m_main_v_state2(s10, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s10, c_n2)) | (~m_main_v_state2(s10, c_t2)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(1234,plain,
% 0.69/0.89 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s10, c_n2)) | (~m_main_v_state2(s10, c_t2)))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(1235,plain,
% 0.69/0.89 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s10, c_n2)) | (~m_main_v_state2(s10, c_t2))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[1234, 1233])).
% 0.69/0.89 tff(1236,plain,
% 0.69/0.89 (~m_main_v_state2(s10, c_n2)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[1235, 77, 1232])).
% 0.69/0.89 tff(1237,plain,
% 0.69/0.89 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s10, c_n2) | (~node8(s10)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s10, c_n2) | (~node8(s10)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(1238,plain,
% 0.69/0.89 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s10, c_n2) | (~node8(s10)))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(1239,plain,
% 0.69/0.89 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s10, c_n2) | (~node8(s10))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[1238, 1237])).
% 0.69/0.89 tff(1240,plain,
% 0.69/0.89 (~node8(s10)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[1239, 271, 1236])).
% 0.69/0.89 tff(1241,plain,
% 0.69/0.89 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s10, c_n2) | (~node9(s10)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s10, c_n2) | (~node9(s10)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(1242,plain,
% 0.69/0.89 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s10, c_n2) | (~node9(s10)))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(1243,plain,
% 0.69/0.89 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s10, c_n2) | (~node9(s10))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[1242, 1241])).
% 0.69/0.89 tff(1244,plain,
% 0.69/0.89 (~node9(s10)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[1243, 88, 1236])).
% 0.69/0.89 tff(1245,plain,
% 0.69/0.89 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s10, c_n2) | (~node10(s10)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s10, c_n2) | (~node10(s10)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(1246,plain,
% 0.69/0.89 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s10, c_n2) | (~node10(s10)))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(1247,plain,
% 0.69/0.89 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s10, c_n2) | (~node10(s10))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[1246, 1245])).
% 0.69/0.89 tff(1248,plain,
% 0.69/0.89 (~node10(s10)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[1247, 249, 1236])).
% 0.69/0.89 tff(1249,plain,
% 0.69/0.89 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s10, c_t2)) | (~m_main_v_state2(s10, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s10, c_t2)) | (~m_main_v_state2(s10, c_c2)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(1250,plain,
% 0.69/0.89 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s10, c_t2)) | (~m_main_v_state2(s10, c_c2)))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(1251,plain,
% 0.69/0.89 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s10, c_t2)) | (~m_main_v_state2(s10, c_c2))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[1250, 1249])).
% 0.69/0.89 tff(1252,plain,
% 0.69/0.89 (~m_main_v_state2(s10, c_c2)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[1251, 260, 1232])).
% 0.69/0.89 tff(1253,plain,
% 0.69/0.89 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s9, c_n2)) | (~m_main_v_state2(s9, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s9, c_n2)) | (~m_main_v_state2(s9, c_c2)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(1254,plain,
% 0.69/0.89 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s9, c_n2)) | (~m_main_v_state2(s9, c_c2)))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(1255,plain,
% 0.69/0.89 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s9, c_n2)) | (~m_main_v_state2(s9, c_c2))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[1254, 1253])).
% 0.69/0.89 tff(1256,plain,
% 0.69/0.89 (~m_main_v_state2(s9, c_c2)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[1255, 697, 1188])).
% 0.69/0.89 tff(1257,plain,
% 0.69/0.89 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s9, c_c2) | (~node3(s9)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s9, c_c2) | (~node3(s9)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(1258,plain,
% 0.69/0.89 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s9, c_c2) | (~node3(s9)))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(1259,plain,
% 0.69/0.89 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s9, c_c2) | (~node3(s9))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[1258, 1257])).
% 0.69/0.89 tff(1260,plain,
% 0.69/0.89 (~node3(s9)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[1259, 399, 1256])).
% 0.69/0.89 tff(1261,plain,
% 0.69/0.89 (((~![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(s8, c_n1) | (~m_main_v_state1(s9, c_n1)) | (~node6(s8, s9)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s8, c_n1) | (~m_main_v_state1(s9, c_n1)) | (~node6(s8, s9)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(1262,plain,
% 0.69/0.89 (((~node6(s8, s9)) | m_main_v_state1(s8, c_n1) | (~m_main_v_state1(s9, c_n1))) <=> (m_main_v_state1(s8, c_n1) | (~m_main_v_state1(s9, c_n1)) | (~node6(s8, s9)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(1263,plain,
% 0.69/0.89 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s8, s9)) | m_main_v_state1(s8, c_n1) | (~m_main_v_state1(s9, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s8, c_n1) | (~m_main_v_state1(s9, c_n1)) | (~node6(s8, s9))))),
% 0.69/0.89 inference(monotonicity,[status(thm)],[1262])).
% 0.69/0.89 tff(1264,plain,
% 0.69/0.89 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s8, s9)) | m_main_v_state1(s8, c_n1) | (~m_main_v_state1(s9, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s8, c_n1) | (~m_main_v_state1(s9, c_n1)) | (~node6(s8, s9)))),
% 0.69/0.89 inference(transitivity,[status(thm)],[1263, 1261])).
% 0.69/0.89 tff(1265,plain,
% 0.69/0.89 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s8, s9)) | m_main_v_state1(s8, c_n1) | (~m_main_v_state1(s9, c_n1)))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(1266,plain,
% 0.69/0.89 ((~![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(s8, c_n1) | (~m_main_v_state1(s9, c_n1)) | (~node6(s8, s9))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[1265, 1264])).
% 0.69/0.89 tff(1267,plain,
% 0.69/0.89 (~m_main_v_state1(s9, c_n1)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[1266, 835, 1060, 1145])).
% 0.69/0.89 tff(1268,plain,
% 0.69/0.89 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s9, c_n1) | (~node2(s9)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s9, c_n1) | (~node2(s9)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(1269,plain,
% 0.69/0.89 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s9, c_n1) | (~node2(s9)))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(1270,plain,
% 0.69/0.89 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s9, c_n1) | (~node2(s9))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[1269, 1268])).
% 0.69/0.89 tff(1271,plain,
% 0.69/0.89 (~node2(s9)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[1270, 787, 1267])).
% 0.69/0.89 tff(1272,plain,
% 0.69/0.89 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s9, c_t2) | (~node1(s9)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s9, c_t2) | (~node1(s9)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(1273,plain,
% 0.69/0.89 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s9, c_t2) | (~node1(s9)))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(1274,plain,
% 0.69/0.89 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s9, c_t2) | (~node1(s9))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[1273, 1272])).
% 0.69/0.89 tff(1275,plain,
% 0.69/0.89 (~node1(s9)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[1274, 195, 1192])).
% 0.69/0.89 tff(1276,plain,
% 0.69/0.89 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s9, s10)) | node7(s9, s10))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s9, s10)) | node7(s9, s10))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(1277,plain,
% 0.69/0.89 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s9, s10)) | node7(s9, s10))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(1278,plain,
% 0.69/0.89 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s9, s10)) | node7(s9, s10)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[1277, 1276])).
% 0.69/0.89 tff(1279,plain,
% 0.69/0.89 (node7(s9, s10)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[1278, 206, 1203])).
% 0.69/0.89 tff(1280,plain,
% 0.69/0.89 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_state1(s10, c_c1) | node1(s9) | node2(s9) | node3(s9) | (~node7(s9, s10)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_state1(s10, c_c1) | node1(s9) | node2(s9) | node3(s9) | (~node7(s9, s10)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(1281,plain,
% 0.69/0.89 (((~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | node1(s9) | node2(s9) | node3(s9) | (~node7(s9, s10)) | m_main_v_state1(s10, c_c1)) <=> ((~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_state1(s10, c_c1) | node1(s9) | node2(s9) | node3(s9) | (~node7(s9, s10)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(1282,plain,
% 0.69/0.89 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | node1(s9) | node2(s9) | node3(s9) | (~node7(s9, s10)) | m_main_v_state1(s10, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_state1(s10, c_c1) | node1(s9) | node2(s9) | node3(s9) | (~node7(s9, s10))))),
% 0.69/0.89 inference(monotonicity,[status(thm)],[1281])).
% 0.69/0.89 tff(1283,plain,
% 0.69/0.89 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | node1(s9) | node2(s9) | node3(s9) | (~node7(s9, s10)) | m_main_v_state1(s10, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_state1(s10, c_c1) | node1(s9) | node2(s9) | node3(s9) | (~node7(s9, s10)))),
% 0.69/0.89 inference(transitivity,[status(thm)],[1282, 1280])).
% 0.69/0.89 tff(1284,plain,
% 0.69/0.89 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | node1(s9) | node2(s9) | node3(s9) | (~node7(s9, s10)) | m_main_v_state1(s10, c_c1))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(1285,plain,
% 0.69/0.89 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_state1(s10, c_c1) | node1(s9) | node2(s9) | node3(s9) | (~node7(s9, s10))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[1284, 1283])).
% 0.69/0.89 tff(1286,plain,
% 0.69/0.89 ((~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_state1(s10, c_c1) | node1(s9) | node2(s9) | node3(s9)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[1285, 892, 1279])).
% 0.69/0.89 tff(1287,plain,
% 0.69/0.89 (m_main_v_state1(s10, c_c1)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[1286, 1275, 1188, 1152, 1271, 1260])).
% 0.69/0.89 tff(1288,plain,
% 0.69/0.89 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s10, c_n1)) | (~m_main_v_state1(s10, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s10, c_n1)) | (~m_main_v_state1(s10, c_c1)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(1289,plain,
% 0.69/0.89 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s10, c_n1)) | (~m_main_v_state1(s10, c_c1)))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(1290,plain,
% 0.69/0.89 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s10, c_n1)) | (~m_main_v_state1(s10, c_c1))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[1289, 1288])).
% 0.69/0.89 tff(1291,plain,
% 0.69/0.89 (~m_main_v_state1(s10, c_n1)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[1290, 454, 1287])).
% 0.69/0.89 tff(1292,plain,
% 0.69/0.89 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s10, c_n1) | (~node11(s10)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s10, c_n1) | (~node11(s10)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(1293,plain,
% 0.69/0.89 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s10, c_n1) | (~node11(s10)))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(1294,plain,
% 0.69/0.89 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s10, c_n1) | (~node11(s10))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[1293, 1292])).
% 0.69/0.89 tff(1295,plain,
% 0.69/0.89 (~node11(s10)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[1294, 238, 1291])).
% 0.69/0.89 tff(1296,plain,
% 0.69/0.89 (succ(s10, s11) <=> succ(s10, s11)),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(1297,axiom,(succ(s10, s11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound11')).
% 0.69/0.89 tff(1298,plain,
% 0.69/0.89 (succ(s10, s11)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[1297, 1296])).
% 0.69/0.89 tff(1299,plain,
% 0.69/0.89 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s10, s11)) | trans(s10, s11))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s10, s11)) | trans(s10, s11))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(1300,plain,
% 0.69/0.89 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s10, s11)) | trans(s10, s11))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(1301,plain,
% 0.69/0.89 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s10, s11)) | trans(s10, s11)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[1300, 1299])).
% 0.69/0.89 tff(1302,plain,
% 0.69/0.89 (trans(s10, s11)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[1301, 1298, 32])).
% 0.69/0.89 tff(1303,plain,
% 0.69/0.89 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s10, s11)) | node14(s10, s11))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s10, s11)) | node14(s10, s11))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(1304,plain,
% 0.69/0.89 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s10, s11)) | node14(s10, s11))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(1305,plain,
% 0.69/0.89 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s10, s11)) | node14(s10, s11)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[1304, 1303])).
% 0.69/0.89 tff(1306,plain,
% 0.69/0.89 (node14(s10, s11)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[1305, 46, 1302])).
% 0.69/0.89 tff(1307,plain,
% 0.69/0.89 (((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s10, c_c2) | node9(s10) | node8(s10) | node10(s10) | node11(s10) | node12(s10) | node13(s10, s11) | (~node14(s10, s11)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s10, c_c2) | node9(s10) | node8(s10) | node10(s10) | node11(s10) | node12(s10) | node13(s10, s11) | (~node14(s10, s11)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1308,plain,
% 0.69/0.90 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s10, c_c2) | node9(s10) | node8(s10) | node10(s10) | node11(s10) | node12(s10) | node13(s10, s11) | (~node14(s10, s11)))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(1309,plain,
% 0.69/0.90 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s10, c_c2) | node9(s10) | node8(s10) | node10(s10) | node11(s10) | node12(s10) | node13(s10, s11) | (~node14(s10, s11))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1308, 1307])).
% 0.69/0.90 tff(1310,plain,
% 0.69/0.90 (m_main_v_state2(s10, c_c2) | node9(s10) | node8(s10) | node10(s10) | node11(s10) | node12(s10) | node13(s10, s11)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1309, 296, 1306])).
% 0.69/0.90 tff(1311,plain,
% 0.69/0.90 (node13(s10, s11)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1310, 1295, 1252, 1248, 1244, 1240, 1223])).
% 0.69/0.90 tff(1312,plain,
% 0.69/0.90 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s10, c_n2) | (~m_main_v_state2(s11, c_n2)) | (~node13(s10, s11)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s10, c_n2) | (~m_main_v_state2(s11, c_n2)) | (~node13(s10, s11)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1313,plain,
% 0.69/0.90 (((~node13(s10, s11)) | m_main_v_state2(s10, c_n2) | (~m_main_v_state2(s11, c_n2))) <=> (m_main_v_state2(s10, c_n2) | (~m_main_v_state2(s11, c_n2)) | (~node13(s10, s11)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1314,plain,
% 0.69/0.90 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s10, s11)) | m_main_v_state2(s10, c_n2) | (~m_main_v_state2(s11, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s10, c_n2) | (~m_main_v_state2(s11, c_n2)) | (~node13(s10, s11))))),
% 0.69/0.90 inference(monotonicity,[status(thm)],[1313])).
% 0.69/0.90 tff(1315,plain,
% 0.69/0.90 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s10, s11)) | m_main_v_state2(s10, c_n2) | (~m_main_v_state2(s11, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s10, c_n2) | (~m_main_v_state2(s11, c_n2)) | (~node13(s10, s11)))),
% 0.69/0.90 inference(transitivity,[status(thm)],[1314, 1312])).
% 0.69/0.90 tff(1316,plain,
% 0.69/0.90 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s10, s11)) | m_main_v_state2(s10, c_n2) | (~m_main_v_state2(s11, c_n2)))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(1317,plain,
% 0.69/0.90 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s10, c_n2) | (~m_main_v_state2(s11, c_n2)) | (~node13(s10, s11))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1316, 1315])).
% 0.69/0.90 tff(1318,plain,
% 0.69/0.90 (~m_main_v_state2(s11, c_n2)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1317, 311, 1236, 1311])).
% 0.69/0.90 tff(1319,plain,
% 0.69/0.90 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s11, c_n2) | (~node9(s11)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s11, c_n2) | (~node9(s11)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1320,plain,
% 0.69/0.90 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s11, c_n2) | (~node9(s11)))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(1321,plain,
% 0.69/0.90 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s11, c_n2) | (~node9(s11))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1320, 1319])).
% 0.69/0.90 tff(1322,plain,
% 0.69/0.90 (~node9(s11)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1321, 88, 1318])).
% 0.69/0.90 tff(1323,plain,
% 0.69/0.90 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s11, c_n2) | (~node10(s11)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s11, c_n2) | (~node10(s11)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1324,plain,
% 0.69/0.90 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s11, c_n2) | (~node10(s11)))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(1325,plain,
% 0.69/0.90 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s11, c_n2) | (~node10(s11))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1324, 1323])).
% 0.69/0.90 tff(1326,plain,
% 0.69/0.90 (~node10(s11)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1325, 249, 1318])).
% 0.69/0.90 tff(1327,plain,
% 0.69/0.90 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s10, c_t2)) | m_main_v_state2(s11, c_t2) | (~node13(s10, s11)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s10, c_t2)) | m_main_v_state2(s11, c_t2) | (~node13(s10, s11)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1328,plain,
% 0.69/0.90 (((~node13(s10, s11)) | (~m_main_v_state2(s10, c_t2)) | m_main_v_state2(s11, c_t2)) <=> ((~m_main_v_state2(s10, c_t2)) | m_main_v_state2(s11, c_t2) | (~node13(s10, s11)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1329,plain,
% 0.69/0.90 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s10, s11)) | (~m_main_v_state2(s10, c_t2)) | m_main_v_state2(s11, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s10, c_t2)) | m_main_v_state2(s11, c_t2) | (~node13(s10, s11))))),
% 0.69/0.90 inference(monotonicity,[status(thm)],[1328])).
% 0.69/0.90 tff(1330,plain,
% 0.69/0.90 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s10, s11)) | (~m_main_v_state2(s10, c_t2)) | m_main_v_state2(s11, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s10, c_t2)) | m_main_v_state2(s11, c_t2) | (~node13(s10, s11)))),
% 0.69/0.90 inference(transitivity,[status(thm)],[1329, 1327])).
% 0.69/0.90 tff(1331,plain,
% 0.69/0.90 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s10, s11)) | (~m_main_v_state2(s10, c_t2)) | m_main_v_state2(s11, c_t2))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(1332,plain,
% 0.69/0.90 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s10, c_t2)) | m_main_v_state2(s11, c_t2) | (~node13(s10, s11))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1331, 1330])).
% 0.69/0.90 tff(1333,plain,
% 0.69/0.90 (m_main_v_state2(s11, c_t2)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1332, 518, 1232, 1311])).
% 0.69/0.90 tff(1334,plain,
% 0.69/0.90 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s10, c_t1)) | (~m_main_v_state1(s10, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s10, c_t1)) | (~m_main_v_state1(s10, c_c1)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1335,plain,
% 0.69/0.90 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s10, c_t1)) | (~m_main_v_state1(s10, c_c1)))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(1336,plain,
% 0.69/0.90 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s10, c_t1)) | (~m_main_v_state1(s10, c_c1))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1335, 1334])).
% 0.69/0.90 tff(1337,plain,
% 0.69/0.90 (~m_main_v_state1(s10, c_t1)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1336, 539, 1287])).
% 0.69/0.90 tff(1338,plain,
% 0.69/0.90 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s10, c_t1) | (~node5(s10)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s10, c_t1) | (~node5(s10)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1339,plain,
% 0.69/0.90 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s10, c_t1) | (~node5(s10)))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(1340,plain,
% 0.69/0.90 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s10, c_t1) | (~node5(s10))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1339, 1338])).
% 0.69/0.90 tff(1341,plain,
% 0.69/0.90 (~node5(s10)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1340, 550, 1337])).
% 0.69/0.90 tff(1342,plain,
% 0.69/0.90 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s10, c_n2) | (~node4(s10)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s10, c_n2) | (~node4(s10)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1343,plain,
% 0.69/0.90 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s10, c_n2) | (~node4(s10)))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(1344,plain,
% 0.69/0.90 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s10, c_n2) | (~node4(s10))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1343, 1342])).
% 0.69/0.90 tff(1345,plain,
% 0.69/0.90 (~node4(s10)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1344, 388, 1236])).
% 0.69/0.90 tff(1346,plain,
% 0.69/0.90 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s10, c_c2) | (~node3(s10)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s10, c_c2) | (~node3(s10)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1347,plain,
% 0.69/0.90 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s10, c_c2) | (~node3(s10)))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(1348,plain,
% 0.69/0.90 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s10, c_c2) | (~node3(s10))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1347, 1346])).
% 0.69/0.90 tff(1349,plain,
% 0.69/0.90 (~node3(s10)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1348, 399, 1252])).
% 0.69/0.90 tff(1350,plain,
% 0.69/0.90 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s10, c_n2) | (~node2(s10)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s10, c_n2) | (~node2(s10)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1351,plain,
% 0.69/0.90 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s10, c_n2) | (~node2(s10)))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(1352,plain,
% 0.69/0.90 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s10, c_n2) | (~node2(s10))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1351, 1350])).
% 0.69/0.90 tff(1353,plain,
% 0.69/0.90 (~node2(s10)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1352, 410, 1236])).
% 0.69/0.90 tff(1354,plain,
% 0.69/0.90 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s10, c_n1) | (~node1(s10)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s10, c_n1) | (~node1(s10)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1355,plain,
% 0.69/0.90 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s10, c_n1) | (~node1(s10)))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(1356,plain,
% 0.69/0.90 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s10, c_n1) | (~node1(s10))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1355, 1354])).
% 0.69/0.90 tff(1357,plain,
% 0.69/0.90 (~node1(s10)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1356, 421, 1291])).
% 0.69/0.90 tff(1358,plain,
% 0.69/0.90 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s10, s11)) | node7(s10, s11))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s10, s11)) | node7(s10, s11))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1359,plain,
% 0.69/0.90 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s10, s11)) | node7(s10, s11))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(1360,plain,
% 0.69/0.90 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s10, s11)) | node7(s10, s11)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1359, 1358])).
% 0.69/0.90 tff(1361,plain,
% 0.69/0.90 (node7(s10, s11)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1360, 206, 1302])).
% 0.69/0.90 tff(1362,plain,
% 0.69/0.90 (((~![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(s11, c_n1) | (~m_main_v_state1(s10, c_c1)) | node1(s10) | node2(s10) | node3(s10) | node4(s10) | node5(s10) | (~node7(s10, s11)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s11, c_n1) | (~m_main_v_state1(s10, c_c1)) | node1(s10) | node2(s10) | node3(s10) | node4(s10) | node5(s10) | (~node7(s10, s11)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1363,plain,
% 0.69/0.90 (((~m_main_v_state1(s10, c_c1)) | node1(s10) | node2(s10) | node3(s10) | node4(s10) | node5(s10) | (~node7(s10, s11)) | m_main_v_state1(s11, c_n1)) <=> (m_main_v_state1(s11, c_n1) | (~m_main_v_state1(s10, c_c1)) | node1(s10) | node2(s10) | node3(s10) | node4(s10) | node5(s10) | (~node7(s10, s11)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1364,plain,
% 0.69/0.90 (((~![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(s10, c_c1)) | node1(s10) | node2(s10) | node3(s10) | node4(s10) | node5(s10) | (~node7(s10, s11)) | m_main_v_state1(s11, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s11, c_n1) | (~m_main_v_state1(s10, c_c1)) | node1(s10) | node2(s10) | node3(s10) | node4(s10) | node5(s10) | (~node7(s10, s11))))),
% 0.69/0.90 inference(monotonicity,[status(thm)],[1363])).
% 0.69/0.90 tff(1365,plain,
% 0.69/0.90 (((~![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(s10, c_c1)) | node1(s10) | node2(s10) | node3(s10) | node4(s10) | node5(s10) | (~node7(s10, s11)) | m_main_v_state1(s11, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s11, c_n1) | (~m_main_v_state1(s10, c_c1)) | node1(s10) | node2(s10) | node3(s10) | node4(s10) | node5(s10) | (~node7(s10, s11)))),
% 0.69/0.90 inference(transitivity,[status(thm)],[1364, 1362])).
% 0.69/0.90 tff(1366,plain,
% 0.69/0.90 ((~![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(s10, c_c1)) | node1(s10) | node2(s10) | node3(s10) | node4(s10) | node5(s10) | (~node7(s10, s11)) | m_main_v_state1(s11, c_n1))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(1367,plain,
% 0.69/0.90 ((~![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(s11, c_n1) | (~m_main_v_state1(s10, c_c1)) | node1(s10) | node2(s10) | node3(s10) | node4(s10) | node5(s10) | (~node7(s10, s11))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1366, 1365])).
% 0.69/0.90 tff(1368,plain,
% 0.69/0.90 (m_main_v_state1(s11, c_n1) | (~m_main_v_state1(s10, c_c1)) | node1(s10) | node2(s10) | node3(s10) | node4(s10) | node5(s10)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1367, 584, 1361])).
% 0.69/0.90 tff(1369,plain,
% 0.69/0.90 (m_main_v_state1(s11, c_n1)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1368, 1357, 1287, 1353, 1349, 1345, 1341])).
% 0.69/0.90 tff(1370,plain,
% 0.69/0.90 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s11, c_n2) | (~node8(s11)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s11, c_n2) | (~node8(s11)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1371,plain,
% 0.69/0.90 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s11, c_n2) | (~node8(s11)))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(1372,plain,
% 0.69/0.90 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s11, c_n2) | (~node8(s11))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1371, 1370])).
% 0.69/0.90 tff(1373,plain,
% 0.69/0.90 (~node8(s11)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1372, 271, 1318])).
% 0.69/0.90 tff(1374,plain,
% 0.69/0.90 (succ(s11, s12) <=> succ(s11, s12)),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1375,axiom,(succ(s11, s12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound12')).
% 0.69/0.90 tff(1376,plain,
% 0.69/0.90 (succ(s11, s12)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1375, 1374])).
% 0.69/0.90 tff(1377,plain,
% 0.69/0.90 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s11, s12)) | trans(s11, s12))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s11, s12)) | trans(s11, s12))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1378,plain,
% 0.69/0.90 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s11, s12)) | trans(s11, s12))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(1379,plain,
% 0.69/0.90 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s11, s12)) | trans(s11, s12)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1378, 1377])).
% 0.69/0.90 tff(1380,plain,
% 0.69/0.90 (trans(s11, s12)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1379, 1376, 32])).
% 0.69/0.90 tff(1381,plain,
% 0.69/0.90 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s11, s12)) | node14(s11, s12))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s11, s12)) | node14(s11, s12))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1382,plain,
% 0.69/0.90 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s11, s12)) | node14(s11, s12))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(1383,plain,
% 0.69/0.90 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s11, s12)) | node14(s11, s12)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1382, 1381])).
% 0.69/0.90 tff(1384,plain,
% 0.69/0.90 (node14(s11, s12)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1383, 46, 1380])).
% 0.69/0.90 tff(1385,plain,
% 0.69/0.90 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | node9(s11) | node8(s11) | node10(s11) | (~node14(s11, s12)) | m_main_v_state2(s12, c_c2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | node9(s11) | node8(s11) | node10(s11) | (~node14(s11, s12)) | m_main_v_state2(s12, c_c2))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1386,plain,
% 0.69/0.90 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | node9(s11) | node8(s11) | node10(s11) | (~node14(s11, s12)) | m_main_v_state2(s12, c_c2))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(1387,plain,
% 0.69/0.90 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | node9(s11) | node8(s11) | node10(s11) | (~node14(s11, s12)) | m_main_v_state2(s12, c_c2)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1386, 1385])).
% 0.69/0.90 tff(1388,plain,
% 0.69/0.90 ((~m_main_v_state1(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | node9(s11) | node8(s11) | node10(s11) | m_main_v_state2(s12, c_c2)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1387, 617, 1384])).
% 0.69/0.90 tff(1389,plain,
% 0.69/0.90 (m_main_v_state2(s12, c_c2)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1388, 1373, 1369, 1333, 1326, 1322])).
% 0.69/0.90 tff(1390,plain,
% 0.69/0.90 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s12, c_t2)) | (~m_main_v_state2(s12, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s12, c_t2)) | (~m_main_v_state2(s12, c_c2)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1391,plain,
% 0.69/0.90 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s12, c_t2)) | (~m_main_v_state2(s12, c_c2)))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(1392,plain,
% 0.69/0.90 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s12, c_t2)) | (~m_main_v_state2(s12, c_c2))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1391, 1390])).
% 0.69/0.90 tff(1393,plain,
% 0.69/0.90 (~m_main_v_state2(s12, c_t2)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1392, 260, 1389])).
% 0.69/0.90 tff(1394,plain,
% 0.69/0.90 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s12, c_t2) | (~node12(s12)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s12, c_t2) | (~node12(s12)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1395,plain,
% 0.69/0.90 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s12, c_t2) | (~node12(s12)))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(1396,plain,
% 0.69/0.90 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s12, c_t2) | (~node12(s12))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1395, 1394])).
% 0.69/0.90 tff(1397,plain,
% 0.69/0.90 (~node12(s12)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1396, 633, 1393])).
% 0.69/0.90 tff(1398,plain,
% 0.69/0.90 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s11, s12)) | node7(s11, s12))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s11, s12)) | node7(s11, s12))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1399,plain,
% 0.69/0.90 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s11, s12)) | node7(s11, s12))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(1400,plain,
% 0.69/0.90 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s11, s12)) | node7(s11, s12)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1399, 1398])).
% 0.69/0.90 tff(1401,plain,
% 0.69/0.90 (node7(s11, s12)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1400, 206, 1380])).
% 0.69/0.90 tff(1402,plain,
% 0.69/0.90 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | (~node7(s11, s12)) | m_main_v_state1(s12, c_t1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | (~node7(s11, s12)) | m_main_v_state1(s12, c_t1))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1403,plain,
% 0.69/0.90 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | (~node7(s11, s12)) | m_main_v_state1(s12, c_t1))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(1404,plain,
% 0.69/0.90 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | (~node7(s11, s12)) | m_main_v_state1(s12, c_t1)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1403, 1402])).
% 0.69/0.90 tff(1405,plain,
% 0.69/0.90 ((~m_main_v_state1(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | m_main_v_state1(s12, c_t1)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1404, 651, 1401])).
% 0.69/0.90 tff(1406,plain,
% 0.69/0.90 (m_main_v_state1(s12, c_t1)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1405, 1333, 1369])).
% 0.69/0.90 tff(1407,plain,
% 0.69/0.90 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s12, c_n1)) | (~m_main_v_state1(s12, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s12, c_n1)) | (~m_main_v_state1(s12, c_t1)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1408,plain,
% 0.69/0.90 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s12, c_n1)) | (~m_main_v_state1(s12, c_t1)))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(1409,plain,
% 0.69/0.90 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s12, c_n1)) | (~m_main_v_state1(s12, c_t1))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1408, 1407])).
% 0.69/0.90 tff(1410,plain,
% 0.69/0.90 (~m_main_v_state1(s12, c_n1)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1409, 10, 1406])).
% 0.69/0.90 tff(1411,plain,
% 0.69/0.90 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s12, c_n1) | (~node11(s12)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s12, c_n1) | (~node11(s12)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1412,plain,
% 0.69/0.90 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s12, c_n1) | (~node11(s12)))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(1413,plain,
% 0.69/0.90 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s12, c_n1) | (~node11(s12))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1412, 1411])).
% 0.69/0.90 tff(1414,plain,
% 0.69/0.90 (~node11(s12)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1413, 238, 1410])).
% 0.69/0.90 tff(1415,plain,
% 0.69/0.90 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s12, c_t1)) | (~m_main_v_state1(s12, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s12, c_t1)) | (~m_main_v_state1(s12, c_c1)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1416,plain,
% 0.69/0.90 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s12, c_t1)) | (~m_main_v_state1(s12, c_c1)))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(1417,plain,
% 0.69/0.90 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s12, c_t1)) | (~m_main_v_state1(s12, c_c1))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1416, 1415])).
% 0.69/0.90 tff(1418,plain,
% 0.69/0.90 (~m_main_v_state1(s12, c_c1)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1417, 539, 1406])).
% 0.69/0.90 tff(1419,plain,
% 0.69/0.90 (((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s12, c_c1) | (~node10(s12)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s12, c_c1) | (~node10(s12)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1420,plain,
% 0.69/0.90 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s12, c_c1) | (~node10(s12)))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(1421,plain,
% 0.69/0.90 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s12, c_c1) | (~node10(s12))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1420, 1419])).
% 0.69/0.90 tff(1422,plain,
% 0.69/0.90 (~node10(s12)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1421, 675, 1418])).
% 0.69/0.90 tff(1423,plain,
% 0.69/0.90 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s12, c_n1) | (~node9(s12)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s12, c_n1) | (~node9(s12)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1424,plain,
% 0.69/0.90 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s12, c_n1) | (~node9(s12)))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(1425,plain,
% 0.69/0.90 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s12, c_n1) | (~node9(s12))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1424, 1423])).
% 0.69/0.90 tff(1426,plain,
% 0.69/0.90 (~node9(s12)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1425, 686, 1410])).
% 0.69/0.90 tff(1427,plain,
% 0.69/0.90 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s12, c_n2)) | (~m_main_v_state2(s12, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s12, c_n2)) | (~m_main_v_state2(s12, c_c2)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1428,plain,
% 0.69/0.90 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s12, c_n2)) | (~m_main_v_state2(s12, c_c2)))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(1429,plain,
% 0.69/0.90 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s12, c_n2)) | (~m_main_v_state2(s12, c_c2))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1428, 1427])).
% 0.69/0.90 tff(1430,plain,
% 0.69/0.90 (~m_main_v_state2(s12, c_n2)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1429, 697, 1389])).
% 0.69/0.90 tff(1431,plain,
% 0.69/0.90 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s12, c_n2) | (~node8(s12)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s12, c_n2) | (~node8(s12)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1432,plain,
% 0.69/0.90 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s12, c_n2) | (~node8(s12)))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(1433,plain,
% 0.69/0.90 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s12, c_n2) | (~node8(s12))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1432, 1431])).
% 0.69/0.90 tff(1434,plain,
% 0.69/0.90 (~node8(s12)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1433, 271, 1430])).
% 0.69/0.90 tff(1435,plain,
% 0.69/0.90 (succ(s12, s13) <=> succ(s12, s13)),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1436,axiom,(succ(s12, s13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound13')).
% 0.69/0.90 tff(1437,plain,
% 0.69/0.90 (succ(s12, s13)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1436, 1435])).
% 0.69/0.90 tff(1438,plain,
% 0.69/0.90 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s12, s13)) | trans(s12, s13))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s12, s13)) | trans(s12, s13))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1439,plain,
% 0.69/0.90 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s12, s13)) | trans(s12, s13))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(1440,plain,
% 0.69/0.90 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s12, s13)) | trans(s12, s13)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1439, 1438])).
% 0.69/0.90 tff(1441,plain,
% 0.69/0.90 (trans(s12, s13)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1440, 1437, 32])).
% 0.69/0.90 tff(1442,plain,
% 0.69/0.90 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s12, s13)) | node14(s12, s13))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s12, s13)) | node14(s12, s13))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1443,plain,
% 0.69/0.90 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s12, s13)) | node14(s12, s13))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(1444,plain,
% 0.69/0.90 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s12, s13)) | node14(s12, s13)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[1443, 1442])).
% 0.69/0.90 tff(1445,plain,
% 0.69/0.90 (node14(s12, s13)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[1444, 46, 1441])).
% 0.69/0.90 tff(1446,plain,
% 0.69/0.90 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s13, c_n2) | node9(s12) | node8(s12) | node10(s12) | node11(s12) | node12(s12) | (~node14(s12, s13)) | (~m_main_v_state2(s12, c_c2)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s13, c_n2) | node9(s12) | node8(s12) | node10(s12) | node11(s12) | node12(s12) | (~node14(s12, s13)) | (~m_main_v_state2(s12, c_c2)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1447,plain,
% 0.69/0.90 (((~m_main_v_state2(s12, c_c2)) | node9(s12) | node8(s12) | node10(s12) | node11(s12) | node12(s12) | (~node14(s12, s13)) | m_main_v_state2(s13, c_n2)) <=> (m_main_v_state2(s13, c_n2) | node9(s12) | node8(s12) | node10(s12) | node11(s12) | node12(s12) | (~node14(s12, s13)) | (~m_main_v_state2(s12, c_c2)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(1448,plain,
% 0.69/0.90 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s12, c_c2)) | node9(s12) | node8(s12) | node10(s12) | node11(s12) | node12(s12) | (~node14(s12, s13)) | m_main_v_state2(s13, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s13, c_n2) | node9(s12) | node8(s12) | node10(s12) | node11(s12) | node12(s12) | (~node14(s12, s13)) | (~m_main_v_state2(s12, c_c2))))),
% 0.69/0.91 inference(monotonicity,[status(thm)],[1447])).
% 0.69/0.91 tff(1449,plain,
% 0.69/0.91 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s12, c_c2)) | node9(s12) | node8(s12) | node10(s12) | node11(s12) | node12(s12) | (~node14(s12, s13)) | m_main_v_state2(s13, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s13, c_n2) | node9(s12) | node8(s12) | node10(s12) | node11(s12) | node12(s12) | (~node14(s12, s13)) | (~m_main_v_state2(s12, c_c2)))),
% 0.69/0.91 inference(transitivity,[status(thm)],[1448, 1446])).
% 0.69/0.91 tff(1450,plain,
% 0.69/0.91 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s12, c_c2)) | node9(s12) | node8(s12) | node10(s12) | node11(s12) | node12(s12) | (~node14(s12, s13)) | m_main_v_state2(s13, c_n2))),
% 0.69/0.91 inference(quant_inst,[status(thm)],[])).
% 0.69/0.91 tff(1451,plain,
% 0.69/0.91 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s13, c_n2) | node9(s12) | node8(s12) | node10(s12) | node11(s12) | node12(s12) | (~node14(s12, s13)) | (~m_main_v_state2(s12, c_c2))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[1450, 1449])).
% 0.69/0.91 tff(1452,plain,
% 0.69/0.91 (m_main_v_state2(s13, c_n2) | node9(s12) | node8(s12) | node10(s12) | node11(s12) | node12(s12) | (~m_main_v_state2(s12, c_c2))),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[1451, 726, 1445])).
% 0.69/0.91 tff(1453,plain,
% 0.69/0.91 (m_main_v_state2(s13, c_n2)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[1452, 1434, 1389, 1426, 1422, 1414, 1397])).
% 0.69/0.91 tff(1454,plain,
% 0.69/0.91 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s13, c_n2)) | (~m_main_v_state2(s13, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s13, c_n2)) | (~m_main_v_state2(s13, c_c2)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(1455,plain,
% 0.69/0.91 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s13, c_n2)) | (~m_main_v_state2(s13, c_c2)))),
% 0.69/0.91 inference(quant_inst,[status(thm)],[])).
% 0.69/0.91 tff(1456,plain,
% 0.69/0.91 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s13, c_n2)) | (~m_main_v_state2(s13, c_c2))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[1455, 1454])).
% 0.69/0.91 tff(1457,plain,
% 0.69/0.91 (~m_main_v_state2(s13, c_c2)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[1456, 697, 1453])).
% 0.69/0.91 tff(1458,plain,
% 0.69/0.91 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s13, c_c2) | (~node3(s13)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s13, c_c2) | (~node3(s13)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(1459,plain,
% 0.69/0.91 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s13, c_c2) | (~node3(s13)))),
% 0.69/0.91 inference(quant_inst,[status(thm)],[])).
% 0.69/0.91 tff(1460,plain,
% 0.69/0.91 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s13, c_c2) | (~node3(s13))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[1459, 1458])).
% 0.69/0.91 tff(1461,plain,
% 0.69/0.91 (~node3(s13)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[1460, 399, 1457])).
% 0.69/0.91 tff(1462,plain,
% 0.69/0.91 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s12, c_n1) | (~node1(s12)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s12, c_n1) | (~node1(s12)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(1463,plain,
% 0.69/0.91 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s12, c_n1) | (~node1(s12)))),
% 0.69/0.91 inference(quant_inst,[status(thm)],[])).
% 0.69/0.91 tff(1464,plain,
% 0.69/0.91 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s12, c_n1) | (~node1(s12))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[1463, 1462])).
% 0.69/0.91 tff(1465,plain,
% 0.69/0.91 (~node1(s12)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[1464, 421, 1410])).
% 0.69/0.91 tff(1466,plain,
% 0.69/0.91 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s11, s12)) | node18(s11, s12))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s11, s12)) | node18(s11, s12))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(1467,plain,
% 0.69/0.91 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s11, s12)) | node18(s11, s12))),
% 0.69/0.91 inference(quant_inst,[status(thm)],[])).
% 0.69/0.91 tff(1468,plain,
% 0.69/0.91 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s11, s12)) | node18(s11, s12)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[1467, 1466])).
% 0.69/0.91 tff(1469,plain,
% 0.69/0.91 (node18(s11, s12)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[1468, 125, 1380])).
% 0.69/0.91 tff(1470,plain,
% 0.69/0.91 (((~![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(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | (~node18(s11, s12)) | m_main_v_turn(s12, c_2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | (~node18(s11, s12)) | m_main_v_turn(s12, c_2))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(1471,plain,
% 0.69/0.91 ((~![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(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | (~node18(s11, s12)) | m_main_v_turn(s12, c_2))),
% 0.69/0.91 inference(quant_inst,[status(thm)],[])).
% 0.69/0.91 tff(1472,plain,
% 0.69/0.91 ((~![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(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | (~node18(s11, s12)) | m_main_v_turn(s12, c_2)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[1471, 1470])).
% 0.69/0.91 tff(1473,plain,
% 0.69/0.91 ((~m_main_v_state1(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | m_main_v_turn(s12, c_2)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[1472, 760, 1469])).
% 0.69/0.91 tff(1474,plain,
% 0.69/0.91 (m_main_v_turn(s12, c_2)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[1473, 1333, 1369])).
% 0.69/0.91 tff(1475,plain,
% 0.69/0.91 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s12, c_1)) | (~m_main_v_turn(s12, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s12, c_1)) | (~m_main_v_turn(s12, c_2)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(1476,plain,
% 0.69/0.91 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s12, c_1)) | (~m_main_v_turn(s12, c_2)))),
% 0.69/0.91 inference(quant_inst,[status(thm)],[])).
% 0.69/0.91 tff(1477,plain,
% 0.69/0.91 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s12, c_1)) | (~m_main_v_turn(s12, c_2))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[1476, 1475])).
% 0.69/0.91 tff(1478,plain,
% 0.69/0.91 (~m_main_v_turn(s12, c_1)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[1477, 156, 1474])).
% 0.69/0.91 tff(1479,plain,
% 0.69/0.91 (((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s12, c_1) | (~node5(s12)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s12, c_1) | (~node5(s12)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(1480,plain,
% 0.69/0.91 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s12, c_1) | (~node5(s12)))),
% 0.69/0.91 inference(quant_inst,[status(thm)],[])).
% 0.69/0.91 tff(1481,plain,
% 0.69/0.91 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s12, c_1) | (~node5(s12))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[1480, 1479])).
% 0.69/0.91 tff(1482,plain,
% 0.69/0.91 (~node5(s12)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[1481, 776, 1478])).
% 0.69/0.91 tff(1483,plain,
% 0.69/0.91 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s12, c_n1) | (~node2(s12)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s12, c_n1) | (~node2(s12)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(1484,plain,
% 0.69/0.91 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s12, c_n1) | (~node2(s12)))),
% 0.69/0.91 inference(quant_inst,[status(thm)],[])).
% 0.69/0.91 tff(1485,plain,
% 0.69/0.91 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s12, c_n1) | (~node2(s12))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[1484, 1483])).
% 0.69/0.91 tff(1486,plain,
% 0.69/0.91 (~node2(s12)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[1485, 787, 1410])).
% 0.69/0.91 tff(1487,plain,
% 0.69/0.91 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s12, c_n1) | (~node3(s12)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s12, c_n1) | (~node3(s12)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(1488,plain,
% 0.69/0.91 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s12, c_n1) | (~node3(s12)))),
% 0.69/0.91 inference(quant_inst,[status(thm)],[])).
% 0.69/0.91 tff(1489,plain,
% 0.69/0.91 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s12, c_n1) | (~node3(s12))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[1488, 1487])).
% 0.69/0.91 tff(1490,plain,
% 0.69/0.91 (~node3(s12)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[1489, 798, 1410])).
% 0.69/0.91 tff(1491,plain,
% 0.69/0.91 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s12, c_n2) | (~node4(s12)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s12, c_n2) | (~node4(s12)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(1492,plain,
% 0.69/0.91 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s12, c_n2) | (~node4(s12)))),
% 0.69/0.91 inference(quant_inst,[status(thm)],[])).
% 0.69/0.91 tff(1493,plain,
% 0.69/0.91 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s12, c_n2) | (~node4(s12))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[1492, 1491])).
% 0.69/0.91 tff(1494,plain,
% 0.69/0.91 (~node4(s12)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[1493, 388, 1430])).
% 0.69/0.91 tff(1495,plain,
% 0.69/0.91 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s12, s13)) | node7(s12, s13))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s12, s13)) | node7(s12, s13))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(1496,plain,
% 0.69/0.91 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s12, s13)) | node7(s12, s13))),
% 0.69/0.91 inference(quant_inst,[status(thm)],[])).
% 0.69/0.91 tff(1497,plain,
% 0.69/0.91 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s12, s13)) | node7(s12, s13)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[1496, 1495])).
% 0.69/0.91 tff(1498,plain,
% 0.69/0.91 (node7(s12, s13)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[1497, 206, 1441])).
% 0.69/0.91 tff(1499,plain,
% 0.69/0.91 (((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s12, c_c1) | node1(s12) | node2(s12) | node3(s12) | node4(s12) | node5(s12) | node6(s12, s13) | (~node7(s12, s13)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s12, c_c1) | node1(s12) | node2(s12) | node3(s12) | node4(s12) | node5(s12) | node6(s12, s13) | (~node7(s12, s13)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(1500,plain,
% 0.69/0.91 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s12, c_c1) | node1(s12) | node2(s12) | node3(s12) | node4(s12) | node5(s12) | node6(s12, s13) | (~node7(s12, s13)))),
% 0.69/0.91 inference(quant_inst,[status(thm)],[])).
% 0.69/0.91 tff(1501,plain,
% 0.69/0.91 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s12, c_c1) | node1(s12) | node2(s12) | node3(s12) | node4(s12) | node5(s12) | node6(s12, s13) | (~node7(s12, s13))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[1500, 1499])).
% 0.69/0.91 tff(1502,plain,
% 0.69/0.91 (m_main_v_state1(s12, c_c1) | node1(s12) | node2(s12) | node3(s12) | node4(s12) | node5(s12) | node6(s12, s13)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[1501, 820, 1498])).
% 0.69/0.91 tff(1503,plain,
% 0.69/0.91 (node6(s12, s13)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[1502, 1494, 1418, 1490, 1486, 1482, 1465])).
% 0.69/0.91 tff(1504,plain,
% 0.69/0.91 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s12, c_n1) | (~m_main_v_state1(s13, c_n1)) | (~node6(s12, s13)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s12, c_n1) | (~m_main_v_state1(s13, c_n1)) | (~node6(s12, s13)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(1505,plain,
% 0.69/0.91 (((~node6(s12, s13)) | m_main_v_state1(s12, c_n1) | (~m_main_v_state1(s13, c_n1))) <=> (m_main_v_state1(s12, c_n1) | (~m_main_v_state1(s13, c_n1)) | (~node6(s12, s13)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(1506,plain,
% 0.69/0.91 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s12, s13)) | m_main_v_state1(s12, c_n1) | (~m_main_v_state1(s13, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s12, c_n1) | (~m_main_v_state1(s13, c_n1)) | (~node6(s12, s13))))),
% 0.69/0.91 inference(monotonicity,[status(thm)],[1505])).
% 0.69/0.91 tff(1507,plain,
% 0.69/0.91 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s12, s13)) | m_main_v_state1(s12, c_n1) | (~m_main_v_state1(s13, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s12, c_n1) | (~m_main_v_state1(s13, c_n1)) | (~node6(s12, s13)))),
% 0.69/0.91 inference(transitivity,[status(thm)],[1506, 1504])).
% 0.69/0.91 tff(1508,plain,
% 0.69/0.91 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s12, s13)) | m_main_v_state1(s12, c_n1) | (~m_main_v_state1(s13, c_n1)))),
% 0.69/0.91 inference(quant_inst,[status(thm)],[])).
% 0.69/0.91 tff(1509,plain,
% 0.69/0.91 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s12, c_n1) | (~m_main_v_state1(s13, c_n1)) | (~node6(s12, s13))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[1508, 1507])).
% 0.69/0.91 tff(1510,plain,
% 0.69/0.91 (~m_main_v_state1(s13, c_n1)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[1509, 835, 1410, 1503])).
% 0.69/0.91 tff(1511,plain,
% 0.69/0.91 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s13, c_n1) | (~node2(s13)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s13, c_n1) | (~node2(s13)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(1512,plain,
% 0.69/0.91 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s13, c_n1) | (~node2(s13)))),
% 0.69/0.91 inference(quant_inst,[status(thm)],[])).
% 0.69/0.91 tff(1513,plain,
% 0.69/0.91 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s13, c_n1) | (~node2(s13))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[1512, 1511])).
% 0.69/0.91 tff(1514,plain,
% 0.69/0.91 (~node2(s13)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[1513, 787, 1510])).
% 0.69/0.91 tff(1515,plain,
% 0.69/0.91 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s12, c_t1)) | m_main_v_state1(s13, c_t1) | (~node6(s12, s13)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s12, c_t1)) | m_main_v_state1(s13, c_t1) | (~node6(s12, s13)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(1516,plain,
% 0.69/0.91 (((~node6(s12, s13)) | (~m_main_v_state1(s12, c_t1)) | m_main_v_state1(s13, c_t1)) <=> ((~m_main_v_state1(s12, c_t1)) | m_main_v_state1(s13, c_t1) | (~node6(s12, s13)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(1517,plain,
% 0.69/0.91 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s12, s13)) | (~m_main_v_state1(s12, c_t1)) | m_main_v_state1(s13, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s12, c_t1)) | m_main_v_state1(s13, c_t1) | (~node6(s12, s13))))),
% 0.69/0.91 inference(monotonicity,[status(thm)],[1516])).
% 0.69/0.91 tff(1518,plain,
% 0.69/0.91 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s12, s13)) | (~m_main_v_state1(s12, c_t1)) | m_main_v_state1(s13, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s12, c_t1)) | m_main_v_state1(s13, c_t1) | (~node6(s12, s13)))),
% 0.69/0.91 inference(transitivity,[status(thm)],[1517, 1515])).
% 0.69/0.91 tff(1519,plain,
% 0.69/0.91 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s12, s13)) | (~m_main_v_state1(s12, c_t1)) | m_main_v_state1(s13, c_t1))),
% 0.69/0.91 inference(quant_inst,[status(thm)],[])).
% 0.69/0.91 tff(1520,plain,
% 0.69/0.91 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s12, c_t1)) | m_main_v_state1(s13, c_t1) | (~node6(s12, s13))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[1519, 1518])).
% 0.69/0.91 tff(1521,plain,
% 0.69/0.91 (m_main_v_state1(s13, c_t1)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[1520, 856, 1406, 1503])).
% 0.69/0.91 tff(1522,plain,
% 0.69/0.91 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s13, c_n2)) | (~m_main_v_state2(s13, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s13, c_n2)) | (~m_main_v_state2(s13, c_t2)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(1523,plain,
% 0.69/0.91 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s13, c_n2)) | (~m_main_v_state2(s13, c_t2)))),
% 0.69/0.91 inference(quant_inst,[status(thm)],[])).
% 0.69/0.91 tff(1524,plain,
% 0.69/0.91 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s13, c_n2)) | (~m_main_v_state2(s13, c_t2))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[1523, 1522])).
% 0.69/0.91 tff(1525,plain,
% 0.69/0.91 (~m_main_v_state2(s13, c_t2)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[1524, 77, 1453])).
% 0.69/0.91 tff(1526,plain,
% 0.69/0.91 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s13, c_t2) | (~node1(s13)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s13, c_t2) | (~node1(s13)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(1527,plain,
% 0.69/0.91 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s13, c_t2) | (~node1(s13)))),
% 0.69/0.91 inference(quant_inst,[status(thm)],[])).
% 0.69/0.91 tff(1528,plain,
% 0.69/0.91 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s13, c_t2) | (~node1(s13))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[1527, 1526])).
% 0.69/0.91 tff(1529,plain,
% 0.69/0.91 (~node1(s13)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[1528, 195, 1525])).
% 0.69/0.91 tff(1530,plain,
% 0.69/0.91 (succ(s13, s14) <=> succ(s13, s14)),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(1531,axiom,(succ(s13, s14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound14')).
% 0.69/0.91 tff(1532,plain,
% 0.69/0.91 (succ(s13, s14)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[1531, 1530])).
% 0.69/0.91 tff(1533,plain,
% 0.69/0.91 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s13, s14)) | trans(s13, s14))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s13, s14)) | trans(s13, s14))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(1534,plain,
% 0.69/0.91 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s13, s14)) | trans(s13, s14))),
% 0.69/0.91 inference(quant_inst,[status(thm)],[])).
% 0.69/0.91 tff(1535,plain,
% 0.69/0.91 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s13, s14)) | trans(s13, s14)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[1534, 1533])).
% 0.69/0.91 tff(1536,plain,
% 0.69/0.91 (trans(s13, s14)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[1535, 1532, 32])).
% 0.69/0.91 tff(1537,plain,
% 0.69/0.91 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s13, s14)) | node7(s13, s14))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s13, s14)) | node7(s13, s14))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(1538,plain,
% 0.69/0.91 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s13, s14)) | node7(s13, s14))),
% 0.69/0.91 inference(quant_inst,[status(thm)],[])).
% 0.69/0.91 tff(1539,plain,
% 0.69/0.91 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s13, s14)) | node7(s13, s14)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[1538, 1537])).
% 0.69/0.91 tff(1540,plain,
% 0.69/0.91 (node7(s13, s14)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[1539, 206, 1536])).
% 0.69/0.91 tff(1541,plain,
% 0.69/0.91 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_state1(s14, c_c1) | node1(s13) | node2(s13) | node3(s13) | (~node7(s13, s14)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_state1(s14, c_c1) | node1(s13) | node2(s13) | node3(s13) | (~node7(s13, s14)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(1542,plain,
% 0.69/0.91 (((~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | node1(s13) | node2(s13) | node3(s13) | (~node7(s13, s14)) | m_main_v_state1(s14, c_c1)) <=> ((~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_state1(s14, c_c1) | node1(s13) | node2(s13) | node3(s13) | (~node7(s13, s14)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(1543,plain,
% 0.69/0.91 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | node1(s13) | node2(s13) | node3(s13) | (~node7(s13, s14)) | m_main_v_state1(s14, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_state1(s14, c_c1) | node1(s13) | node2(s13) | node3(s13) | (~node7(s13, s14))))),
% 0.69/0.91 inference(monotonicity,[status(thm)],[1542])).
% 0.69/0.91 tff(1544,plain,
% 0.69/0.91 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | node1(s13) | node2(s13) | node3(s13) | (~node7(s13, s14)) | m_main_v_state1(s14, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_state1(s14, c_c1) | node1(s13) | node2(s13) | node3(s13) | (~node7(s13, s14)))),
% 0.69/0.91 inference(transitivity,[status(thm)],[1543, 1541])).
% 0.69/0.91 tff(1545,plain,
% 0.69/0.91 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | node1(s13) | node2(s13) | node3(s13) | (~node7(s13, s14)) | m_main_v_state1(s14, c_c1))),
% 0.69/0.91 inference(quant_inst,[status(thm)],[])).
% 0.69/0.91 tff(1546,plain,
% 0.69/0.91 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_state1(s14, c_c1) | node1(s13) | node2(s13) | node3(s13) | (~node7(s13, s14))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[1545, 1544])).
% 0.69/0.91 tff(1547,plain,
% 0.69/0.91 ((~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_state1(s14, c_c1) | node1(s13) | node2(s13) | node3(s13)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[1546, 892, 1540])).
% 0.69/0.91 tff(1548,plain,
% 0.69/0.91 (m_main_v_state1(s14, c_c1)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[1547, 1529, 1453, 1521, 1514, 1461])).
% 0.69/0.91 tff(1549,plain,
% 0.69/0.91 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s14, c_t1)) | (~m_main_v_state1(s14, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s14, c_t1)) | (~m_main_v_state1(s14, c_c1)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(1550,plain,
% 0.69/0.91 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s14, c_t1)) | (~m_main_v_state1(s14, c_c1)))),
% 0.69/0.91 inference(quant_inst,[status(thm)],[])).
% 0.69/0.91 tff(1551,plain,
% 0.69/0.91 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s14, c_t1)) | (~m_main_v_state1(s14, c_c1))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[1550, 1549])).
% 0.69/0.91 tff(1552,plain,
% 0.69/0.91 (~m_main_v_state1(s14, c_t1)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[1551, 539, 1548])).
% 0.69/0.91 tff(1553,plain,
% 0.69/0.91 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s14, c_t1) | (~node5(s14)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s14, c_t1) | (~node5(s14)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(1554,plain,
% 0.69/0.91 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s14, c_t1) | (~node5(s14)))),
% 0.69/0.91 inference(quant_inst,[status(thm)],[])).
% 0.69/0.91 tff(1555,plain,
% 0.69/0.91 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s14, c_t1) | (~node5(s14))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[1554, 1553])).
% 0.69/0.91 tff(1556,plain,
% 0.69/0.91 (~node5(s14)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[1555, 550, 1552])).
% 0.69/0.91 tff(1557,plain,
% 0.69/0.91 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s13, s14)) | node14(s13, s14))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s13, s14)) | node14(s13, s14))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(1558,plain,
% 0.69/0.91 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s13, s14)) | node14(s13, s14))),
% 0.69/0.91 inference(quant_inst,[status(thm)],[])).
% 0.69/0.91 tff(1559,plain,
% 0.69/0.91 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s13, s14)) | node14(s13, s14)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[1558, 1557])).
% 0.69/0.91 tff(1560,plain,
% 0.69/0.91 (node14(s13, s14)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[1559, 46, 1536])).
% 0.69/0.91 tff(1561,plain,
% 0.69/0.91 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | (~node14(s13, s14)) | m_main_v_state2(s14, c_t2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | (~node14(s13, s14)) | m_main_v_state2(s14, c_t2))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(1562,plain,
% 0.69/0.91 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | (~node14(s13, s14)) | m_main_v_state2(s14, c_t2))),
% 0.69/0.91 inference(quant_inst,[status(thm)],[])).
% 0.69/0.91 tff(1563,plain,
% 0.69/0.91 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | (~node14(s13, s14)) | m_main_v_state2(s14, c_t2)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[1562, 1561])).
% 0.69/0.91 tff(1564,plain,
% 0.69/0.91 ((~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_state2(s14, c_t2)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[1563, 922, 1560])).
% 0.69/0.91 tff(1565,plain,
% 0.69/0.91 (m_main_v_state2(s14, c_t2)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[1564, 1521, 1453])).
% 0.69/0.91 tff(1566,plain,
% 0.69/0.91 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s14, c_n2)) | (~m_main_v_state2(s14, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s14, c_n2)) | (~m_main_v_state2(s14, c_t2)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(1567,plain,
% 0.69/0.91 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s14, c_n2)) | (~m_main_v_state2(s14, c_t2)))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(1568,plain,
% 0.69/0.92 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s14, c_n2)) | (~m_main_v_state2(s14, c_t2))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1567, 1566])).
% 0.69/0.92 tff(1569,plain,
% 0.69/0.92 (~m_main_v_state2(s14, c_n2)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1568, 77, 1565])).
% 0.69/0.92 tff(1570,plain,
% 0.69/0.92 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s14, c_n2) | (~node4(s14)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s14, c_n2) | (~node4(s14)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1571,plain,
% 0.69/0.92 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s14, c_n2) | (~node4(s14)))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(1572,plain,
% 0.69/0.92 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s14, c_n2) | (~node4(s14))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1571, 1570])).
% 0.69/0.92 tff(1573,plain,
% 0.69/0.92 (~node4(s14)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1572, 388, 1569])).
% 0.69/0.92 tff(1574,plain,
% 0.69/0.92 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s14, c_t2)) | (~m_main_v_state2(s14, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s14, c_t2)) | (~m_main_v_state2(s14, c_c2)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1575,plain,
% 0.69/0.92 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s14, c_t2)) | (~m_main_v_state2(s14, c_c2)))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(1576,plain,
% 0.69/0.92 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s14, c_t2)) | (~m_main_v_state2(s14, c_c2))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1575, 1574])).
% 0.69/0.92 tff(1577,plain,
% 0.69/0.92 (~m_main_v_state2(s14, c_c2)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1576, 260, 1565])).
% 0.69/0.92 tff(1578,plain,
% 0.69/0.92 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s14, c_c2) | (~node3(s14)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s14, c_c2) | (~node3(s14)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1579,plain,
% 0.69/0.92 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s14, c_c2) | (~node3(s14)))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(1580,plain,
% 0.69/0.92 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s14, c_c2) | (~node3(s14))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1579, 1578])).
% 0.69/0.92 tff(1581,plain,
% 0.69/0.92 (~node3(s14)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1580, 399, 1577])).
% 0.69/0.92 tff(1582,plain,
% 0.69/0.92 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s14, c_n2) | (~node2(s14)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s14, c_n2) | (~node2(s14)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1583,plain,
% 0.69/0.92 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s14, c_n2) | (~node2(s14)))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(1584,plain,
% 0.69/0.92 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s14, c_n2) | (~node2(s14))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1583, 1582])).
% 0.69/0.92 tff(1585,plain,
% 0.69/0.92 (~node2(s14)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1584, 410, 1569])).
% 0.69/0.92 tff(1586,plain,
% 0.69/0.92 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s14, c_n1)) | (~m_main_v_state1(s14, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s14, c_n1)) | (~m_main_v_state1(s14, c_c1)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1587,plain,
% 0.69/0.92 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s14, c_n1)) | (~m_main_v_state1(s14, c_c1)))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(1588,plain,
% 0.69/0.92 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s14, c_n1)) | (~m_main_v_state1(s14, c_c1))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1587, 1586])).
% 0.69/0.92 tff(1589,plain,
% 0.69/0.92 (~m_main_v_state1(s14, c_n1)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1588, 454, 1548])).
% 0.69/0.92 tff(1590,plain,
% 0.69/0.92 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s14, c_n1) | (~node1(s14)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s14, c_n1) | (~node1(s14)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1591,plain,
% 0.69/0.92 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s14, c_n1) | (~node1(s14)))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(1592,plain,
% 0.69/0.92 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s14, c_n1) | (~node1(s14))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1591, 1590])).
% 0.69/0.92 tff(1593,plain,
% 0.69/0.92 (~node1(s14)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1592, 421, 1589])).
% 0.69/0.92 tff(1594,plain,
% 0.69/0.92 (succ(s14, s15) <=> succ(s14, s15)),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1595,axiom,(succ(s14, s15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound15')).
% 0.69/0.92 tff(1596,plain,
% 0.69/0.92 (succ(s14, s15)),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1595, 1594])).
% 0.69/0.92 tff(1597,plain,
% 0.69/0.92 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s14, s15)) | trans(s14, s15))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s14, s15)) | trans(s14, s15))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1598,plain,
% 0.69/0.92 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s14, s15)) | trans(s14, s15))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(1599,plain,
% 0.69/0.92 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s14, s15)) | trans(s14, s15)),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1598, 1597])).
% 0.69/0.92 tff(1600,plain,
% 0.69/0.92 (trans(s14, s15)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1599, 1596, 32])).
% 0.69/0.92 tff(1601,plain,
% 0.69/0.92 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s14, s15)) | node7(s14, s15))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s14, s15)) | node7(s14, s15))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1602,plain,
% 0.69/0.92 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s14, s15)) | node7(s14, s15))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(1603,plain,
% 0.69/0.92 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s14, s15)) | node7(s14, s15)),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1602, 1601])).
% 0.69/0.92 tff(1604,plain,
% 0.69/0.92 (node7(s14, s15)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1603, 206, 1600])).
% 0.69/0.92 tff(1605,plain,
% 0.69/0.92 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s15, c_n1) | (~m_main_v_state1(s14, c_c1)) | node1(s14) | node2(s14) | node3(s14) | node4(s14) | node5(s14) | (~node7(s14, s15)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s15, c_n1) | (~m_main_v_state1(s14, c_c1)) | node1(s14) | node2(s14) | node3(s14) | node4(s14) | node5(s14) | (~node7(s14, s15)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1606,plain,
% 0.69/0.92 (((~m_main_v_state1(s14, c_c1)) | node1(s14) | node2(s14) | node3(s14) | node4(s14) | node5(s14) | (~node7(s14, s15)) | m_main_v_state1(s15, c_n1)) <=> (m_main_v_state1(s15, c_n1) | (~m_main_v_state1(s14, c_c1)) | node1(s14) | node2(s14) | node3(s14) | node4(s14) | node5(s14) | (~node7(s14, s15)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1607,plain,
% 0.69/0.92 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s14, c_c1)) | node1(s14) | node2(s14) | node3(s14) | node4(s14) | node5(s14) | (~node7(s14, s15)) | m_main_v_state1(s15, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s15, c_n1) | (~m_main_v_state1(s14, c_c1)) | node1(s14) | node2(s14) | node3(s14) | node4(s14) | node5(s14) | (~node7(s14, s15))))),
% 0.69/0.92 inference(monotonicity,[status(thm)],[1606])).
% 0.69/0.92 tff(1608,plain,
% 0.69/0.92 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s14, c_c1)) | node1(s14) | node2(s14) | node3(s14) | node4(s14) | node5(s14) | (~node7(s14, s15)) | m_main_v_state1(s15, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s15, c_n1) | (~m_main_v_state1(s14, c_c1)) | node1(s14) | node2(s14) | node3(s14) | node4(s14) | node5(s14) | (~node7(s14, s15)))),
% 0.69/0.92 inference(transitivity,[status(thm)],[1607, 1605])).
% 0.69/0.92 tff(1609,plain,
% 0.69/0.92 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s14, c_c1)) | node1(s14) | node2(s14) | node3(s14) | node4(s14) | node5(s14) | (~node7(s14, s15)) | m_main_v_state1(s15, c_n1))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(1610,plain,
% 0.69/0.92 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s15, c_n1) | (~m_main_v_state1(s14, c_c1)) | node1(s14) | node2(s14) | node3(s14) | node4(s14) | node5(s14) | (~node7(s14, s15))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1609, 1608])).
% 0.69/0.92 tff(1611,plain,
% 0.69/0.92 (m_main_v_state1(s15, c_n1) | (~m_main_v_state1(s14, c_c1)) | node1(s14) | node2(s14) | node3(s14) | node4(s14) | node5(s14)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1610, 584, 1604])).
% 0.69/0.92 tff(1612,plain,
% 0.69/0.92 (m_main_v_state1(s15, c_n1)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1611, 1593, 1548, 1585, 1581, 1573, 1556])).
% 0.69/0.92 tff(1613,plain,
% 0.69/0.92 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s13, c_t2) | (~node15(s13)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s13, c_t2) | (~node15(s13)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1614,plain,
% 0.69/0.92 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s13, c_t2) | (~node15(s13)))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(1615,plain,
% 0.69/0.92 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s13, c_t2) | (~node15(s13))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1614, 1613])).
% 0.69/0.92 tff(1616,plain,
% 0.69/0.92 (~node15(s13)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1615, 103, 1525])).
% 0.69/0.92 tff(1617,plain,
% 0.69/0.92 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s13, s14)) | node18(s13, s14))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s13, s14)) | node18(s13, s14))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1618,plain,
% 0.69/0.92 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s13, s14)) | node18(s13, s14))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(1619,plain,
% 0.69/0.92 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s13, s14)) | node18(s13, s14)),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1618, 1617])).
% 0.69/0.92 tff(1620,plain,
% 0.69/0.92 (node18(s13, s14)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1619, 125, 1536])).
% 0.69/0.92 tff(1621,plain,
% 0.69/0.92 (((~![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(s13) | (~node18(s13, s14)) | (~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_turn(s14, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s13) | (~node18(s13, s14)) | (~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_turn(s14, c_1))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1622,plain,
% 0.69/0.92 (((~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | node15(s13) | (~node18(s13, s14)) | m_main_v_turn(s14, c_1)) <=> (node15(s13) | (~node18(s13, s14)) | (~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_turn(s14, c_1))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1623,plain,
% 0.69/0.92 (((~![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(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | node15(s13) | (~node18(s13, s14)) | m_main_v_turn(s14, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s13) | (~node18(s13, s14)) | (~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_turn(s14, c_1)))),
% 0.69/0.92 inference(monotonicity,[status(thm)],[1622])).
% 0.69/0.92 tff(1624,plain,
% 0.69/0.92 (((~![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(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | node15(s13) | (~node18(s13, s14)) | m_main_v_turn(s14, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s13) | (~node18(s13, s14)) | (~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_turn(s14, c_1))),
% 0.69/0.92 inference(transitivity,[status(thm)],[1623, 1621])).
% 0.69/0.92 tff(1625,plain,
% 0.69/0.92 ((~![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(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | node15(s13) | (~node18(s13, s14)) | m_main_v_turn(s14, c_1))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(1626,plain,
% 0.69/0.92 ((~![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(s13) | (~node18(s13, s14)) | (~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_turn(s14, c_1)),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1625, 1624])).
% 0.69/0.92 tff(1627,plain,
% 0.69/0.92 (node15(s13) | (~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_turn(s14, c_1)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1626, 992, 1620])).
% 0.69/0.92 tff(1628,plain,
% 0.69/0.92 (m_main_v_turn(s14, c_1)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1627, 1616, 1453, 1521])).
% 0.69/0.92 tff(1629,plain,
% 0.69/0.92 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s14, c_1)) | (~m_main_v_turn(s14, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s14, c_1)) | (~m_main_v_turn(s14, c_2)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1630,plain,
% 0.69/0.92 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s14, c_1)) | (~m_main_v_turn(s14, c_2)))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(1631,plain,
% 0.69/0.92 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s14, c_1)) | (~m_main_v_turn(s14, c_2))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1630, 1629])).
% 0.69/0.92 tff(1632,plain,
% 0.69/0.92 (~m_main_v_turn(s14, c_2)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1631, 156, 1628])).
% 0.69/0.92 tff(1633,plain,
% 0.69/0.92 (((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s14, c_2) | (~node12(s14)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s14, c_2) | (~node12(s14)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1634,plain,
% 0.69/0.92 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s14, c_2) | (~node12(s14)))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(1635,plain,
% 0.69/0.92 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s14, c_2) | (~node12(s14))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1634, 1633])).
% 0.69/0.92 tff(1636,plain,
% 0.69/0.92 (~node12(s14)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1635, 184, 1632])).
% 0.69/0.92 tff(1637,plain,
% 0.69/0.92 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s14, c_n2) | (~node8(s14)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s14, c_n2) | (~node8(s14)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1638,plain,
% 0.69/0.92 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s14, c_n2) | (~node8(s14)))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(1639,plain,
% 0.69/0.92 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s14, c_n2) | (~node8(s14))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1638, 1637])).
% 0.69/0.92 tff(1640,plain,
% 0.69/0.92 (~node8(s14)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1639, 271, 1569])).
% 0.69/0.92 tff(1641,plain,
% 0.69/0.92 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s14, c_n2) | (~node9(s14)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s14, c_n2) | (~node9(s14)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1642,plain,
% 0.69/0.92 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s14, c_n2) | (~node9(s14)))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(1643,plain,
% 0.69/0.92 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s14, c_n2) | (~node9(s14))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1642, 1641])).
% 0.69/0.92 tff(1644,plain,
% 0.69/0.92 (~node9(s14)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1643, 88, 1569])).
% 0.69/0.92 tff(1645,plain,
% 0.69/0.92 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s14, c_n2) | (~node10(s14)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s14, c_n2) | (~node10(s14)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1646,plain,
% 0.69/0.92 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s14, c_n2) | (~node10(s14)))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(1647,plain,
% 0.69/0.92 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s14, c_n2) | (~node10(s14))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1646, 1645])).
% 0.69/0.92 tff(1648,plain,
% 0.69/0.92 (~node10(s14)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1647, 249, 1569])).
% 0.69/0.92 tff(1649,plain,
% 0.69/0.92 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s14, c_n1) | (~node11(s14)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s14, c_n1) | (~node11(s14)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1650,plain,
% 0.69/0.92 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s14, c_n1) | (~node11(s14)))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(1651,plain,
% 0.69/0.92 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s14, c_n1) | (~node11(s14))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1650, 1649])).
% 0.69/0.92 tff(1652,plain,
% 0.69/0.92 (~node11(s14)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1651, 238, 1589])).
% 0.69/0.92 tff(1653,plain,
% 0.69/0.92 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s14, s15)) | node14(s14, s15))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s14, s15)) | node14(s14, s15))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1654,plain,
% 0.69/0.92 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s14, s15)) | node14(s14, s15))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(1655,plain,
% 0.69/0.92 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s14, s15)) | node14(s14, s15)),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1654, 1653])).
% 0.69/0.92 tff(1656,plain,
% 0.69/0.92 (node14(s14, s15)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1655, 46, 1600])).
% 0.69/0.92 tff(1657,plain,
% 0.69/0.92 (((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s14, c_c2) | node9(s14) | node8(s14) | node10(s14) | node11(s14) | node12(s14) | node13(s14, s15) | (~node14(s14, s15)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s14, c_c2) | node9(s14) | node8(s14) | node10(s14) | node11(s14) | node12(s14) | node13(s14, s15) | (~node14(s14, s15)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1658,plain,
% 0.69/0.92 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s14, c_c2) | node9(s14) | node8(s14) | node10(s14) | node11(s14) | node12(s14) | node13(s14, s15) | (~node14(s14, s15)))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(1659,plain,
% 0.69/0.92 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s14, c_c2) | node9(s14) | node8(s14) | node10(s14) | node11(s14) | node12(s14) | node13(s14, s15) | (~node14(s14, s15))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1658, 1657])).
% 0.69/0.92 tff(1660,plain,
% 0.69/0.92 (m_main_v_state2(s14, c_c2) | node9(s14) | node8(s14) | node10(s14) | node11(s14) | node12(s14) | node13(s14, s15)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1659, 296, 1656])).
% 0.69/0.92 tff(1661,plain,
% 0.69/0.92 (node13(s14, s15)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1660, 1652, 1577, 1648, 1644, 1640, 1636])).
% 0.69/0.92 tff(1662,plain,
% 0.69/0.92 (((~![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(s14, c_t2)) | m_main_v_state2(s15, c_t2) | (~node13(s14, s15)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s14, c_t2)) | m_main_v_state2(s15, c_t2) | (~node13(s14, s15)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1663,plain,
% 0.69/0.92 (((~node13(s14, s15)) | (~m_main_v_state2(s14, c_t2)) | m_main_v_state2(s15, c_t2)) <=> ((~m_main_v_state2(s14, c_t2)) | m_main_v_state2(s15, c_t2) | (~node13(s14, s15)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1664,plain,
% 0.69/0.92 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s14, s15)) | (~m_main_v_state2(s14, c_t2)) | m_main_v_state2(s15, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s14, c_t2)) | m_main_v_state2(s15, c_t2) | (~node13(s14, s15))))),
% 0.69/0.92 inference(monotonicity,[status(thm)],[1663])).
% 0.69/0.92 tff(1665,plain,
% 0.69/0.92 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s14, s15)) | (~m_main_v_state2(s14, c_t2)) | m_main_v_state2(s15, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s14, c_t2)) | m_main_v_state2(s15, c_t2) | (~node13(s14, s15)))),
% 0.69/0.92 inference(transitivity,[status(thm)],[1664, 1662])).
% 0.69/0.92 tff(1666,plain,
% 0.69/0.92 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s14, s15)) | (~m_main_v_state2(s14, c_t2)) | m_main_v_state2(s15, c_t2))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(1667,plain,
% 0.69/0.92 ((~![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(s14, c_t2)) | m_main_v_state2(s15, c_t2) | (~node13(s14, s15))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1666, 1665])).
% 0.69/0.92 tff(1668,plain,
% 0.69/0.92 (m_main_v_state2(s15, c_t2)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1667, 518, 1565, 1661])).
% 0.69/0.92 tff(1669,plain,
% 0.69/0.92 (succ(s15, s16) <=> succ(s15, s16)),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1670,axiom,(succ(s15, s16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound16')).
% 0.69/0.92 tff(1671,plain,
% 0.69/0.92 (succ(s15, s16)),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1670, 1669])).
% 0.69/0.92 tff(1672,plain,
% 0.69/0.92 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s15, s16)) | trans(s15, s16))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s15, s16)) | trans(s15, s16))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1673,plain,
% 0.69/0.92 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s15, s16)) | trans(s15, s16))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(1674,plain,
% 0.69/0.92 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s15, s16)) | trans(s15, s16)),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1673, 1672])).
% 0.69/0.92 tff(1675,plain,
% 0.69/0.92 (trans(s15, s16)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1674, 1671, 32])).
% 0.69/0.92 tff(1676,plain,
% 0.69/0.92 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s15, s16)) | node7(s15, s16))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s15, s16)) | node7(s15, s16))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1677,plain,
% 0.69/0.92 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s15, s16)) | node7(s15, s16))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(1678,plain,
% 0.69/0.92 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s15, s16)) | node7(s15, s16)),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1677, 1676])).
% 0.69/0.92 tff(1679,plain,
% 0.69/0.92 (node7(s15, s16)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1678, 206, 1675])).
% 0.69/0.92 tff(1680,plain,
% 0.69/0.92 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | (~node7(s15, s16)) | m_main_v_state1(s16, c_t1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | (~node7(s15, s16)) | m_main_v_state1(s16, c_t1))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1681,plain,
% 0.69/0.92 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | (~node7(s15, s16)) | m_main_v_state1(s16, c_t1))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(1682,plain,
% 0.69/0.92 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | (~node7(s15, s16)) | m_main_v_state1(s16, c_t1)),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1681, 1680])).
% 0.69/0.92 tff(1683,plain,
% 0.69/0.92 ((~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | m_main_v_state1(s16, c_t1)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1682, 651, 1679])).
% 0.69/0.92 tff(1684,plain,
% 0.69/0.92 (m_main_v_state1(s16, c_t1)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1683, 1668, 1612])).
% 0.69/0.92 tff(1685,plain,
% 0.69/0.92 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s16, c_n1)) | (~m_main_v_state1(s16, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s16, c_n1)) | (~m_main_v_state1(s16, c_t1)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1686,plain,
% 0.69/0.92 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s16, c_n1)) | (~m_main_v_state1(s16, c_t1)))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(1687,plain,
% 0.69/0.92 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s16, c_n1)) | (~m_main_v_state1(s16, c_t1))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1686, 1685])).
% 0.69/0.92 tff(1688,plain,
% 0.69/0.92 (~m_main_v_state1(s16, c_n1)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1687, 10, 1684])).
% 0.69/0.92 tff(1689,plain,
% 0.69/0.92 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s16, c_n1) | (~node1(s16)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s16, c_n1) | (~node1(s16)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1690,plain,
% 0.69/0.92 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s16, c_n1) | (~node1(s16)))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(1691,plain,
% 0.69/0.92 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s16, c_n1) | (~node1(s16))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1690, 1689])).
% 0.69/0.92 tff(1692,plain,
% 0.69/0.92 (~node1(s16)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1691, 421, 1688])).
% 0.69/0.92 tff(1693,plain,
% 0.69/0.92 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s15, s16)) | node18(s15, s16))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s15, s16)) | node18(s15, s16))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1694,plain,
% 0.69/0.92 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s15, s16)) | node18(s15, s16))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(1695,plain,
% 0.69/0.92 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s15, s16)) | node18(s15, s16)),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1694, 1693])).
% 0.69/0.92 tff(1696,plain,
% 0.69/0.92 (node18(s15, s16)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1695, 125, 1675])).
% 0.69/0.92 tff(1697,plain,
% 0.69/0.92 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | (~node18(s15, s16)) | m_main_v_turn(s16, c_2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | (~node18(s15, s16)) | m_main_v_turn(s16, c_2))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1698,plain,
% 0.69/0.92 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | (~node18(s15, s16)) | m_main_v_turn(s16, c_2))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(1699,plain,
% 0.69/0.92 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | (~node18(s15, s16)) | m_main_v_turn(s16, c_2)),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1698, 1697])).
% 0.69/0.92 tff(1700,plain,
% 0.69/0.92 ((~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | m_main_v_turn(s16, c_2)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1699, 760, 1696])).
% 0.69/0.92 tff(1701,plain,
% 0.69/0.92 (m_main_v_turn(s16, c_2)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1700, 1668, 1612])).
% 0.69/0.92 tff(1702,plain,
% 0.69/0.92 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s16, c_1)) | (~m_main_v_turn(s16, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s16, c_1)) | (~m_main_v_turn(s16, c_2)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1703,plain,
% 0.69/0.92 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s16, c_1)) | (~m_main_v_turn(s16, c_2)))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(1704,plain,
% 0.69/0.92 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s16, c_1)) | (~m_main_v_turn(s16, c_2))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1703, 1702])).
% 0.69/0.92 tff(1705,plain,
% 0.69/0.92 (~m_main_v_turn(s16, c_1)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1704, 156, 1701])).
% 0.69/0.92 tff(1706,plain,
% 0.69/0.92 (((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s16, c_1) | (~node5(s16)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s16, c_1) | (~node5(s16)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1707,plain,
% 0.69/0.92 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s16, c_1) | (~node5(s16)))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(1708,plain,
% 0.69/0.92 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s16, c_1) | (~node5(s16))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[1707, 1706])).
% 0.69/0.92 tff(1709,plain,
% 0.69/0.92 (~node5(s16)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[1708, 776, 1705])).
% 0.69/0.92 tff(1710,plain,
% 0.69/0.92 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s16, c_n1) | (~node2(s16)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s16, c_n1) | (~node2(s16)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(1711,plain,
% 0.69/0.92 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s16, c_n1) | (~node2(s16)))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.93 tff(1712,plain,
% 0.69/0.93 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s16, c_n1) | (~node2(s16))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[1711, 1710])).
% 0.69/0.93 tff(1713,plain,
% 0.69/0.93 (~node2(s16)),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[1712, 787, 1688])).
% 0.69/0.93 tff(1714,plain,
% 0.69/0.93 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s16, c_n1) | (~node3(s16)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s16, c_n1) | (~node3(s16)))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(1715,plain,
% 0.69/0.93 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s16, c_n1) | (~node3(s16)))),
% 0.69/0.93 inference(quant_inst,[status(thm)],[])).
% 0.69/0.93 tff(1716,plain,
% 0.69/0.93 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s16, c_n1) | (~node3(s16))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[1715, 1714])).
% 0.69/0.93 tff(1717,plain,
% 0.69/0.93 (~node3(s16)),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[1716, 798, 1688])).
% 0.69/0.93 tff(1718,plain,
% 0.69/0.93 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s16, c_t1)) | (~m_main_v_state1(s16, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s16, c_t1)) | (~m_main_v_state1(s16, c_c1)))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(1719,plain,
% 0.69/0.93 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s16, c_t1)) | (~m_main_v_state1(s16, c_c1)))),
% 0.69/0.93 inference(quant_inst,[status(thm)],[])).
% 0.69/0.93 tff(1720,plain,
% 0.69/0.93 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s16, c_t1)) | (~m_main_v_state1(s16, c_c1))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[1719, 1718])).
% 0.69/0.93 tff(1721,plain,
% 0.69/0.93 (~m_main_v_state1(s16, c_c1)),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[1720, 539, 1684])).
% 0.69/0.93 tff(1722,plain,
% 0.69/0.93 (((~![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(s14, c_n2) | (~m_main_v_state2(s15, c_n2)) | (~node13(s14, s15)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s14, c_n2) | (~m_main_v_state2(s15, c_n2)) | (~node13(s14, s15)))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(1723,plain,
% 0.69/0.93 (((~node13(s14, s15)) | m_main_v_state2(s14, c_n2) | (~m_main_v_state2(s15, c_n2))) <=> (m_main_v_state2(s14, c_n2) | (~m_main_v_state2(s15, c_n2)) | (~node13(s14, s15)))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(1724,plain,
% 0.69/0.93 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s14, s15)) | m_main_v_state2(s14, c_n2) | (~m_main_v_state2(s15, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s14, c_n2) | (~m_main_v_state2(s15, c_n2)) | (~node13(s14, s15))))),
% 0.69/0.93 inference(monotonicity,[status(thm)],[1723])).
% 0.69/0.93 tff(1725,plain,
% 0.69/0.93 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s14, s15)) | m_main_v_state2(s14, c_n2) | (~m_main_v_state2(s15, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s14, c_n2) | (~m_main_v_state2(s15, c_n2)) | (~node13(s14, s15)))),
% 0.69/0.93 inference(transitivity,[status(thm)],[1724, 1722])).
% 0.69/0.93 tff(1726,plain,
% 0.69/0.93 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s14, s15)) | m_main_v_state2(s14, c_n2) | (~m_main_v_state2(s15, c_n2)))),
% 0.69/0.93 inference(quant_inst,[status(thm)],[])).
% 0.69/0.93 tff(1727,plain,
% 0.69/0.93 ((~![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(s14, c_n2) | (~m_main_v_state2(s15, c_n2)) | (~node13(s14, s15))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[1726, 1725])).
% 0.69/0.93 tff(1728,plain,
% 0.69/0.93 (~m_main_v_state2(s15, c_n2)),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[1727, 311, 1569, 1661])).
% 0.69/0.93 tff(1729,plain,
% 0.69/0.93 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s15, c_n2) | (~node9(s15)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s15, c_n2) | (~node9(s15)))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(1730,plain,
% 0.69/0.93 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s15, c_n2) | (~node9(s15)))),
% 0.69/0.93 inference(quant_inst,[status(thm)],[])).
% 0.69/0.93 tff(1731,plain,
% 0.69/0.93 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s15, c_n2) | (~node9(s15))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[1730, 1729])).
% 0.69/0.93 tff(1732,plain,
% 0.69/0.93 (~node9(s15)),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[1731, 88, 1728])).
% 0.69/0.93 tff(1733,plain,
% 0.69/0.93 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s15, c_n2) | (~node10(s15)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s15, c_n2) | (~node10(s15)))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(1734,plain,
% 0.69/0.93 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s15, c_n2) | (~node10(s15)))),
% 0.69/0.93 inference(quant_inst,[status(thm)],[])).
% 0.69/0.93 tff(1735,plain,
% 0.69/0.93 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s15, c_n2) | (~node10(s15))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[1734, 1733])).
% 0.69/0.93 tff(1736,plain,
% 0.69/0.93 (~node10(s15)),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[1735, 249, 1728])).
% 0.69/0.93 tff(1737,plain,
% 0.69/0.93 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s15, c_n2) | (~node8(s15)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s15, c_n2) | (~node8(s15)))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(1738,plain,
% 0.69/0.93 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s15, c_n2) | (~node8(s15)))),
% 0.69/0.93 inference(quant_inst,[status(thm)],[])).
% 0.69/0.93 tff(1739,plain,
% 0.69/0.93 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s15, c_n2) | (~node8(s15))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[1738, 1737])).
% 0.69/0.93 tff(1740,plain,
% 0.69/0.93 (~node8(s15)),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[1739, 271, 1728])).
% 0.69/0.93 tff(1741,plain,
% 0.69/0.93 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s15, s16)) | node14(s15, s16))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s15, s16)) | node14(s15, s16))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(1742,plain,
% 0.69/0.93 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s15, s16)) | node14(s15, s16))),
% 0.69/0.93 inference(quant_inst,[status(thm)],[])).
% 0.69/0.93 tff(1743,plain,
% 0.69/0.93 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s15, s16)) | node14(s15, s16)),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[1742, 1741])).
% 0.69/0.93 tff(1744,plain,
% 0.69/0.93 (node14(s15, s16)),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[1743, 46, 1675])).
% 0.69/0.93 tff(1745,plain,
% 0.69/0.93 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | node9(s15) | node8(s15) | node10(s15) | (~node14(s15, s16)) | m_main_v_state2(s16, c_c2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | node9(s15) | node8(s15) | node10(s15) | (~node14(s15, s16)) | m_main_v_state2(s16, c_c2))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(1746,plain,
% 0.69/0.93 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | node9(s15) | node8(s15) | node10(s15) | (~node14(s15, s16)) | m_main_v_state2(s16, c_c2))),
% 0.69/0.93 inference(quant_inst,[status(thm)],[])).
% 0.69/0.93 tff(1747,plain,
% 0.69/0.93 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | node9(s15) | node8(s15) | node10(s15) | (~node14(s15, s16)) | m_main_v_state2(s16, c_c2)),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[1746, 1745])).
% 0.69/0.93 tff(1748,plain,
% 0.69/0.93 ((~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | node9(s15) | node8(s15) | node10(s15) | m_main_v_state2(s16, c_c2)),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[1747, 617, 1744])).
% 0.69/0.93 tff(1749,plain,
% 0.69/0.93 (m_main_v_state2(s16, c_c2)),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[1748, 1740, 1612, 1668, 1736, 1732])).
% 0.69/0.93 tff(1750,plain,
% 0.69/0.93 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s16, c_n2)) | (~m_main_v_state2(s16, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s16, c_n2)) | (~m_main_v_state2(s16, c_c2)))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(1751,plain,
% 0.69/0.93 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s16, c_n2)) | (~m_main_v_state2(s16, c_c2)))),
% 0.69/0.93 inference(quant_inst,[status(thm)],[])).
% 0.69/0.93 tff(1752,plain,
% 0.69/0.93 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s16, c_n2)) | (~m_main_v_state2(s16, c_c2))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[1751, 1750])).
% 0.69/0.93 tff(1753,plain,
% 0.69/0.93 (~m_main_v_state2(s16, c_n2)),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[1752, 697, 1749])).
% 0.69/0.93 tff(1754,plain,
% 0.69/0.93 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s16, c_n2) | (~node4(s16)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s16, c_n2) | (~node4(s16)))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(1755,plain,
% 0.69/0.93 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s16, c_n2) | (~node4(s16)))),
% 0.69/0.93 inference(quant_inst,[status(thm)],[])).
% 0.69/0.93 tff(1756,plain,
% 0.69/0.93 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s16, c_n2) | (~node4(s16))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[1755, 1754])).
% 0.69/0.93 tff(1757,plain,
% 0.69/0.93 (~node4(s16)),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[1756, 388, 1753])).
% 0.69/0.93 tff(1758,plain,
% 0.69/0.93 (succ(s16, s17) <=> succ(s16, s17)),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(1759,axiom,(succ(s16, s17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound17')).
% 0.69/0.93 tff(1760,plain,
% 0.69/0.93 (succ(s16, s17)),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[1759, 1758])).
% 0.69/0.93 tff(1761,plain,
% 0.69/0.93 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s16, s17)) | trans(s16, s17))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s16, s17)) | trans(s16, s17))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(1762,plain,
% 0.69/0.93 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s16, s17)) | trans(s16, s17))),
% 0.69/0.93 inference(quant_inst,[status(thm)],[])).
% 0.69/0.93 tff(1763,plain,
% 0.69/0.93 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s16, s17)) | trans(s16, s17)),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[1762, 1761])).
% 0.69/0.93 tff(1764,plain,
% 0.69/0.93 (trans(s16, s17)),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[1763, 1760, 32])).
% 0.69/0.93 tff(1765,plain,
% 0.69/0.93 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s16, s17)) | node7(s16, s17))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s16, s17)) | node7(s16, s17))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(1766,plain,
% 0.69/0.93 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s16, s17)) | node7(s16, s17))),
% 0.69/0.93 inference(quant_inst,[status(thm)],[])).
% 0.69/0.93 tff(1767,plain,
% 0.69/0.93 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s16, s17)) | node7(s16, s17)),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[1766, 1765])).
% 0.69/0.93 tff(1768,plain,
% 0.69/0.93 (node7(s16, s17)),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[1767, 206, 1764])).
% 0.69/0.93 tff(1769,plain,
% 0.69/0.93 (((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s16, c_c1) | node1(s16) | node2(s16) | node3(s16) | node4(s16) | node5(s16) | node6(s16, s17) | (~node7(s16, s17)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s16, c_c1) | node1(s16) | node2(s16) | node3(s16) | node4(s16) | node5(s16) | node6(s16, s17) | (~node7(s16, s17)))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(1770,plain,
% 0.69/0.93 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s16, c_c1) | node1(s16) | node2(s16) | node3(s16) | node4(s16) | node5(s16) | node6(s16, s17) | (~node7(s16, s17)))),
% 0.69/0.93 inference(quant_inst,[status(thm)],[])).
% 0.69/0.93 tff(1771,plain,
% 0.69/0.93 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s16, c_c1) | node1(s16) | node2(s16) | node3(s16) | node4(s16) | node5(s16) | node6(s16, s17) | (~node7(s16, s17))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[1770, 1769])).
% 0.69/0.93 tff(1772,plain,
% 0.69/0.93 (m_main_v_state1(s16, c_c1) | node1(s16) | node2(s16) | node3(s16) | node4(s16) | node5(s16) | node6(s16, s17)),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[1771, 820, 1768])).
% 0.69/0.93 tff(1773,plain,
% 0.69/0.93 (node6(s16, s17)),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[1772, 1757, 1721, 1717, 1713, 1709, 1692])).
% 0.69/0.93 tff(1774,plain,
% 0.69/0.93 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s16, c_t1)) | m_main_v_state1(s17, c_t1) | (~node6(s16, s17)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s16, c_t1)) | m_main_v_state1(s17, c_t1) | (~node6(s16, s17)))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(1775,plain,
% 0.69/0.93 (((~node6(s16, s17)) | (~m_main_v_state1(s16, c_t1)) | m_main_v_state1(s17, c_t1)) <=> ((~m_main_v_state1(s16, c_t1)) | m_main_v_state1(s17, c_t1) | (~node6(s16, s17)))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(1776,plain,
% 0.69/0.93 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s16, s17)) | (~m_main_v_state1(s16, c_t1)) | m_main_v_state1(s17, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s16, c_t1)) | m_main_v_state1(s17, c_t1) | (~node6(s16, s17))))),
% 0.69/0.93 inference(monotonicity,[status(thm)],[1775])).
% 0.69/0.93 tff(1777,plain,
% 0.69/0.93 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s16, s17)) | (~m_main_v_state1(s16, c_t1)) | m_main_v_state1(s17, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s16, c_t1)) | m_main_v_state1(s17, c_t1) | (~node6(s16, s17)))),
% 0.69/0.93 inference(transitivity,[status(thm)],[1776, 1774])).
% 0.69/0.93 tff(1778,plain,
% 0.69/0.93 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s16, s17)) | (~m_main_v_state1(s16, c_t1)) | m_main_v_state1(s17, c_t1))),
% 0.69/0.93 inference(quant_inst,[status(thm)],[])).
% 0.69/0.93 tff(1779,plain,
% 0.69/0.93 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s16, c_t1)) | m_main_v_state1(s17, c_t1) | (~node6(s16, s17))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[1778, 1777])).
% 0.69/0.93 tff(1780,plain,
% 0.69/0.93 (m_main_v_state1(s17, c_t1)),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[1779, 856, 1684, 1773])).
% 0.69/0.93 tff(1781,plain,
% 0.69/0.93 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s16, c_t2)) | (~m_main_v_state2(s16, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s16, c_t2)) | (~m_main_v_state2(s16, c_c2)))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(1782,plain,
% 0.69/0.93 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s16, c_t2)) | (~m_main_v_state2(s16, c_c2)))),
% 0.69/0.93 inference(quant_inst,[status(thm)],[])).
% 0.69/0.93 tff(1783,plain,
% 0.69/0.93 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s16, c_t2)) | (~m_main_v_state2(s16, c_c2))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[1782, 1781])).
% 0.69/0.93 tff(1784,plain,
% 0.69/0.93 (~m_main_v_state2(s16, c_t2)),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[1783, 260, 1749])).
% 0.69/0.93 tff(1785,plain,
% 0.69/0.93 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s16, c_t2) | (~node12(s16)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s16, c_t2) | (~node12(s16)))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(1786,plain,
% 0.69/0.93 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s16, c_t2) | (~node12(s16)))),
% 0.69/0.93 inference(quant_inst,[status(thm)],[])).
% 0.69/0.93 tff(1787,plain,
% 0.69/0.93 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s16, c_t2) | (~node12(s16))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[1786, 1785])).
% 0.69/0.93 tff(1788,plain,
% 0.69/0.93 (~node12(s16)),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[1787, 633, 1784])).
% 0.69/0.93 tff(1789,plain,
% 0.69/0.93 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s16, c_n1) | (~node11(s16)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s16, c_n1) | (~node11(s16)))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(1790,plain,
% 0.69/0.93 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s16, c_n1) | (~node11(s16)))),
% 0.69/0.93 inference(quant_inst,[status(thm)],[])).
% 0.69/0.93 tff(1791,plain,
% 0.69/0.93 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s16, c_n1) | (~node11(s16))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[1790, 1789])).
% 0.69/0.93 tff(1792,plain,
% 0.69/0.93 (~node11(s16)),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[1791, 238, 1688])).
% 0.69/0.93 tff(1793,plain,
% 0.69/0.93 (((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s16, c_c1) | (~node10(s16)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s16, c_c1) | (~node10(s16)))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(1794,plain,
% 0.69/0.93 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s16, c_c1) | (~node10(s16)))),
% 0.69/0.93 inference(quant_inst,[status(thm)],[])).
% 0.69/0.93 tff(1795,plain,
% 0.69/0.93 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s16, c_c1) | (~node10(s16))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[1794, 1793])).
% 0.69/0.93 tff(1796,plain,
% 0.69/0.93 (~node10(s16)),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[1795, 675, 1721])).
% 0.69/0.93 tff(1797,plain,
% 0.69/0.93 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s16, c_n1) | (~node9(s16)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s16, c_n1) | (~node9(s16)))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(1798,plain,
% 0.69/0.93 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s16, c_n1) | (~node9(s16)))),
% 0.69/0.93 inference(quant_inst,[status(thm)],[])).
% 0.69/0.93 tff(1799,plain,
% 0.69/0.93 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s16, c_n1) | (~node9(s16))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[1798, 1797])).
% 0.69/0.93 tff(1800,plain,
% 0.69/0.93 (~node9(s16)),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[1799, 686, 1688])).
% 0.69/0.93 tff(1801,plain,
% 0.69/0.93 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s16, c_n2) | (~node8(s16)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s16, c_n2) | (~node8(s16)))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(1802,plain,
% 0.69/0.93 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s16, c_n2) | (~node8(s16)))),
% 0.69/0.93 inference(quant_inst,[status(thm)],[])).
% 0.69/0.93 tff(1803,plain,
% 0.69/0.93 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s16, c_n2) | (~node8(s16))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[1802, 1801])).
% 0.69/0.93 tff(1804,plain,
% 0.69/0.93 (~node8(s16)),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[1803, 271, 1753])).
% 0.69/0.93 tff(1805,plain,
% 0.69/0.93 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s16, s17)) | node14(s16, s17))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s16, s17)) | node14(s16, s17))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1806,plain,
% 0.77/0.93 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s16, s17)) | node14(s16, s17))),
% 0.77/0.93 inference(quant_inst,[status(thm)],[])).
% 0.77/0.93 tff(1807,plain,
% 0.77/0.93 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s16, s17)) | node14(s16, s17)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[1806, 1805])).
% 0.77/0.93 tff(1808,plain,
% 0.77/0.93 (node14(s16, s17)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1807, 46, 1764])).
% 0.77/0.93 tff(1809,plain,
% 0.77/0.93 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s17, c_n2) | node9(s16) | node8(s16) | node10(s16) | node11(s16) | node12(s16) | (~node14(s16, s17)) | (~m_main_v_state2(s16, c_c2)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s17, c_n2) | node9(s16) | node8(s16) | node10(s16) | node11(s16) | node12(s16) | (~node14(s16, s17)) | (~m_main_v_state2(s16, c_c2)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1810,plain,
% 0.77/0.93 (((~m_main_v_state2(s16, c_c2)) | node9(s16) | node8(s16) | node10(s16) | node11(s16) | node12(s16) | (~node14(s16, s17)) | m_main_v_state2(s17, c_n2)) <=> (m_main_v_state2(s17, c_n2) | node9(s16) | node8(s16) | node10(s16) | node11(s16) | node12(s16) | (~node14(s16, s17)) | (~m_main_v_state2(s16, c_c2)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1811,plain,
% 0.77/0.93 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s16, c_c2)) | node9(s16) | node8(s16) | node10(s16) | node11(s16) | node12(s16) | (~node14(s16, s17)) | m_main_v_state2(s17, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s17, c_n2) | node9(s16) | node8(s16) | node10(s16) | node11(s16) | node12(s16) | (~node14(s16, s17)) | (~m_main_v_state2(s16, c_c2))))),
% 0.77/0.93 inference(monotonicity,[status(thm)],[1810])).
% 0.77/0.93 tff(1812,plain,
% 0.77/0.93 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s16, c_c2)) | node9(s16) | node8(s16) | node10(s16) | node11(s16) | node12(s16) | (~node14(s16, s17)) | m_main_v_state2(s17, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s17, c_n2) | node9(s16) | node8(s16) | node10(s16) | node11(s16) | node12(s16) | (~node14(s16, s17)) | (~m_main_v_state2(s16, c_c2)))),
% 0.77/0.93 inference(transitivity,[status(thm)],[1811, 1809])).
% 0.77/0.93 tff(1813,plain,
% 0.77/0.93 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s16, c_c2)) | node9(s16) | node8(s16) | node10(s16) | node11(s16) | node12(s16) | (~node14(s16, s17)) | m_main_v_state2(s17, c_n2))),
% 0.77/0.93 inference(quant_inst,[status(thm)],[])).
% 0.77/0.93 tff(1814,plain,
% 0.77/0.93 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s17, c_n2) | node9(s16) | node8(s16) | node10(s16) | node11(s16) | node12(s16) | (~node14(s16, s17)) | (~m_main_v_state2(s16, c_c2))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[1813, 1812])).
% 0.77/0.93 tff(1815,plain,
% 0.77/0.93 (m_main_v_state2(s17, c_n2) | node9(s16) | node8(s16) | node10(s16) | node11(s16) | node12(s16) | (~m_main_v_state2(s16, c_c2))),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1814, 726, 1808])).
% 0.77/0.93 tff(1816,plain,
% 0.77/0.93 (m_main_v_state2(s17, c_n2)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1815, 1804, 1749, 1800, 1796, 1792, 1788])).
% 0.77/0.93 tff(1817,plain,
% 0.77/0.93 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s17, c_n2)) | (~m_main_v_state2(s17, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s17, c_n2)) | (~m_main_v_state2(s17, c_t2)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1818,plain,
% 0.77/0.93 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s17, c_n2)) | (~m_main_v_state2(s17, c_t2)))),
% 0.77/0.93 inference(quant_inst,[status(thm)],[])).
% 0.77/0.93 tff(1819,plain,
% 0.77/0.93 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s17, c_n2)) | (~m_main_v_state2(s17, c_t2))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[1818, 1817])).
% 0.77/0.93 tff(1820,plain,
% 0.77/0.93 (~m_main_v_state2(s17, c_t2)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1819, 77, 1816])).
% 0.77/0.93 tff(1821,plain,
% 0.77/0.93 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s17, c_t2) | (~node15(s17)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s17, c_t2) | (~node15(s17)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1822,plain,
% 0.77/0.93 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s17, c_t2) | (~node15(s17)))),
% 0.77/0.93 inference(quant_inst,[status(thm)],[])).
% 0.77/0.93 tff(1823,plain,
% 0.77/0.93 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s17, c_t2) | (~node15(s17))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[1822, 1821])).
% 0.77/0.93 tff(1824,plain,
% 0.77/0.93 (~node15(s17)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1823, 103, 1820])).
% 0.77/0.93 tff(1825,plain,
% 0.77/0.93 (succ(s17, s18) <=> succ(s17, s18)),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1826,axiom,(succ(s17, s18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound18')).
% 0.77/0.93 tff(1827,plain,
% 0.77/0.93 (succ(s17, s18)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[1826, 1825])).
% 0.77/0.93 tff(1828,plain,
% 0.77/0.93 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s17, s18)) | trans(s17, s18))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s17, s18)) | trans(s17, s18))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1829,plain,
% 0.77/0.93 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s17, s18)) | trans(s17, s18))),
% 0.77/0.93 inference(quant_inst,[status(thm)],[])).
% 0.77/0.93 tff(1830,plain,
% 0.77/0.93 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s17, s18)) | trans(s17, s18)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[1829, 1828])).
% 0.77/0.93 tff(1831,plain,
% 0.77/0.93 (trans(s17, s18)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1830, 1827, 32])).
% 0.77/0.93 tff(1832,plain,
% 0.77/0.93 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s17, s18)) | node18(s17, s18))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s17, s18)) | node18(s17, s18))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1833,plain,
% 0.77/0.93 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s17, s18)) | node18(s17, s18))),
% 0.77/0.93 inference(quant_inst,[status(thm)],[])).
% 0.77/0.93 tff(1834,plain,
% 0.77/0.93 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s17, s18)) | node18(s17, s18)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[1833, 1832])).
% 0.77/0.93 tff(1835,plain,
% 0.77/0.93 (node18(s17, s18)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1834, 125, 1831])).
% 0.77/0.93 tff(1836,plain,
% 0.77/0.93 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s17) | (~node18(s17, s18)) | (~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_turn(s18, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s17) | (~node18(s17, s18)) | (~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_turn(s18, c_1))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1837,plain,
% 0.77/0.93 (((~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | node15(s17) | (~node18(s17, s18)) | m_main_v_turn(s18, c_1)) <=> (node15(s17) | (~node18(s17, s18)) | (~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_turn(s18, c_1))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1838,plain,
% 0.77/0.94 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | node15(s17) | (~node18(s17, s18)) | m_main_v_turn(s18, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s17) | (~node18(s17, s18)) | (~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_turn(s18, c_1)))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[1837])).
% 0.77/0.94 tff(1839,plain,
% 0.77/0.94 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | node15(s17) | (~node18(s17, s18)) | m_main_v_turn(s18, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s17) | (~node18(s17, s18)) | (~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_turn(s18, c_1))),
% 0.77/0.94 inference(transitivity,[status(thm)],[1838, 1836])).
% 0.77/0.94 tff(1840,plain,
% 0.77/0.94 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | node15(s17) | (~node18(s17, s18)) | m_main_v_turn(s18, c_1))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1841,plain,
% 0.77/0.94 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s17) | (~node18(s17, s18)) | (~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_turn(s18, c_1)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1840, 1839])).
% 0.77/0.94 tff(1842,plain,
% 0.77/0.94 (node15(s17) | (~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_turn(s18, c_1)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1841, 992, 1835])).
% 0.77/0.94 tff(1843,plain,
% 0.77/0.94 (m_main_v_turn(s18, c_1)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1842, 1824, 1816, 1780])).
% 0.77/0.94 tff(1844,plain,
% 0.77/0.94 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s18, c_1)) | (~m_main_v_turn(s18, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s18, c_1)) | (~m_main_v_turn(s18, c_2)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1845,plain,
% 0.77/0.94 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s18, c_1)) | (~m_main_v_turn(s18, c_2)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1846,plain,
% 0.77/0.94 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s18, c_1)) | (~m_main_v_turn(s18, c_2))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1845, 1844])).
% 0.77/0.94 tff(1847,plain,
% 0.77/0.94 (~m_main_v_turn(s18, c_2)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1846, 156, 1843])).
% 0.77/0.94 tff(1848,plain,
% 0.77/0.94 (((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s18, c_2) | (~node12(s18)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s18, c_2) | (~node12(s18)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1849,plain,
% 0.77/0.94 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s18, c_2) | (~node12(s18)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1850,plain,
% 0.77/0.94 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s18, c_2) | (~node12(s18))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1849, 1848])).
% 0.77/0.94 tff(1851,plain,
% 0.77/0.94 (~node12(s18)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1850, 184, 1847])).
% 0.77/0.94 tff(1852,plain,
% 0.77/0.94 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s17, s18)) | node14(s17, s18))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s17, s18)) | node14(s17, s18))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1853,plain,
% 0.77/0.94 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s17, s18)) | node14(s17, s18))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1854,plain,
% 0.77/0.94 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s17, s18)) | node14(s17, s18)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1853, 1852])).
% 0.77/0.94 tff(1855,plain,
% 0.77/0.94 (node14(s17, s18)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1854, 46, 1831])).
% 0.77/0.94 tff(1856,plain,
% 0.77/0.94 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | (~node14(s17, s18)) | m_main_v_state2(s18, c_t2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | (~node14(s17, s18)) | m_main_v_state2(s18, c_t2))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1857,plain,
% 0.77/0.94 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | (~node14(s17, s18)) | m_main_v_state2(s18, c_t2))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1858,plain,
% 0.77/0.94 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | (~node14(s17, s18)) | m_main_v_state2(s18, c_t2)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1857, 1856])).
% 0.77/0.94 tff(1859,plain,
% 0.77/0.94 ((~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_state2(s18, c_t2)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1858, 922, 1855])).
% 0.77/0.94 tff(1860,plain,
% 0.77/0.94 (m_main_v_state2(s18, c_t2)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1859, 1780, 1816])).
% 0.77/0.94 tff(1861,plain,
% 0.77/0.94 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s18, c_n2)) | (~m_main_v_state2(s18, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s18, c_n2)) | (~m_main_v_state2(s18, c_t2)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1862,plain,
% 0.77/0.94 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s18, c_n2)) | (~m_main_v_state2(s18, c_t2)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1863,plain,
% 0.77/0.94 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s18, c_n2)) | (~m_main_v_state2(s18, c_t2))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1862, 1861])).
% 0.77/0.94 tff(1864,plain,
% 0.77/0.94 (~m_main_v_state2(s18, c_n2)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1863, 77, 1860])).
% 0.77/0.94 tff(1865,plain,
% 0.77/0.94 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s18, c_n2) | (~node8(s18)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s18, c_n2) | (~node8(s18)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1866,plain,
% 0.77/0.94 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s18, c_n2) | (~node8(s18)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1867,plain,
% 0.77/0.94 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s18, c_n2) | (~node8(s18))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1866, 1865])).
% 0.77/0.94 tff(1868,plain,
% 0.77/0.94 (~node8(s18)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1867, 271, 1864])).
% 0.77/0.94 tff(1869,plain,
% 0.77/0.94 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s18, c_n2) | (~node9(s18)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s18, c_n2) | (~node9(s18)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1870,plain,
% 0.77/0.94 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s18, c_n2) | (~node9(s18)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1871,plain,
% 0.77/0.94 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s18, c_n2) | (~node9(s18))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1870, 1869])).
% 0.77/0.94 tff(1872,plain,
% 0.77/0.94 (~node9(s18)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1871, 88, 1864])).
% 0.77/0.94 tff(1873,plain,
% 0.77/0.94 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s18, c_n2) | (~node10(s18)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s18, c_n2) | (~node10(s18)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1874,plain,
% 0.77/0.94 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s18, c_n2) | (~node10(s18)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1875,plain,
% 0.77/0.94 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s18, c_n2) | (~node10(s18))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1874, 1873])).
% 0.77/0.94 tff(1876,plain,
% 0.77/0.94 (~node10(s18)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1875, 249, 1864])).
% 0.77/0.94 tff(1877,plain,
% 0.77/0.94 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s18, c_t2)) | (~m_main_v_state2(s18, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s18, c_t2)) | (~m_main_v_state2(s18, c_c2)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1878,plain,
% 0.77/0.94 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s18, c_t2)) | (~m_main_v_state2(s18, c_c2)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1879,plain,
% 0.77/0.94 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s18, c_t2)) | (~m_main_v_state2(s18, c_c2))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1878, 1877])).
% 0.77/0.94 tff(1880,plain,
% 0.77/0.94 (~m_main_v_state2(s18, c_c2)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1879, 260, 1860])).
% 0.77/0.94 tff(1881,plain,
% 0.77/0.94 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s17, c_n2)) | (~m_main_v_state2(s17, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s17, c_n2)) | (~m_main_v_state2(s17, c_c2)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1882,plain,
% 0.77/0.94 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s17, c_n2)) | (~m_main_v_state2(s17, c_c2)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1883,plain,
% 0.77/0.94 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s17, c_n2)) | (~m_main_v_state2(s17, c_c2))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1882, 1881])).
% 0.77/0.94 tff(1884,plain,
% 0.77/0.94 (~m_main_v_state2(s17, c_c2)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1883, 697, 1816])).
% 0.77/0.94 tff(1885,plain,
% 0.77/0.94 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s17, c_c2) | (~node3(s17)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s17, c_c2) | (~node3(s17)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1886,plain,
% 0.77/0.94 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s17, c_c2) | (~node3(s17)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1887,plain,
% 0.77/0.94 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s17, c_c2) | (~node3(s17))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1886, 1885])).
% 0.77/0.94 tff(1888,plain,
% 0.77/0.94 (~node3(s17)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1887, 399, 1884])).
% 0.77/0.94 tff(1889,plain,
% 0.77/0.94 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s16, c_n1) | (~m_main_v_state1(s17, c_n1)) | (~node6(s16, s17)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s16, c_n1) | (~m_main_v_state1(s17, c_n1)) | (~node6(s16, s17)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1890,plain,
% 0.77/0.94 (((~node6(s16, s17)) | m_main_v_state1(s16, c_n1) | (~m_main_v_state1(s17, c_n1))) <=> (m_main_v_state1(s16, c_n1) | (~m_main_v_state1(s17, c_n1)) | (~node6(s16, s17)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1891,plain,
% 0.77/0.94 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s16, s17)) | m_main_v_state1(s16, c_n1) | (~m_main_v_state1(s17, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s16, c_n1) | (~m_main_v_state1(s17, c_n1)) | (~node6(s16, s17))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[1890])).
% 0.77/0.94 tff(1892,plain,
% 0.77/0.94 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s16, s17)) | m_main_v_state1(s16, c_n1) | (~m_main_v_state1(s17, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s16, c_n1) | (~m_main_v_state1(s17, c_n1)) | (~node6(s16, s17)))),
% 0.77/0.94 inference(transitivity,[status(thm)],[1891, 1889])).
% 0.77/0.94 tff(1893,plain,
% 0.77/0.94 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s16, s17)) | m_main_v_state1(s16, c_n1) | (~m_main_v_state1(s17, c_n1)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1894,plain,
% 0.77/0.94 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s16, c_n1) | (~m_main_v_state1(s17, c_n1)) | (~node6(s16, s17))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1893, 1892])).
% 0.77/0.94 tff(1895,plain,
% 0.77/0.94 (~m_main_v_state1(s17, c_n1)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1894, 835, 1688, 1773])).
% 0.77/0.94 tff(1896,plain,
% 0.77/0.94 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s17, c_n1) | (~node2(s17)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s17, c_n1) | (~node2(s17)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1897,plain,
% 0.77/0.94 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s17, c_n1) | (~node2(s17)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1898,plain,
% 0.77/0.94 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s17, c_n1) | (~node2(s17))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1897, 1896])).
% 0.77/0.94 tff(1899,plain,
% 0.77/0.94 (~node2(s17)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1898, 787, 1895])).
% 0.77/0.94 tff(1900,plain,
% 0.77/0.94 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s17, c_t2) | (~node1(s17)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s17, c_t2) | (~node1(s17)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1901,plain,
% 0.77/0.94 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s17, c_t2) | (~node1(s17)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1902,plain,
% 0.77/0.94 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s17, c_t2) | (~node1(s17))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1901, 1900])).
% 0.77/0.94 tff(1903,plain,
% 0.77/0.94 (~node1(s17)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1902, 195, 1820])).
% 0.77/0.94 tff(1904,plain,
% 0.77/0.94 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s17, s18)) | node7(s17, s18))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s17, s18)) | node7(s17, s18))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1905,plain,
% 0.77/0.94 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s17, s18)) | node7(s17, s18))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1906,plain,
% 0.77/0.94 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s17, s18)) | node7(s17, s18)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1905, 1904])).
% 0.77/0.94 tff(1907,plain,
% 0.77/0.94 (node7(s17, s18)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1906, 206, 1831])).
% 0.77/0.94 tff(1908,plain,
% 0.77/0.94 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_state1(s18, c_c1) | node1(s17) | node2(s17) | node3(s17) | (~node7(s17, s18)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_state1(s18, c_c1) | node1(s17) | node2(s17) | node3(s17) | (~node7(s17, s18)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1909,plain,
% 0.77/0.94 (((~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | node1(s17) | node2(s17) | node3(s17) | (~node7(s17, s18)) | m_main_v_state1(s18, c_c1)) <=> ((~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_state1(s18, c_c1) | node1(s17) | node2(s17) | node3(s17) | (~node7(s17, s18)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1910,plain,
% 0.77/0.94 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | node1(s17) | node2(s17) | node3(s17) | (~node7(s17, s18)) | m_main_v_state1(s18, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_state1(s18, c_c1) | node1(s17) | node2(s17) | node3(s17) | (~node7(s17, s18))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[1909])).
% 0.77/0.94 tff(1911,plain,
% 0.77/0.94 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | node1(s17) | node2(s17) | node3(s17) | (~node7(s17, s18)) | m_main_v_state1(s18, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_state1(s18, c_c1) | node1(s17) | node2(s17) | node3(s17) | (~node7(s17, s18)))),
% 0.77/0.94 inference(transitivity,[status(thm)],[1910, 1908])).
% 0.77/0.94 tff(1912,plain,
% 0.77/0.94 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | node1(s17) | node2(s17) | node3(s17) | (~node7(s17, s18)) | m_main_v_state1(s18, c_c1))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1913,plain,
% 0.77/0.94 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_state1(s18, c_c1) | node1(s17) | node2(s17) | node3(s17) | (~node7(s17, s18))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1912, 1911])).
% 0.77/0.94 tff(1914,plain,
% 0.77/0.94 ((~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_state1(s18, c_c1) | node1(s17) | node2(s17) | node3(s17)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1913, 892, 1907])).
% 0.77/0.94 tff(1915,plain,
% 0.77/0.94 (m_main_v_state1(s18, c_c1)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1914, 1903, 1816, 1780, 1899, 1888])).
% 0.77/0.94 tff(1916,plain,
% 0.77/0.94 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s18, c_n1)) | (~m_main_v_state1(s18, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s18, c_n1)) | (~m_main_v_state1(s18, c_c1)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1917,plain,
% 0.77/0.94 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s18, c_n1)) | (~m_main_v_state1(s18, c_c1)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1918,plain,
% 0.77/0.94 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s18, c_n1)) | (~m_main_v_state1(s18, c_c1))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1917, 1916])).
% 0.77/0.94 tff(1919,plain,
% 0.77/0.94 (~m_main_v_state1(s18, c_n1)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1918, 454, 1915])).
% 0.77/0.94 tff(1920,plain,
% 0.77/0.94 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s18, c_n1) | (~node11(s18)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s18, c_n1) | (~node11(s18)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1921,plain,
% 0.77/0.94 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s18, c_n1) | (~node11(s18)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1922,plain,
% 0.77/0.94 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s18, c_n1) | (~node11(s18))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1921, 1920])).
% 0.77/0.94 tff(1923,plain,
% 0.77/0.94 (~node11(s18)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1922, 238, 1919])).
% 0.77/0.94 tff(1924,plain,
% 0.77/0.94 (succ(s18, s19) <=> succ(s18, s19)),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1925,axiom,(succ(s18, s19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound19')).
% 0.77/0.94 tff(1926,plain,
% 0.77/0.94 (succ(s18, s19)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1925, 1924])).
% 0.77/0.94 tff(1927,plain,
% 0.77/0.94 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s18, s19)) | trans(s18, s19))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s18, s19)) | trans(s18, s19))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1928,plain,
% 0.77/0.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s18, s19)) | trans(s18, s19))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1929,plain,
% 0.77/0.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s18, s19)) | trans(s18, s19)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1928, 1927])).
% 0.77/0.94 tff(1930,plain,
% 0.77/0.94 (trans(s18, s19)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1929, 1926, 32])).
% 0.77/0.94 tff(1931,plain,
% 0.77/0.94 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s18, s19)) | node14(s18, s19))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s18, s19)) | node14(s18, s19))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1932,plain,
% 0.77/0.94 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s18, s19)) | node14(s18, s19))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1933,plain,
% 0.77/0.94 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s18, s19)) | node14(s18, s19)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1932, 1931])).
% 0.77/0.94 tff(1934,plain,
% 0.77/0.94 (node14(s18, s19)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1933, 46, 1930])).
% 0.77/0.94 tff(1935,plain,
% 0.77/0.94 (((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s18, c_c2) | node9(s18) | node8(s18) | node10(s18) | node11(s18) | node12(s18) | node13(s18, s19) | (~node14(s18, s19)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s18, c_c2) | node9(s18) | node8(s18) | node10(s18) | node11(s18) | node12(s18) | node13(s18, s19) | (~node14(s18, s19)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1936,plain,
% 0.77/0.94 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s18, c_c2) | node9(s18) | node8(s18) | node10(s18) | node11(s18) | node12(s18) | node13(s18, s19) | (~node14(s18, s19)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1937,plain,
% 0.77/0.94 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s18, c_c2) | node9(s18) | node8(s18) | node10(s18) | node11(s18) | node12(s18) | node13(s18, s19) | (~node14(s18, s19))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1936, 1935])).
% 0.77/0.94 tff(1938,plain,
% 0.77/0.94 (m_main_v_state2(s18, c_c2) | node9(s18) | node8(s18) | node10(s18) | node11(s18) | node12(s18) | node13(s18, s19)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1937, 296, 1934])).
% 0.77/0.94 tff(1939,plain,
% 0.77/0.94 (node13(s18, s19)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1938, 1923, 1880, 1876, 1872, 1868, 1851])).
% 0.77/0.94 tff(1940,plain,
% 0.77/0.94 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s18, c_n2) | (~m_main_v_state2(s19, c_n2)) | (~node13(s18, s19)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s18, c_n2) | (~m_main_v_state2(s19, c_n2)) | (~node13(s18, s19)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1941,plain,
% 0.77/0.94 (((~node13(s18, s19)) | m_main_v_state2(s18, c_n2) | (~m_main_v_state2(s19, c_n2))) <=> (m_main_v_state2(s18, c_n2) | (~m_main_v_state2(s19, c_n2)) | (~node13(s18, s19)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1942,plain,
% 0.77/0.94 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s18, s19)) | m_main_v_state2(s18, c_n2) | (~m_main_v_state2(s19, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s18, c_n2) | (~m_main_v_state2(s19, c_n2)) | (~node13(s18, s19))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[1941])).
% 0.77/0.94 tff(1943,plain,
% 0.77/0.94 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s18, s19)) | m_main_v_state2(s18, c_n2) | (~m_main_v_state2(s19, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s18, c_n2) | (~m_main_v_state2(s19, c_n2)) | (~node13(s18, s19)))),
% 0.77/0.94 inference(transitivity,[status(thm)],[1942, 1940])).
% 0.77/0.94 tff(1944,plain,
% 0.77/0.94 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s18, s19)) | m_main_v_state2(s18, c_n2) | (~m_main_v_state2(s19, c_n2)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1945,plain,
% 0.77/0.94 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s18, c_n2) | (~m_main_v_state2(s19, c_n2)) | (~node13(s18, s19))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1944, 1943])).
% 0.77/0.94 tff(1946,plain,
% 0.77/0.94 (~m_main_v_state2(s19, c_n2)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1945, 311, 1864, 1939])).
% 0.77/0.94 tff(1947,plain,
% 0.77/0.94 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s19, c_n2) | (~node9(s19)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s19, c_n2) | (~node9(s19)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1948,plain,
% 0.77/0.94 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s19, c_n2) | (~node9(s19)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1949,plain,
% 0.77/0.94 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s19, c_n2) | (~node9(s19))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1948, 1947])).
% 0.77/0.94 tff(1950,plain,
% 0.77/0.94 (~node9(s19)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1949, 88, 1946])).
% 0.77/0.94 tff(1951,plain,
% 0.77/0.94 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s19, c_n2) | (~node10(s19)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s19, c_n2) | (~node10(s19)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1952,plain,
% 0.77/0.94 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s19, c_n2) | (~node10(s19)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1953,plain,
% 0.77/0.94 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s19, c_n2) | (~node10(s19))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1952, 1951])).
% 0.77/0.94 tff(1954,plain,
% 0.77/0.94 (~node10(s19)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1953, 249, 1946])).
% 0.77/0.94 tff(1955,plain,
% 0.77/0.94 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s18, c_t2)) | m_main_v_state2(s19, c_t2) | (~node13(s18, s19)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s18, c_t2)) | m_main_v_state2(s19, c_t2) | (~node13(s18, s19)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1956,plain,
% 0.77/0.95 (((~node13(s18, s19)) | (~m_main_v_state2(s18, c_t2)) | m_main_v_state2(s19, c_t2)) <=> ((~m_main_v_state2(s18, c_t2)) | m_main_v_state2(s19, c_t2) | (~node13(s18, s19)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1957,plain,
% 0.77/0.95 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s18, s19)) | (~m_main_v_state2(s18, c_t2)) | m_main_v_state2(s19, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s18, c_t2)) | m_main_v_state2(s19, c_t2) | (~node13(s18, s19))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[1956])).
% 0.77/0.95 tff(1958,plain,
% 0.77/0.95 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s18, s19)) | (~m_main_v_state2(s18, c_t2)) | m_main_v_state2(s19, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s18, c_t2)) | m_main_v_state2(s19, c_t2) | (~node13(s18, s19)))),
% 0.77/0.95 inference(transitivity,[status(thm)],[1957, 1955])).
% 0.77/0.95 tff(1959,plain,
% 0.77/0.95 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s18, s19)) | (~m_main_v_state2(s18, c_t2)) | m_main_v_state2(s19, c_t2))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(1960,plain,
% 0.77/0.95 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s18, c_t2)) | m_main_v_state2(s19, c_t2) | (~node13(s18, s19))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1959, 1958])).
% 0.77/0.95 tff(1961,plain,
% 0.77/0.95 (m_main_v_state2(s19, c_t2)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1960, 518, 1860, 1939])).
% 0.77/0.95 tff(1962,plain,
% 0.77/0.95 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s18, c_t1)) | (~m_main_v_state1(s18, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s18, c_t1)) | (~m_main_v_state1(s18, c_c1)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1963,plain,
% 0.77/0.95 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s18, c_t1)) | (~m_main_v_state1(s18, c_c1)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(1964,plain,
% 0.77/0.95 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s18, c_t1)) | (~m_main_v_state1(s18, c_c1))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1963, 1962])).
% 0.77/0.95 tff(1965,plain,
% 0.77/0.95 (~m_main_v_state1(s18, c_t1)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1964, 539, 1915])).
% 0.77/0.95 tff(1966,plain,
% 0.77/0.95 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s18, c_t1) | (~node5(s18)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s18, c_t1) | (~node5(s18)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1967,plain,
% 0.77/0.95 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s18, c_t1) | (~node5(s18)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(1968,plain,
% 0.77/0.95 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s18, c_t1) | (~node5(s18))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1967, 1966])).
% 0.77/0.95 tff(1969,plain,
% 0.77/0.95 (~node5(s18)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1968, 550, 1965])).
% 0.77/0.95 tff(1970,plain,
% 0.77/0.95 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s18, c_n2) | (~node4(s18)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s18, c_n2) | (~node4(s18)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1971,plain,
% 0.77/0.95 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s18, c_n2) | (~node4(s18)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(1972,plain,
% 0.77/0.95 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s18, c_n2) | (~node4(s18))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1971, 1970])).
% 0.77/0.95 tff(1973,plain,
% 0.77/0.95 (~node4(s18)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1972, 388, 1864])).
% 0.77/0.95 tff(1974,plain,
% 0.77/0.95 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s18, c_c2) | (~node3(s18)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s18, c_c2) | (~node3(s18)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1975,plain,
% 0.77/0.95 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s18, c_c2) | (~node3(s18)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(1976,plain,
% 0.77/0.95 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s18, c_c2) | (~node3(s18))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1975, 1974])).
% 0.77/0.95 tff(1977,plain,
% 0.77/0.95 (~node3(s18)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1976, 399, 1880])).
% 0.77/0.95 tff(1978,plain,
% 0.77/0.95 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s18, c_n2) | (~node2(s18)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s18, c_n2) | (~node2(s18)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1979,plain,
% 0.77/0.95 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s18, c_n2) | (~node2(s18)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(1980,plain,
% 0.77/0.95 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s18, c_n2) | (~node2(s18))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1979, 1978])).
% 0.77/0.95 tff(1981,plain,
% 0.77/0.95 (~node2(s18)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1980, 410, 1864])).
% 0.77/0.95 tff(1982,plain,
% 0.77/0.95 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s18, c_n1) | (~node1(s18)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s18, c_n1) | (~node1(s18)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1983,plain,
% 0.77/0.95 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s18, c_n1) | (~node1(s18)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(1984,plain,
% 0.77/0.95 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s18, c_n1) | (~node1(s18))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1983, 1982])).
% 0.77/0.95 tff(1985,plain,
% 0.77/0.95 (~node1(s18)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1984, 421, 1919])).
% 0.77/0.95 tff(1986,plain,
% 0.77/0.95 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s18, s19)) | node7(s18, s19))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s18, s19)) | node7(s18, s19))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1987,plain,
% 0.77/0.95 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s18, s19)) | node7(s18, s19))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(1988,plain,
% 0.77/0.95 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s18, s19)) | node7(s18, s19)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1987, 1986])).
% 0.77/0.95 tff(1989,plain,
% 0.77/0.95 (node7(s18, s19)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1988, 206, 1930])).
% 0.77/0.95 tff(1990,plain,
% 0.77/0.95 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s19, c_n1) | (~m_main_v_state1(s18, c_c1)) | node1(s18) | node2(s18) | node3(s18) | node4(s18) | node5(s18) | (~node7(s18, s19)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s19, c_n1) | (~m_main_v_state1(s18, c_c1)) | node1(s18) | node2(s18) | node3(s18) | node4(s18) | node5(s18) | (~node7(s18, s19)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1991,plain,
% 0.77/0.95 (((~m_main_v_state1(s18, c_c1)) | node1(s18) | node2(s18) | node3(s18) | node4(s18) | node5(s18) | (~node7(s18, s19)) | m_main_v_state1(s19, c_n1)) <=> (m_main_v_state1(s19, c_n1) | (~m_main_v_state1(s18, c_c1)) | node1(s18) | node2(s18) | node3(s18) | node4(s18) | node5(s18) | (~node7(s18, s19)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1992,plain,
% 0.77/0.95 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s18, c_c1)) | node1(s18) | node2(s18) | node3(s18) | node4(s18) | node5(s18) | (~node7(s18, s19)) | m_main_v_state1(s19, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s19, c_n1) | (~m_main_v_state1(s18, c_c1)) | node1(s18) | node2(s18) | node3(s18) | node4(s18) | node5(s18) | (~node7(s18, s19))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[1991])).
% 0.77/0.95 tff(1993,plain,
% 0.77/0.95 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s18, c_c1)) | node1(s18) | node2(s18) | node3(s18) | node4(s18) | node5(s18) | (~node7(s18, s19)) | m_main_v_state1(s19, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s19, c_n1) | (~m_main_v_state1(s18, c_c1)) | node1(s18) | node2(s18) | node3(s18) | node4(s18) | node5(s18) | (~node7(s18, s19)))),
% 0.77/0.95 inference(transitivity,[status(thm)],[1992, 1990])).
% 0.77/0.95 tff(1994,plain,
% 0.77/0.95 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s18, c_c1)) | node1(s18) | node2(s18) | node3(s18) | node4(s18) | node5(s18) | (~node7(s18, s19)) | m_main_v_state1(s19, c_n1))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(1995,plain,
% 0.77/0.95 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s19, c_n1) | (~m_main_v_state1(s18, c_c1)) | node1(s18) | node2(s18) | node3(s18) | node4(s18) | node5(s18) | (~node7(s18, s19))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1994, 1993])).
% 0.77/0.95 tff(1996,plain,
% 0.77/0.95 (m_main_v_state1(s19, c_n1) | (~m_main_v_state1(s18, c_c1)) | node1(s18) | node2(s18) | node3(s18) | node4(s18) | node5(s18)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1995, 584, 1989])).
% 0.77/0.95 tff(1997,plain,
% 0.77/0.95 (m_main_v_state1(s19, c_n1)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1996, 1985, 1915, 1981, 1977, 1973, 1969])).
% 0.77/0.95 tff(1998,plain,
% 0.77/0.95 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s19, c_n2) | (~node8(s19)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s19, c_n2) | (~node8(s19)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1999,plain,
% 0.77/0.95 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s19, c_n2) | (~node8(s19)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(2000,plain,
% 0.77/0.95 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s19, c_n2) | (~node8(s19))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1999, 1998])).
% 0.77/0.95 tff(2001,plain,
% 0.77/0.95 (~node8(s19)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[2000, 271, 1946])).
% 0.77/0.95 tff(2002,plain,
% 0.77/0.95 (succ(s19, s20) <=> succ(s19, s20)),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(2003,axiom,(succ(s19, s20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound20')).
% 0.77/0.95 tff(2004,plain,
% 0.77/0.95 (succ(s19, s20)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[2003, 2002])).
% 0.77/0.95 tff(2005,plain,
% 0.77/0.95 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s19, s20)) | trans(s19, s20))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s19, s20)) | trans(s19, s20))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(2006,plain,
% 0.77/0.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s19, s20)) | trans(s19, s20))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(2007,plain,
% 0.77/0.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s19, s20)) | trans(s19, s20)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[2006, 2005])).
% 0.77/0.95 tff(2008,plain,
% 0.77/0.95 (trans(s19, s20)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[2007, 2004, 32])).
% 0.77/0.95 tff(2009,plain,
% 0.77/0.95 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s19, s20)) | node14(s19, s20))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s19, s20)) | node14(s19, s20))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(2010,plain,
% 0.77/0.95 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s19, s20)) | node14(s19, s20))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(2011,plain,
% 0.77/0.95 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s19, s20)) | node14(s19, s20)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[2010, 2009])).
% 0.77/0.95 tff(2012,plain,
% 0.77/0.95 (node14(s19, s20)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[2011, 46, 2008])).
% 0.77/0.95 tff(2013,plain,
% 0.77/0.95 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | node9(s19) | node8(s19) | node10(s19) | (~node14(s19, s20)) | m_main_v_state2(s20, c_c2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | node9(s19) | node8(s19) | node10(s19) | (~node14(s19, s20)) | m_main_v_state2(s20, c_c2))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(2014,plain,
% 0.77/0.95 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | node9(s19) | node8(s19) | node10(s19) | (~node14(s19, s20)) | m_main_v_state2(s20, c_c2))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(2015,plain,
% 0.77/0.95 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | node9(s19) | node8(s19) | node10(s19) | (~node14(s19, s20)) | m_main_v_state2(s20, c_c2)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[2014, 2013])).
% 0.77/0.95 tff(2016,plain,
% 0.77/0.95 ((~m_main_v_state1(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | node9(s19) | node8(s19) | node10(s19) | m_main_v_state2(s20, c_c2)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[2015, 617, 2012])).
% 0.77/0.95 tff(2017,plain,
% 0.77/0.95 (m_main_v_state2(s20, c_c2)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[2016, 2001, 1997, 1961, 1954, 1950])).
% 0.77/0.95 tff(2018,plain,
% 0.77/0.95 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s20, c_t2)) | (~m_main_v_state2(s20, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s20, c_t2)) | (~m_main_v_state2(s20, c_c2)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(2019,plain,
% 0.77/0.95 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s20, c_t2)) | (~m_main_v_state2(s20, c_c2)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(2020,plain,
% 0.77/0.95 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s20, c_t2)) | (~m_main_v_state2(s20, c_c2))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[2019, 2018])).
% 0.77/0.95 tff(2021,plain,
% 0.77/0.95 (~m_main_v_state2(s20, c_t2)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[2020, 260, 2017])).
% 0.77/0.95 tff(2022,plain,
% 0.77/0.95 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s20, c_t2) | (~node12(s20)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s20, c_t2) | (~node12(s20)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(2023,plain,
% 0.77/0.95 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s20, c_t2) | (~node12(s20)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(2024,plain,
% 0.77/0.95 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s20, c_t2) | (~node12(s20))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[2023, 2022])).
% 0.77/0.95 tff(2025,plain,
% 0.77/0.95 (~node12(s20)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[2024, 633, 2021])).
% 0.77/0.95 tff(2026,plain,
% 0.77/0.95 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s19, s20)) | node7(s19, s20))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s19, s20)) | node7(s19, s20))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(2027,plain,
% 0.77/0.95 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s19, s20)) | node7(s19, s20))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(2028,plain,
% 0.77/0.95 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s19, s20)) | node7(s19, s20)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[2027, 2026])).
% 0.77/0.95 tff(2029,plain,
% 0.77/0.95 (node7(s19, s20)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[2028, 206, 2008])).
% 0.77/0.95 tff(2030,plain,
% 0.77/0.95 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | (~node7(s19, s20)) | m_main_v_state1(s20, c_t1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | (~node7(s19, s20)) | m_main_v_state1(s20, c_t1))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(2031,plain,
% 0.77/0.95 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | (~node7(s19, s20)) | m_main_v_state1(s20, c_t1))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(2032,plain,
% 0.77/0.95 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | (~node7(s19, s20)) | m_main_v_state1(s20, c_t1)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[2031, 2030])).
% 0.77/0.95 tff(2033,plain,
% 0.77/0.95 ((~m_main_v_state1(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | m_main_v_state1(s20, c_t1)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[2032, 651, 2029])).
% 0.77/0.95 tff(2034,plain,
% 0.77/0.95 (m_main_v_state1(s20, c_t1)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[2033, 1961, 1997])).
% 0.77/0.95 tff(2035,plain,
% 0.77/0.95 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s20, c_n1)) | (~m_main_v_state1(s20, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s20, c_n1)) | (~m_main_v_state1(s20, c_t1)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(2036,plain,
% 0.77/0.95 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s20, c_n1)) | (~m_main_v_state1(s20, c_t1)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(2037,plain,
% 0.77/0.95 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s20, c_n1)) | (~m_main_v_state1(s20, c_t1))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[2036, 2035])).
% 0.77/0.95 tff(2038,plain,
% 0.77/0.95 (~m_main_v_state1(s20, c_n1)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[2037, 10, 2034])).
% 0.77/0.95 tff(2039,plain,
% 0.77/0.95 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s20, c_n1) | (~node11(s20)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s20, c_n1) | (~node11(s20)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(2040,plain,
% 0.77/0.95 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s20, c_n1) | (~node11(s20)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(2041,plain,
% 0.77/0.95 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s20, c_n1) | (~node11(s20))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[2040, 2039])).
% 0.77/0.95 tff(2042,plain,
% 0.77/0.95 (~node11(s20)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[2041, 238, 2038])).
% 0.77/0.95 tff(2043,plain,
% 0.77/0.95 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s20, c_t1)) | (~m_main_v_state1(s20, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s20, c_t1)) | (~m_main_v_state1(s20, c_c1)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(2044,plain,
% 0.77/0.95 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s20, c_t1)) | (~m_main_v_state1(s20, c_c1)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(2045,plain,
% 0.77/0.95 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s20, c_t1)) | (~m_main_v_state1(s20, c_c1))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[2044, 2043])).
% 0.77/0.95 tff(2046,plain,
% 0.77/0.95 (~m_main_v_state1(s20, c_c1)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[2045, 539, 2034])).
% 0.77/0.95 tff(2047,plain,
% 0.77/0.95 (((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s20, c_c1) | (~node10(s20)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s20, c_c1) | (~node10(s20)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(2048,plain,
% 0.77/0.95 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s20, c_c1) | (~node10(s20)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(2049,plain,
% 0.77/0.95 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s20, c_c1) | (~node10(s20))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[2048, 2047])).
% 0.77/0.95 tff(2050,plain,
% 0.77/0.95 (~node10(s20)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[2049, 675, 2046])).
% 0.77/0.95 tff(2051,plain,
% 0.77/0.95 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s20, c_n1) | (~node9(s20)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s20, c_n1) | (~node9(s20)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(2052,plain,
% 0.77/0.95 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s20, c_n1) | (~node9(s20)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(2053,plain,
% 0.77/0.95 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s20, c_n1) | (~node9(s20))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[2052, 2051])).
% 0.77/0.95 tff(2054,plain,
% 0.77/0.95 (~node9(s20)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[2053, 686, 2038])).
% 0.77/0.95 tff(2055,plain,
% 0.77/0.95 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s20, c_n2)) | (~m_main_v_state2(s20, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s20, c_n2)) | (~m_main_v_state2(s20, c_c2)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(2056,plain,
% 0.77/0.95 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s20, c_n2)) | (~m_main_v_state2(s20, c_c2)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(2057,plain,
% 0.77/0.95 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s20, c_n2)) | (~m_main_v_state2(s20, c_c2))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[2056, 2055])).
% 0.77/0.95 tff(2058,plain,
% 0.77/0.95 (~m_main_v_state2(s20, c_n2)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[2057, 697, 2017])).
% 0.77/0.95 tff(2059,plain,
% 0.77/0.95 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s20, c_n2) | (~node8(s20)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s20, c_n2) | (~node8(s20)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(2060,plain,
% 0.77/0.95 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s20, c_n2) | (~node8(s20)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(2061,plain,
% 0.77/0.95 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s20, c_n2) | (~node8(s20))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[2060, 2059])).
% 0.77/0.95 tff(2062,plain,
% 0.77/0.95 (~node8(s20)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[2061, 271, 2058])).
% 0.77/0.95 tff(2063,plain,
% 0.77/0.95 (succ(s20, s21) <=> succ(s20, s21)),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(2064,axiom,(succ(s20, s21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound21')).
% 0.77/0.95 tff(2065,plain,
% 0.77/0.95 (succ(s20, s21)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[2064, 2063])).
% 0.77/0.95 tff(2066,plain,
% 0.77/0.95 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s20, s21)) | trans(s20, s21))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s20, s21)) | trans(s20, s21))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(2067,plain,
% 0.77/0.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s20, s21)) | trans(s20, s21))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(2068,plain,
% 0.77/0.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s20, s21)) | trans(s20, s21)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[2067, 2066])).
% 0.77/0.95 tff(2069,plain,
% 0.77/0.95 (trans(s20, s21)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[2068, 2065, 32])).
% 0.77/0.95 tff(2070,plain,
% 0.77/0.95 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s20, s21)) | node14(s20, s21))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s20, s21)) | node14(s20, s21))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(2071,plain,
% 0.77/0.95 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s20, s21)) | node14(s20, s21))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(2072,plain,
% 0.77/0.95 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s20, s21)) | node14(s20, s21)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[2071, 2070])).
% 0.77/0.95 tff(2073,plain,
% 0.77/0.95 (node14(s20, s21)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[2072, 46, 2069])).
% 0.77/0.95 tff(2074,plain,
% 0.77/0.95 (((~![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(s21, c_n2) | node9(s20) | node8(s20) | node10(s20) | node11(s20) | node12(s20) | (~node14(s20, s21)) | (~m_main_v_state2(s20, c_c2)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s21, c_n2) | node9(s20) | node8(s20) | node10(s20) | node11(s20) | node12(s20) | (~node14(s20, s21)) | (~m_main_v_state2(s20, c_c2)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(2075,plain,
% 0.77/0.95 (((~m_main_v_state2(s20, c_c2)) | node9(s20) | node8(s20) | node10(s20) | node11(s20) | node12(s20) | (~node14(s20, s21)) | m_main_v_state2(s21, c_n2)) <=> (m_main_v_state2(s21, c_n2) | node9(s20) | node8(s20) | node10(s20) | node11(s20) | node12(s20) | (~node14(s20, s21)) | (~m_main_v_state2(s20, c_c2)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(2076,plain,
% 0.77/0.95 (((~![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(s20, c_c2)) | node9(s20) | node8(s20) | node10(s20) | node11(s20) | node12(s20) | (~node14(s20, s21)) | m_main_v_state2(s21, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s21, c_n2) | node9(s20) | node8(s20) | node10(s20) | node11(s20) | node12(s20) | (~node14(s20, s21)) | (~m_main_v_state2(s20, c_c2))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[2075])).
% 0.77/0.95 tff(2077,plain,
% 0.77/0.95 (((~![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(s20, c_c2)) | node9(s20) | node8(s20) | node10(s20) | node11(s20) | node12(s20) | (~node14(s20, s21)) | m_main_v_state2(s21, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s21, c_n2) | node9(s20) | node8(s20) | node10(s20) | node11(s20) | node12(s20) | (~node14(s20, s21)) | (~m_main_v_state2(s20, c_c2)))),
% 0.77/0.95 inference(transitivity,[status(thm)],[2076, 2074])).
% 0.77/0.95 tff(2078,plain,
% 0.77/0.95 ((~![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(s20, c_c2)) | node9(s20) | node8(s20) | node10(s20) | node11(s20) | node12(s20) | (~node14(s20, s21)) | m_main_v_state2(s21, c_n2))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(2079,plain,
% 0.77/0.95 ((~![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(s21, c_n2) | node9(s20) | node8(s20) | node10(s20) | node11(s20) | node12(s20) | (~node14(s20, s21)) | (~m_main_v_state2(s20, c_c2))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[2078, 2077])).
% 0.77/0.95 tff(2080,plain,
% 0.77/0.95 (m_main_v_state2(s21, c_n2) | node9(s20) | node8(s20) | node10(s20) | node11(s20) | node12(s20) | (~m_main_v_state2(s20, c_c2))),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[2079, 726, 2073])).
% 0.77/0.95 tff(2081,plain,
% 0.77/0.95 (m_main_v_state2(s21, c_n2)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[2080, 2062, 2017, 2054, 2050, 2042, 2025])).
% 0.77/0.95 tff(2082,plain,
% 0.77/0.95 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s21, c_n2)) | (~m_main_v_state2(s21, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s21, c_n2)) | (~m_main_v_state2(s21, c_c2)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(2083,plain,
% 0.77/0.95 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s21, c_n2)) | (~m_main_v_state2(s21, c_c2)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(2084,plain,
% 0.77/0.95 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s21, c_n2)) | (~m_main_v_state2(s21, c_c2))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[2083, 2082])).
% 0.77/0.95 tff(2085,plain,
% 0.77/0.95 (~m_main_v_state2(s21, c_c2)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[2084, 697, 2081])).
% 0.77/0.95 tff(2086,plain,
% 0.77/0.95 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s21, c_c2) | (~node3(s21)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s21, c_c2) | (~node3(s21)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(2087,plain,
% 0.77/0.95 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s21, c_c2) | (~node3(s21)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(2088,plain,
% 0.77/0.95 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s21, c_c2) | (~node3(s21))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[2087, 2086])).
% 0.77/0.95 tff(2089,plain,
% 0.77/0.95 (~node3(s21)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[2088, 399, 2085])).
% 0.77/0.95 tff(2090,plain,
% 0.77/0.95 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s20, c_n1) | (~node1(s20)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s20, c_n1) | (~node1(s20)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(2091,plain,
% 0.77/0.95 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s20, c_n1) | (~node1(s20)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(2092,plain,
% 0.77/0.95 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s20, c_n1) | (~node1(s20))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[2091, 2090])).
% 0.77/0.95 tff(2093,plain,
% 0.77/0.95 (~node1(s20)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[2092, 421, 2038])).
% 0.77/0.95 tff(2094,plain,
% 0.77/0.95 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s19, s20)) | node18(s19, s20))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s19, s20)) | node18(s19, s20))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(2095,plain,
% 0.77/0.95 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s19, s20)) | node18(s19, s20))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(2096,plain,
% 0.77/0.95 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s19, s20)) | node18(s19, s20)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[2095, 2094])).
% 0.77/0.95 tff(2097,plain,
% 0.77/0.95 (node18(s19, s20)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[2096, 125, 2008])).
% 0.77/0.95 tff(2098,plain,
% 0.77/0.95 (((~![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(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | (~node18(s19, s20)) | m_main_v_turn(s20, c_2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | (~node18(s19, s20)) | m_main_v_turn(s20, c_2))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2099,plain,
% 0.77/0.96 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | (~node18(s19, s20)) | m_main_v_turn(s20, c_2))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(2100,plain,
% 0.77/0.96 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | (~node18(s19, s20)) | m_main_v_turn(s20, c_2)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[2099, 2098])).
% 0.77/0.96 tff(2101,plain,
% 0.77/0.96 ((~m_main_v_state1(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | m_main_v_turn(s20, c_2)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[2100, 760, 2097])).
% 0.77/0.96 tff(2102,plain,
% 0.77/0.96 (m_main_v_turn(s20, c_2)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[2101, 1961, 1997])).
% 0.77/0.96 tff(2103,plain,
% 0.77/0.96 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s20, c_1)) | (~m_main_v_turn(s20, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s20, c_1)) | (~m_main_v_turn(s20, c_2)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2104,plain,
% 0.77/0.96 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s20, c_1)) | (~m_main_v_turn(s20, c_2)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(2105,plain,
% 0.77/0.96 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s20, c_1)) | (~m_main_v_turn(s20, c_2))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[2104, 2103])).
% 0.77/0.96 tff(2106,plain,
% 0.77/0.96 (~m_main_v_turn(s20, c_1)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[2105, 156, 2102])).
% 0.77/0.96 tff(2107,plain,
% 0.77/0.96 (((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s20, c_1) | (~node5(s20)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s20, c_1) | (~node5(s20)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2108,plain,
% 0.77/0.96 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s20, c_1) | (~node5(s20)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(2109,plain,
% 0.77/0.96 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s20, c_1) | (~node5(s20))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[2108, 2107])).
% 0.77/0.96 tff(2110,plain,
% 0.77/0.96 (~node5(s20)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[2109, 776, 2106])).
% 0.77/0.96 tff(2111,plain,
% 0.77/0.96 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s20, c_n1) | (~node2(s20)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s20, c_n1) | (~node2(s20)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2112,plain,
% 0.77/0.96 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s20, c_n1) | (~node2(s20)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(2113,plain,
% 0.77/0.96 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s20, c_n1) | (~node2(s20))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[2112, 2111])).
% 0.77/0.96 tff(2114,plain,
% 0.77/0.96 (~node2(s20)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[2113, 787, 2038])).
% 0.77/0.96 tff(2115,plain,
% 0.77/0.96 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s20, c_n1) | (~node3(s20)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s20, c_n1) | (~node3(s20)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2116,plain,
% 0.77/0.96 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s20, c_n1) | (~node3(s20)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(2117,plain,
% 0.77/0.96 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s20, c_n1) | (~node3(s20))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[2116, 2115])).
% 0.77/0.96 tff(2118,plain,
% 0.77/0.96 (~node3(s20)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[2117, 798, 2038])).
% 0.77/0.96 tff(2119,plain,
% 0.77/0.96 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s20, c_n2) | (~node4(s20)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s20, c_n2) | (~node4(s20)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2120,plain,
% 0.77/0.96 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s20, c_n2) | (~node4(s20)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(2121,plain,
% 0.77/0.96 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s20, c_n2) | (~node4(s20))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[2120, 2119])).
% 0.77/0.96 tff(2122,plain,
% 0.77/0.96 (~node4(s20)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[2121, 388, 2058])).
% 0.77/0.96 tff(2123,plain,
% 0.77/0.96 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s20, s21)) | node7(s20, s21))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s20, s21)) | node7(s20, s21))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2124,plain,
% 0.77/0.96 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s20, s21)) | node7(s20, s21))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(2125,plain,
% 0.77/0.96 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s20, s21)) | node7(s20, s21)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[2124, 2123])).
% 0.77/0.96 tff(2126,plain,
% 0.77/0.96 (node7(s20, s21)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[2125, 206, 2069])).
% 0.77/0.96 tff(2127,plain,
% 0.77/0.96 (((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s20, c_c1) | node1(s20) | node2(s20) | node3(s20) | node4(s20) | node5(s20) | node6(s20, s21) | (~node7(s20, s21)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s20, c_c1) | node1(s20) | node2(s20) | node3(s20) | node4(s20) | node5(s20) | node6(s20, s21) | (~node7(s20, s21)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2128,plain,
% 0.77/0.96 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s20, c_c1) | node1(s20) | node2(s20) | node3(s20) | node4(s20) | node5(s20) | node6(s20, s21) | (~node7(s20, s21)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(2129,plain,
% 0.77/0.96 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s20, c_c1) | node1(s20) | node2(s20) | node3(s20) | node4(s20) | node5(s20) | node6(s20, s21) | (~node7(s20, s21))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[2128, 2127])).
% 0.77/0.96 tff(2130,plain,
% 0.77/0.96 (m_main_v_state1(s20, c_c1) | node1(s20) | node2(s20) | node3(s20) | node4(s20) | node5(s20) | node6(s20, s21)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[2129, 820, 2126])).
% 0.77/0.96 tff(2131,plain,
% 0.77/0.96 (node6(s20, s21)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[2130, 2122, 2046, 2118, 2114, 2110, 2093])).
% 0.77/0.96 tff(2132,plain,
% 0.77/0.96 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s20, c_n1) | (~m_main_v_state1(s21, c_n1)) | (~node6(s20, s21)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s20, c_n1) | (~m_main_v_state1(s21, c_n1)) | (~node6(s20, s21)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2133,plain,
% 0.77/0.96 (((~node6(s20, s21)) | m_main_v_state1(s20, c_n1) | (~m_main_v_state1(s21, c_n1))) <=> (m_main_v_state1(s20, c_n1) | (~m_main_v_state1(s21, c_n1)) | (~node6(s20, s21)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2134,plain,
% 0.77/0.96 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s20, s21)) | m_main_v_state1(s20, c_n1) | (~m_main_v_state1(s21, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s20, c_n1) | (~m_main_v_state1(s21, c_n1)) | (~node6(s20, s21))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[2133])).
% 0.77/0.96 tff(2135,plain,
% 0.77/0.96 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s20, s21)) | m_main_v_state1(s20, c_n1) | (~m_main_v_state1(s21, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s20, c_n1) | (~m_main_v_state1(s21, c_n1)) | (~node6(s20, s21)))),
% 0.77/0.96 inference(transitivity,[status(thm)],[2134, 2132])).
% 0.77/0.96 tff(2136,plain,
% 0.77/0.96 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s20, s21)) | m_main_v_state1(s20, c_n1) | (~m_main_v_state1(s21, c_n1)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(2137,plain,
% 0.77/0.96 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s20, c_n1) | (~m_main_v_state1(s21, c_n1)) | (~node6(s20, s21))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[2136, 2135])).
% 0.77/0.96 tff(2138,plain,
% 0.77/0.96 (~m_main_v_state1(s21, c_n1)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[2137, 835, 2038, 2131])).
% 0.77/0.96 tff(2139,plain,
% 0.77/0.96 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s21, c_n1) | (~node2(s21)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s21, c_n1) | (~node2(s21)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2140,plain,
% 0.77/0.96 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s21, c_n1) | (~node2(s21)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(2141,plain,
% 0.77/0.96 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s21, c_n1) | (~node2(s21))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[2140, 2139])).
% 0.77/0.96 tff(2142,plain,
% 0.77/0.96 (~node2(s21)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[2141, 787, 2138])).
% 0.77/0.96 tff(2143,plain,
% 0.77/0.96 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s20, c_t1)) | m_main_v_state1(s21, c_t1) | (~node6(s20, s21)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s20, c_t1)) | m_main_v_state1(s21, c_t1) | (~node6(s20, s21)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2144,plain,
% 0.77/0.96 (((~node6(s20, s21)) | (~m_main_v_state1(s20, c_t1)) | m_main_v_state1(s21, c_t1)) <=> ((~m_main_v_state1(s20, c_t1)) | m_main_v_state1(s21, c_t1) | (~node6(s20, s21)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2145,plain,
% 0.77/0.96 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s20, s21)) | (~m_main_v_state1(s20, c_t1)) | m_main_v_state1(s21, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s20, c_t1)) | m_main_v_state1(s21, c_t1) | (~node6(s20, s21))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[2144])).
% 0.77/0.96 tff(2146,plain,
% 0.77/0.96 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s20, s21)) | (~m_main_v_state1(s20, c_t1)) | m_main_v_state1(s21, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s20, c_t1)) | m_main_v_state1(s21, c_t1) | (~node6(s20, s21)))),
% 0.77/0.96 inference(transitivity,[status(thm)],[2145, 2143])).
% 0.77/0.96 tff(2147,plain,
% 0.77/0.96 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s20, s21)) | (~m_main_v_state1(s20, c_t1)) | m_main_v_state1(s21, c_t1))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(2148,plain,
% 0.77/0.96 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s20, c_t1)) | m_main_v_state1(s21, c_t1) | (~node6(s20, s21))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[2147, 2146])).
% 0.77/0.96 tff(2149,plain,
% 0.77/0.96 (m_main_v_state1(s21, c_t1)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[2148, 856, 2034, 2131])).
% 0.77/0.96 tff(2150,plain,
% 0.77/0.96 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s21, c_n2)) | (~m_main_v_state2(s21, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s21, c_n2)) | (~m_main_v_state2(s21, c_t2)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2151,plain,
% 0.77/0.96 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s21, c_n2)) | (~m_main_v_state2(s21, c_t2)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(2152,plain,
% 0.77/0.96 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s21, c_n2)) | (~m_main_v_state2(s21, c_t2))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[2151, 2150])).
% 0.77/0.96 tff(2153,plain,
% 0.77/0.96 (~m_main_v_state2(s21, c_t2)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[2152, 77, 2081])).
% 0.77/0.96 tff(2154,plain,
% 0.77/0.96 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s21, c_t2) | (~node1(s21)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s21, c_t2) | (~node1(s21)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2155,plain,
% 0.77/0.96 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s21, c_t2) | (~node1(s21)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(2156,plain,
% 0.77/0.96 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s21, c_t2) | (~node1(s21))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[2155, 2154])).
% 0.77/0.96 tff(2157,plain,
% 0.77/0.96 (~node1(s21)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[2156, 195, 2153])).
% 0.77/0.96 tff(2158,plain,
% 0.77/0.96 (succ(s21, s22) <=> succ(s21, s22)),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2159,axiom,(succ(s21, s22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound22')).
% 0.77/0.96 tff(2160,plain,
% 0.77/0.96 (succ(s21, s22)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[2159, 2158])).
% 0.77/0.96 tff(2161,plain,
% 0.77/0.96 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s21, s22)) | trans(s21, s22))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s21, s22)) | trans(s21, s22))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2162,plain,
% 0.77/0.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s21, s22)) | trans(s21, s22))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(2163,plain,
% 0.77/0.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s21, s22)) | trans(s21, s22)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[2162, 2161])).
% 0.77/0.96 tff(2164,plain,
% 0.77/0.96 (trans(s21, s22)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[2163, 2160, 32])).
% 0.77/0.96 tff(2165,plain,
% 0.77/0.96 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s21, s22)) | node7(s21, s22))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s21, s22)) | node7(s21, s22))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2166,plain,
% 0.77/0.96 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s21, s22)) | node7(s21, s22))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(2167,plain,
% 0.77/0.96 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s21, s22)) | node7(s21, s22)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[2166, 2165])).
% 0.77/0.96 tff(2168,plain,
% 0.77/0.96 (node7(s21, s22)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[2167, 206, 2164])).
% 0.77/0.96 tff(2169,plain,
% 0.77/0.96 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_state1(s22, c_c1) | node1(s21) | node2(s21) | node3(s21) | (~node7(s21, s22)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_state1(s22, c_c1) | node1(s21) | node2(s21) | node3(s21) | (~node7(s21, s22)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2170,plain,
% 0.77/0.96 (((~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | node1(s21) | node2(s21) | node3(s21) | (~node7(s21, s22)) | m_main_v_state1(s22, c_c1)) <=> ((~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_state1(s22, c_c1) | node1(s21) | node2(s21) | node3(s21) | (~node7(s21, s22)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2171,plain,
% 0.77/0.96 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | node1(s21) | node2(s21) | node3(s21) | (~node7(s21, s22)) | m_main_v_state1(s22, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_state1(s22, c_c1) | node1(s21) | node2(s21) | node3(s21) | (~node7(s21, s22))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[2170])).
% 0.77/0.96 tff(2172,plain,
% 0.77/0.96 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | node1(s21) | node2(s21) | node3(s21) | (~node7(s21, s22)) | m_main_v_state1(s22, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_state1(s22, c_c1) | node1(s21) | node2(s21) | node3(s21) | (~node7(s21, s22)))),
% 0.77/0.96 inference(transitivity,[status(thm)],[2171, 2169])).
% 0.77/0.96 tff(2173,plain,
% 0.77/0.96 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | node1(s21) | node2(s21) | node3(s21) | (~node7(s21, s22)) | m_main_v_state1(s22, c_c1))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(2174,plain,
% 0.77/0.96 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_state1(s22, c_c1) | node1(s21) | node2(s21) | node3(s21) | (~node7(s21, s22))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[2173, 2172])).
% 0.77/0.96 tff(2175,plain,
% 0.77/0.96 ((~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_state1(s22, c_c1) | node1(s21) | node2(s21) | node3(s21)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[2174, 892, 2168])).
% 0.77/0.96 tff(2176,plain,
% 0.77/0.96 (m_main_v_state1(s22, c_c1)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[2175, 2157, 2081, 2149, 2142, 2089])).
% 0.77/0.96 tff(2177,plain,
% 0.77/0.96 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s22, c_t1)) | (~m_main_v_state1(s22, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s22, c_t1)) | (~m_main_v_state1(s22, c_c1)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2178,plain,
% 0.77/0.96 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s22, c_t1)) | (~m_main_v_state1(s22, c_c1)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(2179,plain,
% 0.77/0.96 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s22, c_t1)) | (~m_main_v_state1(s22, c_c1))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[2178, 2177])).
% 0.77/0.96 tff(2180,plain,
% 0.77/0.96 (~m_main_v_state1(s22, c_t1)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[2179, 539, 2176])).
% 0.77/0.96 tff(2181,plain,
% 0.77/0.96 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s22, c_t1) | (~node5(s22)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s22, c_t1) | (~node5(s22)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2182,plain,
% 0.77/0.96 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s22, c_t1) | (~node5(s22)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(2183,plain,
% 0.77/0.96 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s22, c_t1) | (~node5(s22))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[2182, 2181])).
% 0.77/0.96 tff(2184,plain,
% 0.77/0.96 (~node5(s22)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[2183, 550, 2180])).
% 0.77/0.96 tff(2185,plain,
% 0.77/0.96 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s21, s22)) | node14(s21, s22))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s21, s22)) | node14(s21, s22))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2186,plain,
% 0.77/0.96 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s21, s22)) | node14(s21, s22))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(2187,plain,
% 0.77/0.96 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s21, s22)) | node14(s21, s22)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[2186, 2185])).
% 0.77/0.96 tff(2188,plain,
% 0.77/0.96 (node14(s21, s22)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[2187, 46, 2164])).
% 0.77/0.96 tff(2189,plain,
% 0.77/0.96 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | (~node14(s21, s22)) | m_main_v_state2(s22, c_t2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | (~node14(s21, s22)) | m_main_v_state2(s22, c_t2))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2190,plain,
% 0.77/0.96 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | (~node14(s21, s22)) | m_main_v_state2(s22, c_t2))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(2191,plain,
% 0.77/0.96 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | (~node14(s21, s22)) | m_main_v_state2(s22, c_t2)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[2190, 2189])).
% 0.77/0.96 tff(2192,plain,
% 0.77/0.96 ((~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_state2(s22, c_t2)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[2191, 922, 2188])).
% 0.77/0.96 tff(2193,plain,
% 0.77/0.96 (m_main_v_state2(s22, c_t2)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[2192, 2149, 2081])).
% 0.77/0.96 tff(2194,plain,
% 0.77/0.96 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s22, c_n2)) | (~m_main_v_state2(s22, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s22, c_n2)) | (~m_main_v_state2(s22, c_t2)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2195,plain,
% 0.77/0.96 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s22, c_n2)) | (~m_main_v_state2(s22, c_t2)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(2196,plain,
% 0.77/0.96 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s22, c_n2)) | (~m_main_v_state2(s22, c_t2))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[2195, 2194])).
% 0.77/0.96 tff(2197,plain,
% 0.77/0.96 (~m_main_v_state2(s22, c_n2)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[2196, 77, 2193])).
% 0.77/0.96 tff(2198,plain,
% 0.77/0.96 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s22, c_n2) | (~node4(s22)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s22, c_n2) | (~node4(s22)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2199,plain,
% 0.77/0.96 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s22, c_n2) | (~node4(s22)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(2200,plain,
% 0.77/0.96 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s22, c_n2) | (~node4(s22))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[2199, 2198])).
% 0.77/0.96 tff(2201,plain,
% 0.77/0.96 (~node4(s22)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[2200, 388, 2197])).
% 0.77/0.96 tff(2202,plain,
% 0.77/0.96 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s22, c_t2)) | (~m_main_v_state2(s22, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s22, c_t2)) | (~m_main_v_state2(s22, c_c2)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2203,plain,
% 0.77/0.96 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s22, c_t2)) | (~m_main_v_state2(s22, c_c2)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(2204,plain,
% 0.77/0.96 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s22, c_t2)) | (~m_main_v_state2(s22, c_c2))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[2203, 2202])).
% 0.77/0.96 tff(2205,plain,
% 0.77/0.96 (~m_main_v_state2(s22, c_c2)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[2204, 260, 2193])).
% 0.77/0.96 tff(2206,plain,
% 0.77/0.96 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s22, c_c2) | (~node3(s22)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s22, c_c2) | (~node3(s22)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2207,plain,
% 0.77/0.96 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s22, c_c2) | (~node3(s22)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(2208,plain,
% 0.77/0.96 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s22, c_c2) | (~node3(s22))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[2207, 2206])).
% 0.77/0.96 tff(2209,plain,
% 0.77/0.96 (~node3(s22)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[2208, 399, 2205])).
% 0.77/0.96 tff(2210,plain,
% 0.77/0.96 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s22, c_n2) | (~node2(s22)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s22, c_n2) | (~node2(s22)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2211,plain,
% 0.77/0.96 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s22, c_n2) | (~node2(s22)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(2212,plain,
% 0.77/0.96 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s22, c_n2) | (~node2(s22))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[2211, 2210])).
% 0.77/0.96 tff(2213,plain,
% 0.77/0.96 (~node2(s22)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[2212, 410, 2197])).
% 0.77/0.96 tff(2214,plain,
% 0.77/0.96 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s22, c_n1)) | (~m_main_v_state1(s22, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s22, c_n1)) | (~m_main_v_state1(s22, c_c1)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2215,plain,
% 0.77/0.96 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s22, c_n1)) | (~m_main_v_state1(s22, c_c1)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(2216,plain,
% 0.77/0.96 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s22, c_n1)) | (~m_main_v_state1(s22, c_c1))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[2215, 2214])).
% 0.77/0.96 tff(2217,plain,
% 0.77/0.96 (~m_main_v_state1(s22, c_n1)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[2216, 454, 2176])).
% 0.77/0.96 tff(2218,plain,
% 0.77/0.96 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s22, c_n1) | (~node1(s22)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s22, c_n1) | (~node1(s22)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(2219,plain,
% 0.77/0.96 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s22, c_n1) | (~node1(s22)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(2220,plain,
% 0.77/0.96 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s22, c_n1) | (~node1(s22))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[2219, 2218])).
% 0.77/0.96 tff(2221,plain,
% 0.77/0.96 (~node1(s22)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[2220, 421, 2217])).
% 0.77/0.96 tff(2222,plain,
% 0.77/0.96 (succ(s22, s23) <=> succ(s22, s23)),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2223,axiom,(succ(s22, s23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound23')).
% 0.77/0.97 tff(2224,plain,
% 0.77/0.97 (succ(s22, s23)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[2223, 2222])).
% 0.77/0.97 tff(2225,plain,
% 0.77/0.97 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s22, s23)) | trans(s22, s23))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s22, s23)) | trans(s22, s23))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2226,plain,
% 0.77/0.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s22, s23)) | trans(s22, s23))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(2227,plain,
% 0.77/0.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s22, s23)) | trans(s22, s23)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[2226, 2225])).
% 0.77/0.97 tff(2228,plain,
% 0.77/0.97 (trans(s22, s23)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2227, 2224, 32])).
% 0.77/0.97 tff(2229,plain,
% 0.77/0.97 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s22, s23)) | node7(s22, s23))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s22, s23)) | node7(s22, s23))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2230,plain,
% 0.77/0.97 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s22, s23)) | node7(s22, s23))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(2231,plain,
% 0.77/0.97 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s22, s23)) | node7(s22, s23)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[2230, 2229])).
% 0.77/0.97 tff(2232,plain,
% 0.77/0.97 (node7(s22, s23)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2231, 206, 2228])).
% 0.77/0.97 tff(2233,plain,
% 0.77/0.97 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s23, c_n1) | (~m_main_v_state1(s22, c_c1)) | node1(s22) | node2(s22) | node3(s22) | node4(s22) | node5(s22) | (~node7(s22, s23)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s23, c_n1) | (~m_main_v_state1(s22, c_c1)) | node1(s22) | node2(s22) | node3(s22) | node4(s22) | node5(s22) | (~node7(s22, s23)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2234,plain,
% 0.77/0.97 (((~m_main_v_state1(s22, c_c1)) | node1(s22) | node2(s22) | node3(s22) | node4(s22) | node5(s22) | (~node7(s22, s23)) | m_main_v_state1(s23, c_n1)) <=> (m_main_v_state1(s23, c_n1) | (~m_main_v_state1(s22, c_c1)) | node1(s22) | node2(s22) | node3(s22) | node4(s22) | node5(s22) | (~node7(s22, s23)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2235,plain,
% 0.77/0.97 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s22, c_c1)) | node1(s22) | node2(s22) | node3(s22) | node4(s22) | node5(s22) | (~node7(s22, s23)) | m_main_v_state1(s23, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(s23, c_n1) | (~m_main_v_state1(s22, c_c1)) | node1(s22) | node2(s22) | node3(s22) | node4(s22) | node5(s22) | (~node7(s22, s23))))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[2234])).
% 0.77/0.97 tff(2236,plain,
% 0.77/0.97 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s22, c_c1)) | node1(s22) | node2(s22) | node3(s22) | node4(s22) | node5(s22) | (~node7(s22, s23)) | m_main_v_state1(s23, c_n1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s23, c_n1) | (~m_main_v_state1(s22, c_c1)) | node1(s22) | node2(s22) | node3(s22) | node4(s22) | node5(s22) | (~node7(s22, s23)))),
% 0.77/0.97 inference(transitivity,[status(thm)],[2235, 2233])).
% 0.77/0.97 tff(2237,plain,
% 0.77/0.97 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s22, c_c1)) | node1(s22) | node2(s22) | node3(s22) | node4(s22) | node5(s22) | (~node7(s22, s23)) | m_main_v_state1(s23, c_n1))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(2238,plain,
% 0.77/0.97 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s23, c_n1) | (~m_main_v_state1(s22, c_c1)) | node1(s22) | node2(s22) | node3(s22) | node4(s22) | node5(s22) | (~node7(s22, s23))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[2237, 2236])).
% 0.77/0.97 tff(2239,plain,
% 0.77/0.97 (m_main_v_state1(s23, c_n1) | (~m_main_v_state1(s22, c_c1)) | node1(s22) | node2(s22) | node3(s22) | node4(s22) | node5(s22)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2238, 584, 2232])).
% 0.77/0.97 tff(2240,plain,
% 0.77/0.97 (m_main_v_state1(s23, c_n1)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2239, 2221, 2176, 2213, 2209, 2201, 2184])).
% 0.77/0.97 tff(2241,plain,
% 0.77/0.97 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s21, c_t2) | (~node15(s21)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s21, c_t2) | (~node15(s21)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2242,plain,
% 0.77/0.97 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s21, c_t2) | (~node15(s21)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(2243,plain,
% 0.77/0.97 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s21, c_t2) | (~node15(s21))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[2242, 2241])).
% 0.77/0.97 tff(2244,plain,
% 0.77/0.97 (~node15(s21)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2243, 103, 2153])).
% 0.77/0.97 tff(2245,plain,
% 0.77/0.97 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s21, s22)) | node18(s21, s22))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s21, s22)) | node18(s21, s22))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2246,plain,
% 0.77/0.97 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s21, s22)) | node18(s21, s22))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(2247,plain,
% 0.77/0.97 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s21, s22)) | node18(s21, s22)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[2246, 2245])).
% 0.77/0.97 tff(2248,plain,
% 0.77/0.97 (node18(s21, s22)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2247, 125, 2164])).
% 0.77/0.97 tff(2249,plain,
% 0.77/0.97 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s21) | (~node18(s21, s22)) | (~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_turn(s22, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s21) | (~node18(s21, s22)) | (~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_turn(s22, c_1))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2250,plain,
% 0.77/0.97 (((~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | node15(s21) | (~node18(s21, s22)) | m_main_v_turn(s22, c_1)) <=> (node15(s21) | (~node18(s21, s22)) | (~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_turn(s22, c_1))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2251,plain,
% 0.77/0.97 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | node15(s21) | (~node18(s21, s22)) | m_main_v_turn(s22, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(s21) | (~node18(s21, s22)) | (~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_turn(s22, c_1)))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[2250])).
% 0.77/0.97 tff(2252,plain,
% 0.77/0.97 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | node15(s21) | (~node18(s21, s22)) | m_main_v_turn(s22, c_1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s21) | (~node18(s21, s22)) | (~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_turn(s22, c_1))),
% 0.77/0.97 inference(transitivity,[status(thm)],[2251, 2249])).
% 0.77/0.97 tff(2253,plain,
% 0.77/0.97 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | node15(s21) | (~node18(s21, s22)) | m_main_v_turn(s22, c_1))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(2254,plain,
% 0.77/0.97 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(s21) | (~node18(s21, s22)) | (~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_turn(s22, c_1)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[2253, 2252])).
% 0.77/0.97 tff(2255,plain,
% 0.77/0.97 (node15(s21) | (~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_turn(s22, c_1)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2254, 992, 2248])).
% 0.77/0.97 tff(2256,plain,
% 0.77/0.97 (m_main_v_turn(s22, c_1)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2255, 2244, 2081, 2149])).
% 0.77/0.97 tff(2257,plain,
% 0.77/0.97 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s22, c_1)) | (~m_main_v_turn(s22, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s22, c_1)) | (~m_main_v_turn(s22, c_2)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2258,plain,
% 0.77/0.97 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s22, c_1)) | (~m_main_v_turn(s22, c_2)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(2259,plain,
% 0.77/0.97 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s22, c_1)) | (~m_main_v_turn(s22, c_2))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[2258, 2257])).
% 0.77/0.97 tff(2260,plain,
% 0.77/0.97 (~m_main_v_turn(s22, c_2)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2259, 156, 2256])).
% 0.77/0.97 tff(2261,plain,
% 0.77/0.97 (((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s22, c_2) | (~node12(s22)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s22, c_2) | (~node12(s22)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2262,plain,
% 0.77/0.97 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s22, c_2) | (~node12(s22)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(2263,plain,
% 0.77/0.97 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s22, c_2) | (~node12(s22))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[2262, 2261])).
% 0.77/0.97 tff(2264,plain,
% 0.77/0.97 (~node12(s22)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2263, 184, 2260])).
% 0.77/0.97 tff(2265,plain,
% 0.77/0.97 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s22, c_n2) | (~node8(s22)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s22, c_n2) | (~node8(s22)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2266,plain,
% 0.77/0.97 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s22, c_n2) | (~node8(s22)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(2267,plain,
% 0.77/0.97 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s22, c_n2) | (~node8(s22))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[2266, 2265])).
% 0.77/0.97 tff(2268,plain,
% 0.77/0.97 (~node8(s22)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2267, 271, 2197])).
% 0.77/0.97 tff(2269,plain,
% 0.77/0.97 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s22, c_n2) | (~node9(s22)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s22, c_n2) | (~node9(s22)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2270,plain,
% 0.77/0.97 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s22, c_n2) | (~node9(s22)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(2271,plain,
% 0.77/0.97 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s22, c_n2) | (~node9(s22))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[2270, 2269])).
% 0.77/0.97 tff(2272,plain,
% 0.77/0.97 (~node9(s22)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2271, 88, 2197])).
% 0.77/0.97 tff(2273,plain,
% 0.77/0.97 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s22, c_n2) | (~node10(s22)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s22, c_n2) | (~node10(s22)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2274,plain,
% 0.77/0.97 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s22, c_n2) | (~node10(s22)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(2275,plain,
% 0.77/0.97 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s22, c_n2) | (~node10(s22))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[2274, 2273])).
% 0.77/0.97 tff(2276,plain,
% 0.77/0.97 (~node10(s22)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2275, 249, 2197])).
% 0.77/0.97 tff(2277,plain,
% 0.77/0.97 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s22, c_n1) | (~node11(s22)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s22, c_n1) | (~node11(s22)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2278,plain,
% 0.77/0.97 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s22, c_n1) | (~node11(s22)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(2279,plain,
% 0.77/0.97 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s22, c_n1) | (~node11(s22))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[2278, 2277])).
% 0.77/0.97 tff(2280,plain,
% 0.77/0.97 (~node11(s22)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2279, 238, 2217])).
% 0.77/0.97 tff(2281,plain,
% 0.77/0.97 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s22, s23)) | node14(s22, s23))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s22, s23)) | node14(s22, s23))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2282,plain,
% 0.77/0.97 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s22, s23)) | node14(s22, s23))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(2283,plain,
% 0.77/0.97 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s22, s23)) | node14(s22, s23)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[2282, 2281])).
% 0.77/0.97 tff(2284,plain,
% 0.77/0.97 (node14(s22, s23)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2283, 46, 2228])).
% 0.77/0.97 tff(2285,plain,
% 0.77/0.97 (((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s22, c_c2) | node9(s22) | node8(s22) | node10(s22) | node11(s22) | node12(s22) | node13(s22, s23) | (~node14(s22, s23)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s22, c_c2) | node9(s22) | node8(s22) | node10(s22) | node11(s22) | node12(s22) | node13(s22, s23) | (~node14(s22, s23)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2286,plain,
% 0.77/0.97 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s22, c_c2) | node9(s22) | node8(s22) | node10(s22) | node11(s22) | node12(s22) | node13(s22, s23) | (~node14(s22, s23)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(2287,plain,
% 0.77/0.97 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s22, c_c2) | node9(s22) | node8(s22) | node10(s22) | node11(s22) | node12(s22) | node13(s22, s23) | (~node14(s22, s23))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[2286, 2285])).
% 0.77/0.97 tff(2288,plain,
% 0.77/0.97 (m_main_v_state2(s22, c_c2) | node9(s22) | node8(s22) | node10(s22) | node11(s22) | node12(s22) | node13(s22, s23)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2287, 296, 2284])).
% 0.77/0.97 tff(2289,plain,
% 0.77/0.97 (node13(s22, s23)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2288, 2280, 2205, 2276, 2272, 2268, 2264])).
% 0.77/0.97 tff(2290,plain,
% 0.77/0.97 (((~![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(s22, c_t2)) | m_main_v_state2(s23, c_t2) | (~node13(s22, s23)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s22, c_t2)) | m_main_v_state2(s23, c_t2) | (~node13(s22, s23)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2291,plain,
% 0.77/0.97 (((~node13(s22, s23)) | (~m_main_v_state2(s22, c_t2)) | m_main_v_state2(s23, c_t2)) <=> ((~m_main_v_state2(s22, c_t2)) | m_main_v_state2(s23, c_t2) | (~node13(s22, s23)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2292,plain,
% 0.77/0.97 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s22, s23)) | (~m_main_v_state2(s22, c_t2)) | m_main_v_state2(s23, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(s22, c_t2)) | m_main_v_state2(s23, c_t2) | (~node13(s22, s23))))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[2291])).
% 0.77/0.97 tff(2293,plain,
% 0.77/0.97 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s22, s23)) | (~m_main_v_state2(s22, c_t2)) | m_main_v_state2(s23, c_t2))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s22, c_t2)) | m_main_v_state2(s23, c_t2) | (~node13(s22, s23)))),
% 0.77/0.97 inference(transitivity,[status(thm)],[2292, 2290])).
% 0.77/0.97 tff(2294,plain,
% 0.77/0.97 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s22, s23)) | (~m_main_v_state2(s22, c_t2)) | m_main_v_state2(s23, c_t2))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(2295,plain,
% 0.77/0.97 ((~![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(s22, c_t2)) | m_main_v_state2(s23, c_t2) | (~node13(s22, s23))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[2294, 2293])).
% 0.77/0.97 tff(2296,plain,
% 0.77/0.97 (m_main_v_state2(s23, c_t2)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2295, 518, 2193, 2289])).
% 0.77/0.97 tff(2297,plain,
% 0.77/0.97 (succ(s23, s24) <=> succ(s23, s24)),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2298,axiom,(succ(s23, s24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound24')).
% 0.77/0.97 tff(2299,plain,
% 0.77/0.97 (succ(s23, s24)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[2298, 2297])).
% 0.77/0.97 tff(2300,plain,
% 0.77/0.97 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s23, s24)) | trans(s23, s24))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s23, s24)) | trans(s23, s24))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2301,plain,
% 0.77/0.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s23, s24)) | trans(s23, s24))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(2302,plain,
% 0.77/0.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s23, s24)) | trans(s23, s24)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[2301, 2300])).
% 0.77/0.97 tff(2303,plain,
% 0.77/0.97 (trans(s23, s24)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2302, 2299, 32])).
% 0.77/0.97 tff(2304,plain,
% 0.77/0.97 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s23, s24)) | node7(s23, s24))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s23, s24)) | node7(s23, s24))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2305,plain,
% 0.77/0.97 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s23, s24)) | node7(s23, s24))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(2306,plain,
% 0.77/0.97 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s23, s24)) | node7(s23, s24)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[2305, 2304])).
% 0.77/0.97 tff(2307,plain,
% 0.77/0.97 (node7(s23, s24)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2306, 206, 2303])).
% 0.77/0.97 tff(2308,plain,
% 0.77/0.97 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | (~node7(s23, s24)) | m_main_v_state1(s24, c_t1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | (~node7(s23, s24)) | m_main_v_state1(s24, c_t1))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2309,plain,
% 0.77/0.97 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | (~node7(s23, s24)) | m_main_v_state1(s24, c_t1))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(2310,plain,
% 0.77/0.97 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | (~node7(s23, s24)) | m_main_v_state1(s24, c_t1)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[2309, 2308])).
% 0.77/0.97 tff(2311,plain,
% 0.77/0.97 ((~m_main_v_state1(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | m_main_v_state1(s24, c_t1)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2310, 651, 2307])).
% 0.77/0.97 tff(2312,plain,
% 0.77/0.97 (m_main_v_state1(s24, c_t1)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2311, 2296, 2240])).
% 0.77/0.97 tff(2313,plain,
% 0.77/0.97 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s24, c_n1)) | (~m_main_v_state1(s24, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s24, c_n1)) | (~m_main_v_state1(s24, c_t1)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2314,plain,
% 0.77/0.97 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s24, c_n1)) | (~m_main_v_state1(s24, c_t1)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(2315,plain,
% 0.77/0.97 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s24, c_n1)) | (~m_main_v_state1(s24, c_t1))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[2314, 2313])).
% 0.77/0.97 tff(2316,plain,
% 0.77/0.97 (~m_main_v_state1(s24, c_n1)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2315, 10, 2312])).
% 0.77/0.97 tff(2317,plain,
% 0.77/0.97 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s24, c_n1) | (~node1(s24)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s24, c_n1) | (~node1(s24)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2318,plain,
% 0.77/0.97 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s24, c_n1) | (~node1(s24)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(2319,plain,
% 0.77/0.97 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s24, c_n1) | (~node1(s24))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[2318, 2317])).
% 0.77/0.97 tff(2320,plain,
% 0.77/0.97 (~node1(s24)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2319, 421, 2316])).
% 0.77/0.97 tff(2321,plain,
% 0.77/0.97 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s23, s24)) | node18(s23, s24))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s23, s24)) | node18(s23, s24))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2322,plain,
% 0.77/0.97 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s23, s24)) | node18(s23, s24))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(2323,plain,
% 0.77/0.97 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s23, s24)) | node18(s23, s24)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[2322, 2321])).
% 0.77/0.97 tff(2324,plain,
% 0.77/0.97 (node18(s23, s24)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2323, 125, 2303])).
% 0.77/0.97 tff(2325,plain,
% 0.77/0.97 (((~![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(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | (~node18(s23, s24)) | m_main_v_turn(s24, c_2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | (~node18(s23, s24)) | m_main_v_turn(s24, c_2))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2326,plain,
% 0.77/0.97 ((~![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(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | (~node18(s23, s24)) | m_main_v_turn(s24, c_2))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(2327,plain,
% 0.77/0.97 ((~![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(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | (~node18(s23, s24)) | m_main_v_turn(s24, c_2)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[2326, 2325])).
% 0.77/0.97 tff(2328,plain,
% 0.77/0.97 ((~m_main_v_state1(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | m_main_v_turn(s24, c_2)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2327, 760, 2324])).
% 0.77/0.97 tff(2329,plain,
% 0.77/0.97 (m_main_v_turn(s24, c_2)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2328, 2296, 2240])).
% 0.77/0.97 tff(2330,plain,
% 0.77/0.97 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s24, c_1)) | (~m_main_v_turn(s24, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s24, c_1)) | (~m_main_v_turn(s24, c_2)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2331,plain,
% 0.77/0.97 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s24, c_1)) | (~m_main_v_turn(s24, c_2)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(2332,plain,
% 0.77/0.97 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s24, c_1)) | (~m_main_v_turn(s24, c_2))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[2331, 2330])).
% 0.77/0.97 tff(2333,plain,
% 0.77/0.97 (~m_main_v_turn(s24, c_1)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2332, 156, 2329])).
% 0.77/0.97 tff(2334,plain,
% 0.77/0.97 (((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s24, c_1) | (~node5(s24)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s24, c_1) | (~node5(s24)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2335,plain,
% 0.77/0.97 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s24, c_1) | (~node5(s24)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(2336,plain,
% 0.77/0.97 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s24, c_1) | (~node5(s24))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[2335, 2334])).
% 0.77/0.97 tff(2337,plain,
% 0.77/0.97 (~node5(s24)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2336, 776, 2333])).
% 0.77/0.97 tff(2338,plain,
% 0.77/0.97 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s24, c_n1) | (~node2(s24)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s24, c_n1) | (~node2(s24)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2339,plain,
% 0.77/0.97 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s24, c_n1) | (~node2(s24)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(2340,plain,
% 0.77/0.97 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s24, c_n1) | (~node2(s24))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[2339, 2338])).
% 0.77/0.97 tff(2341,plain,
% 0.77/0.97 (~node2(s24)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2340, 787, 2316])).
% 0.77/0.97 tff(2342,plain,
% 0.77/0.97 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s24, c_n1) | (~node3(s24)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s24, c_n1) | (~node3(s24)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2343,plain,
% 0.77/0.97 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s24, c_n1) | (~node3(s24)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(2344,plain,
% 0.77/0.97 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s24, c_n1) | (~node3(s24))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[2343, 2342])).
% 0.77/0.97 tff(2345,plain,
% 0.77/0.97 (~node3(s24)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2344, 798, 2316])).
% 0.77/0.97 tff(2346,plain,
% 0.77/0.97 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s24, c_t1)) | (~m_main_v_state1(s24, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s24, c_t1)) | (~m_main_v_state1(s24, c_c1)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2347,plain,
% 0.77/0.97 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s24, c_t1)) | (~m_main_v_state1(s24, c_c1)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(2348,plain,
% 0.77/0.97 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s24, c_t1)) | (~m_main_v_state1(s24, c_c1))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[2347, 2346])).
% 0.77/0.97 tff(2349,plain,
% 0.77/0.97 (~m_main_v_state1(s24, c_c1)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2348, 539, 2312])).
% 0.77/0.97 tff(2350,plain,
% 0.77/0.97 (((~![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(s22, c_n2) | (~m_main_v_state2(s23, c_n2)) | (~node13(s22, s23)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s22, c_n2) | (~m_main_v_state2(s23, c_n2)) | (~node13(s22, s23)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2351,plain,
% 0.77/0.97 (((~node13(s22, s23)) | m_main_v_state2(s22, c_n2) | (~m_main_v_state2(s23, c_n2))) <=> (m_main_v_state2(s22, c_n2) | (~m_main_v_state2(s23, c_n2)) | (~node13(s22, s23)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2352,plain,
% 0.77/0.97 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s22, s23)) | m_main_v_state2(s22, c_n2) | (~m_main_v_state2(s23, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(s22, c_n2) | (~m_main_v_state2(s23, c_n2)) | (~node13(s22, s23))))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[2351])).
% 0.77/0.97 tff(2353,plain,
% 0.77/0.97 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s22, s23)) | m_main_v_state2(s22, c_n2) | (~m_main_v_state2(s23, c_n2)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s22, c_n2) | (~m_main_v_state2(s23, c_n2)) | (~node13(s22, s23)))),
% 0.77/0.97 inference(transitivity,[status(thm)],[2352, 2350])).
% 0.77/0.97 tff(2354,plain,
% 0.77/0.97 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s22, s23)) | m_main_v_state2(s22, c_n2) | (~m_main_v_state2(s23, c_n2)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(2355,plain,
% 0.77/0.97 ((~![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(s22, c_n2) | (~m_main_v_state2(s23, c_n2)) | (~node13(s22, s23))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[2354, 2353])).
% 0.77/0.97 tff(2356,plain,
% 0.77/0.97 (~m_main_v_state2(s23, c_n2)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2355, 311, 2197, 2289])).
% 0.77/0.97 tff(2357,plain,
% 0.77/0.97 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s23, c_n2) | (~node9(s23)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s23, c_n2) | (~node9(s23)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2358,plain,
% 0.77/0.97 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s23, c_n2) | (~node9(s23)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(2359,plain,
% 0.77/0.97 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s23, c_n2) | (~node9(s23))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[2358, 2357])).
% 0.77/0.97 tff(2360,plain,
% 0.77/0.97 (~node9(s23)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[2359, 88, 2356])).
% 0.77/0.97 tff(2361,plain,
% 0.77/0.97 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s23, c_n2) | (~node10(s23)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s23, c_n2) | (~node10(s23)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(2362,plain,
% 0.77/0.97 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s23, c_n2) | (~node10(s23)))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(2363,plain,
% 0.77/0.98 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s23, c_n2) | (~node10(s23))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[2362, 2361])).
% 0.77/0.98 tff(2364,plain,
% 0.77/0.98 (~node10(s23)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2363, 249, 2356])).
% 0.77/0.98 tff(2365,plain,
% 0.77/0.98 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s23, c_n2) | (~node8(s23)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s23, c_n2) | (~node8(s23)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2366,plain,
% 0.77/0.98 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s23, c_n2) | (~node8(s23)))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(2367,plain,
% 0.77/0.98 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s23, c_n2) | (~node8(s23))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[2366, 2365])).
% 0.77/0.98 tff(2368,plain,
% 0.77/0.98 (~node8(s23)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2367, 271, 2356])).
% 0.77/0.98 tff(2369,plain,
% 0.77/0.98 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s23, s24)) | node14(s23, s24))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s23, s24)) | node14(s23, s24))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2370,plain,
% 0.77/0.98 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s23, s24)) | node14(s23, s24))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(2371,plain,
% 0.77/0.98 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s23, s24)) | node14(s23, s24)),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[2370, 2369])).
% 0.77/0.98 tff(2372,plain,
% 0.77/0.98 (node14(s23, s24)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2371, 46, 2303])).
% 0.77/0.98 tff(2373,plain,
% 0.77/0.98 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | node9(s23) | node8(s23) | node10(s23) | (~node14(s23, s24)) | m_main_v_state2(s24, c_c2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | node9(s23) | node8(s23) | node10(s23) | (~node14(s23, s24)) | m_main_v_state2(s24, c_c2))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2374,plain,
% 0.77/0.98 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | node9(s23) | node8(s23) | node10(s23) | (~node14(s23, s24)) | m_main_v_state2(s24, c_c2))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(2375,plain,
% 0.77/0.98 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | node9(s23) | node8(s23) | node10(s23) | (~node14(s23, s24)) | m_main_v_state2(s24, c_c2)),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[2374, 2373])).
% 0.77/0.98 tff(2376,plain,
% 0.77/0.98 ((~m_main_v_state1(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | node9(s23) | node8(s23) | node10(s23) | m_main_v_state2(s24, c_c2)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2375, 617, 2372])).
% 0.77/0.98 tff(2377,plain,
% 0.77/0.98 (m_main_v_state2(s24, c_c2)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2376, 2368, 2240, 2296, 2364, 2360])).
% 0.77/0.98 tff(2378,plain,
% 0.77/0.98 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s24, c_n2)) | (~m_main_v_state2(s24, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s24, c_n2)) | (~m_main_v_state2(s24, c_c2)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2379,plain,
% 0.77/0.98 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s24, c_n2)) | (~m_main_v_state2(s24, c_c2)))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(2380,plain,
% 0.77/0.98 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s24, c_n2)) | (~m_main_v_state2(s24, c_c2))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[2379, 2378])).
% 0.77/0.98 tff(2381,plain,
% 0.77/0.98 (~m_main_v_state2(s24, c_n2)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2380, 697, 2377])).
% 0.77/0.98 tff(2382,plain,
% 0.77/0.98 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s24, c_n2) | (~node4(s24)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s24, c_n2) | (~node4(s24)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2383,plain,
% 0.77/0.98 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s24, c_n2) | (~node4(s24)))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(2384,plain,
% 0.77/0.98 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s24, c_n2) | (~node4(s24))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[2383, 2382])).
% 0.77/0.98 tff(2385,plain,
% 0.77/0.98 (~node4(s24)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2384, 388, 2381])).
% 0.77/0.98 tff(2386,plain,
% 0.77/0.98 (succ(s24, s25) <=> succ(s24, s25)),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2387,axiom,(succ(s24, s25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound25')).
% 0.77/0.98 tff(2388,plain,
% 0.77/0.98 (succ(s24, s25)),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[2387, 2386])).
% 0.77/0.98 tff(2389,plain,
% 0.77/0.98 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s24, s25)) | trans(s24, s25))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s24, s25)) | trans(s24, s25))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2390,plain,
% 0.77/0.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s24, s25)) | trans(s24, s25))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(2391,plain,
% 0.77/0.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s24, s25)) | trans(s24, s25)),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[2390, 2389])).
% 0.77/0.98 tff(2392,plain,
% 0.77/0.98 (trans(s24, s25)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2391, 2388, 32])).
% 0.77/0.98 tff(2393,plain,
% 0.77/0.98 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s24, s25)) | node7(s24, s25))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s24, s25)) | node7(s24, s25))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2394,plain,
% 0.77/0.98 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s24, s25)) | node7(s24, s25))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(2395,plain,
% 0.77/0.98 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s24, s25)) | node7(s24, s25)),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[2394, 2393])).
% 0.77/0.98 tff(2396,plain,
% 0.77/0.98 (node7(s24, s25)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2395, 206, 2392])).
% 0.77/0.98 tff(2397,plain,
% 0.77/0.98 (((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s24, c_c1) | node1(s24) | node2(s24) | node3(s24) | node4(s24) | node5(s24) | node6(s24, s25) | (~node7(s24, s25)))) <=> ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s24, c_c1) | node1(s24) | node2(s24) | node3(s24) | node4(s24) | node5(s24) | node6(s24, s25) | (~node7(s24, s25)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2398,plain,
% 0.77/0.98 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s24, c_c1) | node1(s24) | node2(s24) | node3(s24) | node4(s24) | node5(s24) | node6(s24, s25) | (~node7(s24, s25)))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(2399,plain,
% 0.77/0.98 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s24, c_c1) | node1(s24) | node2(s24) | node3(s24) | node4(s24) | node5(s24) | node6(s24, s25) | (~node7(s24, s25))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[2398, 2397])).
% 0.77/0.98 tff(2400,plain,
% 0.77/0.98 (m_main_v_state1(s24, c_c1) | node1(s24) | node2(s24) | node3(s24) | node4(s24) | node5(s24) | node6(s24, s25)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2399, 820, 2396])).
% 0.77/0.98 tff(2401,plain,
% 0.77/0.98 (node6(s24, s25)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2400, 2385, 2349, 2345, 2341, 2337, 2320])).
% 0.77/0.98 tff(2402,plain,
% 0.77/0.98 (((~![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(s24, c_t1)) | m_main_v_state1(s25, c_t1) | (~node6(s24, s25)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s24, c_t1)) | m_main_v_state1(s25, c_t1) | (~node6(s24, s25)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2403,plain,
% 0.77/0.98 (((~node6(s24, s25)) | (~m_main_v_state1(s24, c_t1)) | m_main_v_state1(s25, c_t1)) <=> ((~m_main_v_state1(s24, c_t1)) | m_main_v_state1(s25, c_t1) | (~node6(s24, s25)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2404,plain,
% 0.77/0.98 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s24, s25)) | (~m_main_v_state1(s24, c_t1)) | m_main_v_state1(s25, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(s24, c_t1)) | m_main_v_state1(s25, c_t1) | (~node6(s24, s25))))),
% 0.77/0.98 inference(monotonicity,[status(thm)],[2403])).
% 0.77/0.98 tff(2405,plain,
% 0.77/0.98 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s24, s25)) | (~m_main_v_state1(s24, c_t1)) | m_main_v_state1(s25, c_t1))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s24, c_t1)) | m_main_v_state1(s25, c_t1) | (~node6(s24, s25)))),
% 0.77/0.98 inference(transitivity,[status(thm)],[2404, 2402])).
% 0.77/0.98 tff(2406,plain,
% 0.77/0.98 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s24, s25)) | (~m_main_v_state1(s24, c_t1)) | m_main_v_state1(s25, c_t1))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(2407,plain,
% 0.77/0.98 ((~![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(s24, c_t1)) | m_main_v_state1(s25, c_t1) | (~node6(s24, s25))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[2406, 2405])).
% 0.77/0.98 tff(2408,plain,
% 0.77/0.98 (m_main_v_state1(s25, c_t1)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2407, 856, 2312, 2401])).
% 0.77/0.98 tff(2409,plain,
% 0.77/0.98 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s24, c_t2)) | (~m_main_v_state2(s24, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s24, c_t2)) | (~m_main_v_state2(s24, c_c2)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2410,plain,
% 0.77/0.98 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s24, c_t2)) | (~m_main_v_state2(s24, c_c2)))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(2411,plain,
% 0.77/0.98 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s24, c_t2)) | (~m_main_v_state2(s24, c_c2))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[2410, 2409])).
% 0.77/0.98 tff(2412,plain,
% 0.77/0.98 (~m_main_v_state2(s24, c_t2)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2411, 260, 2377])).
% 0.77/0.98 tff(2413,plain,
% 0.77/0.98 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s24, c_t2) | (~node12(s24)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s24, c_t2) | (~node12(s24)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2414,plain,
% 0.77/0.98 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s24, c_t2) | (~node12(s24)))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(2415,plain,
% 0.77/0.98 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s24, c_t2) | (~node12(s24))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[2414, 2413])).
% 0.77/0.98 tff(2416,plain,
% 0.77/0.98 (~node12(s24)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2415, 633, 2412])).
% 0.77/0.98 tff(2417,plain,
% 0.77/0.98 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s24, c_n1) | (~node11(s24)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s24, c_n1) | (~node11(s24)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2418,plain,
% 0.77/0.98 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s24, c_n1) | (~node11(s24)))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(2419,plain,
% 0.77/0.98 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s24, c_n1) | (~node11(s24))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[2418, 2417])).
% 0.77/0.98 tff(2420,plain,
% 0.77/0.98 (~node11(s24)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2419, 238, 2316])).
% 0.77/0.98 tff(2421,plain,
% 0.77/0.98 (((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s24, c_c1) | (~node10(s24)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s24, c_c1) | (~node10(s24)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2422,plain,
% 0.77/0.98 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s24, c_c1) | (~node10(s24)))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(2423,plain,
% 0.77/0.98 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s24, c_c1) | (~node10(s24))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[2422, 2421])).
% 0.77/0.98 tff(2424,plain,
% 0.77/0.98 (~node10(s24)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2423, 675, 2349])).
% 0.77/0.98 tff(2425,plain,
% 0.77/0.98 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s24, c_n1) | (~node9(s24)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s24, c_n1) | (~node9(s24)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2426,plain,
% 0.77/0.98 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s24, c_n1) | (~node9(s24)))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(2427,plain,
% 0.77/0.98 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s24, c_n1) | (~node9(s24))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[2426, 2425])).
% 0.77/0.98 tff(2428,plain,
% 0.77/0.98 (~node9(s24)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2427, 686, 2316])).
% 0.77/0.98 tff(2429,plain,
% 0.77/0.98 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s24, c_n2) | (~node8(s24)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s24, c_n2) | (~node8(s24)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2430,plain,
% 0.77/0.98 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s24, c_n2) | (~node8(s24)))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(2431,plain,
% 0.77/0.98 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s24, c_n2) | (~node8(s24))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[2430, 2429])).
% 0.77/0.98 tff(2432,plain,
% 0.77/0.98 (~node8(s24)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2431, 271, 2381])).
% 0.77/0.98 tff(2433,plain,
% 0.77/0.98 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s24, s25)) | node14(s24, s25))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s24, s25)) | node14(s24, s25))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2434,plain,
% 0.77/0.98 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s24, s25)) | node14(s24, s25))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(2435,plain,
% 0.77/0.98 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s24, s25)) | node14(s24, s25)),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[2434, 2433])).
% 0.77/0.98 tff(2436,plain,
% 0.77/0.98 (node14(s24, s25)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2435, 46, 2392])).
% 0.77/0.98 tff(2437,plain,
% 0.77/0.98 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s25, c_n2) | node9(s24) | node8(s24) | node10(s24) | node11(s24) | node12(s24) | (~node14(s24, s25)) | (~m_main_v_state2(s24, c_c2)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s25, c_n2) | node9(s24) | node8(s24) | node10(s24) | node11(s24) | node12(s24) | (~node14(s24, s25)) | (~m_main_v_state2(s24, c_c2)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2438,plain,
% 0.77/0.98 (((~m_main_v_state2(s24, c_c2)) | node9(s24) | node8(s24) | node10(s24) | node11(s24) | node12(s24) | (~node14(s24, s25)) | m_main_v_state2(s25, c_n2)) <=> (m_main_v_state2(s25, c_n2) | node9(s24) | node8(s24) | node10(s24) | node11(s24) | node12(s24) | (~node14(s24, s25)) | (~m_main_v_state2(s24, c_c2)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2439,plain,
% 0.77/0.98 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s24, c_c2)) | node9(s24) | node8(s24) | node10(s24) | node11(s24) | node12(s24) | (~node14(s24, s25)) | m_main_v_state2(s25, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(s25, c_n2) | node9(s24) | node8(s24) | node10(s24) | node11(s24) | node12(s24) | (~node14(s24, s25)) | (~m_main_v_state2(s24, c_c2))))),
% 0.77/0.98 inference(monotonicity,[status(thm)],[2438])).
% 0.77/0.98 tff(2440,plain,
% 0.77/0.98 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s24, c_c2)) | node9(s24) | node8(s24) | node10(s24) | node11(s24) | node12(s24) | (~node14(s24, s25)) | m_main_v_state2(s25, c_n2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s25, c_n2) | node9(s24) | node8(s24) | node10(s24) | node11(s24) | node12(s24) | (~node14(s24, s25)) | (~m_main_v_state2(s24, c_c2)))),
% 0.77/0.98 inference(transitivity,[status(thm)],[2439, 2437])).
% 0.77/0.98 tff(2441,plain,
% 0.77/0.98 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s24, c_c2)) | node9(s24) | node8(s24) | node10(s24) | node11(s24) | node12(s24) | (~node14(s24, s25)) | m_main_v_state2(s25, c_n2))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(2442,plain,
% 0.77/0.98 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s25, c_n2) | node9(s24) | node8(s24) | node10(s24) | node11(s24) | node12(s24) | (~node14(s24, s25)) | (~m_main_v_state2(s24, c_c2))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[2441, 2440])).
% 0.77/0.98 tff(2443,plain,
% 0.77/0.98 (m_main_v_state2(s25, c_n2) | node9(s24) | node8(s24) | node10(s24) | node11(s24) | node12(s24) | (~m_main_v_state2(s24, c_c2))),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2442, 726, 2436])).
% 0.77/0.98 tff(2444,plain,
% 0.77/0.98 (m_main_v_state2(s25, c_n2)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2443, 2432, 2377, 2428, 2424, 2420, 2416])).
% 0.77/0.98 tff(2445,plain,
% 0.77/0.98 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s25, c_n2)) | (~m_main_v_state2(s25, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s25, c_n2)) | (~m_main_v_state2(s25, c_t2)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2446,plain,
% 0.77/0.98 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s25, c_n2)) | (~m_main_v_state2(s25, c_t2)))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(2447,plain,
% 0.77/0.98 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s25, c_n2)) | (~m_main_v_state2(s25, c_t2))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[2446, 2445])).
% 0.77/0.98 tff(2448,plain,
% 0.77/0.98 (~m_main_v_state2(s25, c_t2)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2447, 77, 2444])).
% 0.77/0.98 tff(2449,plain,
% 0.77/0.98 (((~![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)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(2450,plain,
% 0.82/0.98 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s25, c_t2) | (~node15(s25)))),
% 0.82/0.98 inference(quant_inst,[status(thm)],[])).
% 0.82/0.98 tff(2451,plain,
% 0.82/0.98 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s25, c_t2) | (~node15(s25))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[2450, 2449])).
% 0.82/0.98 tff(2452,plain,
% 0.82/0.98 (~node15(s25)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[2451, 103, 2448])).
% 0.82/0.98 tff(2453,plain,
% 0.82/0.98 (succ(s25, s26) <=> succ(s25, s26)),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(2454,axiom,(succ(s25, s26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound26')).
% 0.82/0.98 tff(2455,plain,
% 0.82/0.98 (succ(s25, s26)),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[2454, 2453])).
% 0.82/0.98 tff(2456,plain,
% 0.82/0.98 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s25, s26)) | trans(s25, s26))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s25, s26)) | trans(s25, s26))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(2457,plain,
% 0.82/0.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s25, s26)) | trans(s25, s26))),
% 0.82/0.98 inference(quant_inst,[status(thm)],[])).
% 0.82/0.98 tff(2458,plain,
% 0.82/0.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s25, s26)) | trans(s25, s26)),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[2457, 2456])).
% 0.82/0.98 tff(2459,plain,
% 0.82/0.98 (trans(s25, s26)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[2458, 2455, 32])).
% 0.82/0.98 tff(2460,plain,
% 0.82/0.98 (((~![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))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(2461,plain,
% 0.82/0.98 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s25, s26)) | node18(s25, s26))),
% 0.82/0.98 inference(quant_inst,[status(thm)],[])).
% 0.82/0.98 tff(2462,plain,
% 0.82/0.98 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s25, s26)) | node18(s25, s26)),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[2461, 2460])).
% 0.82/0.98 tff(2463,plain,
% 0.82/0.98 (node18(s25, s26)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[2462, 125, 2459])).
% 0.82/0.98 tff(2464,plain,
% 0.82/0.98 (((~![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(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))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(2465,plain,
% 0.82/0.98 (((~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))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(2466,plain,
% 0.82/0.98 (((~![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(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)))),
% 0.82/0.98 inference(monotonicity,[status(thm)],[2465])).
% 0.82/0.98 tff(2467,plain,
% 0.82/0.98 (((~![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(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))),
% 0.82/0.98 inference(transitivity,[status(thm)],[2466, 2464])).
% 0.82/0.98 tff(2468,plain,
% 0.82/0.98 ((~![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(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | node15(s25) | (~node18(s25, s26)) | m_main_v_turn(s26, c_1))),
% 0.82/0.98 inference(quant_inst,[status(thm)],[])).
% 0.82/0.98 tff(2469,plain,
% 0.82/0.98 ((~![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(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)),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[2468, 2467])).
% 0.82/0.98 tff(2470,plain,
% 0.82/0.98 (node15(s25) | (~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | m_main_v_turn(s26, c_1)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[2469, 992, 2463])).
% 0.82/0.98 tff(2471,plain,
% 0.82/0.98 (m_main_v_turn(s26, c_1)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[2470, 2452, 2444, 2408])).
% 0.82/0.98 tff(2472,plain,
% 0.82/0.98 (((~![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)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(2473,plain,
% 0.82/0.98 ((~![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)))),
% 0.82/0.98 inference(quant_inst,[status(thm)],[])).
% 0.82/0.98 tff(2474,plain,
% 0.82/0.98 ((~![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))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[2473, 2472])).
% 0.82/0.98 tff(2475,plain,
% 0.82/0.98 (~m_main_v_turn(s26, c_2)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[2474, 156, 2471])).
% 0.82/0.98 tff(2476,plain,
% 0.82/0.98 (((~![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)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(2477,plain,
% 0.82/0.98 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s26, c_2) | (~node12(s26)))),
% 0.82/0.98 inference(quant_inst,[status(thm)],[])).
% 0.82/0.98 tff(2478,plain,
% 0.82/0.98 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s26, c_2) | (~node12(s26))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[2477, 2476])).
% 0.82/0.98 tff(2479,plain,
% 0.82/0.98 (~node12(s26)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[2478, 184, 2475])).
% 0.82/0.98 tff(2480,plain,
% 0.82/0.98 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s25, s26)) | node14(s25, s26))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s25, s26)) | node14(s25, s26))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(2481,plain,
% 0.82/0.98 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s25, s26)) | node14(s25, s26))),
% 0.82/0.98 inference(quant_inst,[status(thm)],[])).
% 0.82/0.98 tff(2482,plain,
% 0.82/0.98 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s25, s26)) | node14(s25, s26)),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[2481, 2480])).
% 0.82/0.98 tff(2483,plain,
% 0.82/0.98 (node14(s25, s26)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[2482, 46, 2459])).
% 0.82/0.98 tff(2484,plain,
% 0.82/0.98 (((~![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(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | (~node14(s25, s26)) | m_main_v_state2(s26, c_t2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | (~node14(s25, s26)) | m_main_v_state2(s26, c_t2))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2485,plain,
% 0.82/0.99 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | (~node14(s25, s26)) | m_main_v_state2(s26, c_t2))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(2486,plain,
% 0.82/0.99 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | (~node14(s25, s26)) | m_main_v_state2(s26, c_t2)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[2485, 2484])).
% 0.82/0.99 tff(2487,plain,
% 0.82/0.99 ((~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | m_main_v_state2(s26, c_t2)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[2486, 922, 2483])).
% 0.82/0.99 tff(2488,plain,
% 0.82/0.99 (m_main_v_state2(s26, c_t2)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[2487, 2408, 2444])).
% 0.82/0.99 tff(2489,plain,
% 0.82/0.99 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s26, c_n2)) | (~m_main_v_state2(s26, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s26, c_n2)) | (~m_main_v_state2(s26, c_t2)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2490,plain,
% 0.82/0.99 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s26, c_n2)) | (~m_main_v_state2(s26, c_t2)))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(2491,plain,
% 0.82/0.99 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s26, c_n2)) | (~m_main_v_state2(s26, c_t2))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[2490, 2489])).
% 0.82/0.99 tff(2492,plain,
% 0.82/0.99 (~m_main_v_state2(s26, c_n2)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[2491, 77, 2488])).
% 0.82/0.99 tff(2493,plain,
% 0.82/0.99 (((~![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)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2494,plain,
% 0.82/0.99 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s26, c_n2) | (~node8(s26)))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(2495,plain,
% 0.82/0.99 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s26, c_n2) | (~node8(s26))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[2494, 2493])).
% 0.82/0.99 tff(2496,plain,
% 0.82/0.99 (~node8(s26)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[2495, 271, 2492])).
% 0.82/0.99 tff(2497,plain,
% 0.82/0.99 (((~![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)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2498,plain,
% 0.82/0.99 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s26, c_n2) | (~node9(s26)))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(2499,plain,
% 0.82/0.99 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s26, c_n2) | (~node9(s26))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[2498, 2497])).
% 0.82/0.99 tff(2500,plain,
% 0.82/0.99 (~node9(s26)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[2499, 88, 2492])).
% 0.82/0.99 tff(2501,plain,
% 0.82/0.99 (((~![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)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2502,plain,
% 0.82/0.99 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s26, c_n2) | (~node10(s26)))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(2503,plain,
% 0.82/0.99 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s26, c_n2) | (~node10(s26))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[2502, 2501])).
% 0.82/0.99 tff(2504,plain,
% 0.82/0.99 (~node10(s26)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[2503, 249, 2492])).
% 0.82/0.99 tff(2505,plain,
% 0.82/0.99 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s26, c_t2)) | (~m_main_v_state2(s26, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s26, c_t2)) | (~m_main_v_state2(s26, c_c2)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2506,plain,
% 0.82/0.99 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s26, c_t2)) | (~m_main_v_state2(s26, c_c2)))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(2507,plain,
% 0.82/0.99 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s26, c_t2)) | (~m_main_v_state2(s26, c_c2))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[2506, 2505])).
% 0.82/0.99 tff(2508,plain,
% 0.82/0.99 (~m_main_v_state2(s26, c_c2)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[2507, 260, 2488])).
% 0.82/0.99 tff(2509,plain,
% 0.82/0.99 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s25, c_n2)) | (~m_main_v_state2(s25, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s25, c_n2)) | (~m_main_v_state2(s25, c_c2)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2510,plain,
% 0.82/0.99 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s25, c_n2)) | (~m_main_v_state2(s25, c_c2)))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(2511,plain,
% 0.82/0.99 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s25, c_n2)) | (~m_main_v_state2(s25, c_c2))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[2510, 2509])).
% 0.82/0.99 tff(2512,plain,
% 0.82/0.99 (~m_main_v_state2(s25, c_c2)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[2511, 697, 2444])).
% 0.82/0.99 tff(2513,plain,
% 0.82/0.99 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s25, c_c2) | (~node3(s25)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s25, c_c2) | (~node3(s25)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2514,plain,
% 0.82/0.99 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s25, c_c2) | (~node3(s25)))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(2515,plain,
% 0.82/0.99 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s25, c_c2) | (~node3(s25))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[2514, 2513])).
% 0.82/0.99 tff(2516,plain,
% 0.82/0.99 (~node3(s25)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[2515, 399, 2512])).
% 0.82/0.99 tff(2517,plain,
% 0.82/0.99 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s24, c_n1) | (~m_main_v_state1(s25, c_n1)) | (~node6(s24, s25)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s24, c_n1) | (~m_main_v_state1(s25, c_n1)) | (~node6(s24, s25)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2518,plain,
% 0.82/0.99 (((~node6(s24, s25)) | m_main_v_state1(s24, c_n1) | (~m_main_v_state1(s25, c_n1))) <=> (m_main_v_state1(s24, c_n1) | (~m_main_v_state1(s25, c_n1)) | (~node6(s24, s25)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2519,plain,
% 0.82/0.99 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s24, s25)) | m_main_v_state1(s24, c_n1) | (~m_main_v_state1(s25, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(s24, c_n1) | (~m_main_v_state1(s25, c_n1)) | (~node6(s24, s25))))),
% 0.82/0.99 inference(monotonicity,[status(thm)],[2518])).
% 0.82/0.99 tff(2520,plain,
% 0.82/0.99 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s24, s25)) | m_main_v_state1(s24, c_n1) | (~m_main_v_state1(s25, c_n1)))) <=> ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s24, c_n1) | (~m_main_v_state1(s25, c_n1)) | (~node6(s24, s25)))),
% 0.82/0.99 inference(transitivity,[status(thm)],[2519, 2517])).
% 0.82/0.99 tff(2521,plain,
% 0.82/0.99 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s24, s25)) | m_main_v_state1(s24, c_n1) | (~m_main_v_state1(s25, c_n1)))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(2522,plain,
% 0.82/0.99 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s24, c_n1) | (~m_main_v_state1(s25, c_n1)) | (~node6(s24, s25))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[2521, 2520])).
% 0.82/0.99 tff(2523,plain,
% 0.82/0.99 (~m_main_v_state1(s25, c_n1)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[2522, 835, 2316, 2401])).
% 0.82/0.99 tff(2524,plain,
% 0.82/0.99 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s25, c_n1) | (~node2(s25)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s25, c_n1) | (~node2(s25)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2525,plain,
% 0.82/0.99 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s25, c_n1) | (~node2(s25)))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(2526,plain,
% 0.82/0.99 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s25, c_n1) | (~node2(s25))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[2525, 2524])).
% 0.82/0.99 tff(2527,plain,
% 0.82/0.99 (~node2(s25)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[2526, 787, 2523])).
% 0.82/0.99 tff(2528,plain,
% 0.82/0.99 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s25, c_t2) | (~node1(s25)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s25, c_t2) | (~node1(s25)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2529,plain,
% 0.82/0.99 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s25, c_t2) | (~node1(s25)))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(2530,plain,
% 0.82/0.99 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s25, c_t2) | (~node1(s25))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[2529, 2528])).
% 0.82/0.99 tff(2531,plain,
% 0.82/0.99 (~node1(s25)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[2530, 195, 2448])).
% 0.82/0.99 tff(2532,plain,
% 0.82/0.99 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s25, s26)) | node7(s25, s26))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s25, s26)) | node7(s25, s26))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2533,plain,
% 0.82/0.99 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s25, s26)) | node7(s25, s26))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(2534,plain,
% 0.82/0.99 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s25, s26)) | node7(s25, s26)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[2533, 2532])).
% 0.82/0.99 tff(2535,plain,
% 0.82/0.99 (node7(s25, s26)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[2534, 206, 2459])).
% 0.82/0.99 tff(2536,plain,
% 0.82/0.99 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | m_main_v_state1(s26, c_c1) | node1(s25) | node2(s25) | node3(s25) | (~node7(s25, s26)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | m_main_v_state1(s26, c_c1) | node1(s25) | node2(s25) | node3(s25) | (~node7(s25, s26)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2537,plain,
% 0.82/0.99 (((~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | node1(s25) | node2(s25) | node3(s25) | (~node7(s25, s26)) | m_main_v_state1(s26, c_c1)) <=> ((~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | m_main_v_state1(s26, c_c1) | node1(s25) | node2(s25) | node3(s25) | (~node7(s25, s26)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2538,plain,
% 0.82/0.99 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | node1(s25) | node2(s25) | node3(s25) | (~node7(s25, s26)) | m_main_v_state1(s26, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | m_main_v_state1(s26, c_c1) | node1(s25) | node2(s25) | node3(s25) | (~node7(s25, s26))))),
% 0.82/0.99 inference(monotonicity,[status(thm)],[2537])).
% 0.82/0.99 tff(2539,plain,
% 0.82/0.99 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | node1(s25) | node2(s25) | node3(s25) | (~node7(s25, s26)) | m_main_v_state1(s26, c_c1))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | m_main_v_state1(s26, c_c1) | node1(s25) | node2(s25) | node3(s25) | (~node7(s25, s26)))),
% 0.82/0.99 inference(transitivity,[status(thm)],[2538, 2536])).
% 0.82/0.99 tff(2540,plain,
% 0.82/0.99 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | node1(s25) | node2(s25) | node3(s25) | (~node7(s25, s26)) | m_main_v_state1(s26, c_c1))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(2541,plain,
% 0.82/0.99 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | m_main_v_state1(s26, c_c1) | node1(s25) | node2(s25) | node3(s25) | (~node7(s25, s26))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[2540, 2539])).
% 0.82/0.99 tff(2542,plain,
% 0.82/0.99 ((~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | m_main_v_state1(s26, c_c1) | node1(s25) | node2(s25) | node3(s25)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[2541, 892, 2535])).
% 0.82/0.99 tff(2543,plain,
% 0.82/0.99 (m_main_v_state1(s26, c_c1)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[2542, 2531, 2444, 2408, 2527, 2516])).
% 0.82/0.99 tff(2544,plain,
% 0.82/0.99 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s26, c_n1)) | (~m_main_v_state1(s26, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s26, c_n1)) | (~m_main_v_state1(s26, c_c1)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2545,plain,
% 0.82/0.99 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s26, c_n1)) | (~m_main_v_state1(s26, c_c1)))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(2546,plain,
% 0.82/0.99 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s26, c_n1)) | (~m_main_v_state1(s26, c_c1))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[2545, 2544])).
% 0.82/0.99 tff(2547,plain,
% 0.82/0.99 (~m_main_v_state1(s26, c_n1)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[2546, 454, 2543])).
% 0.82/0.99 tff(2548,plain,
% 0.82/0.99 (((~![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)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2549,plain,
% 0.82/0.99 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s26, c_n1) | (~node11(s26)))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(2550,plain,
% 0.82/0.99 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s26, c_n1) | (~node11(s26))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[2549, 2548])).
% 0.82/0.99 tff(2551,plain,
% 0.82/0.99 (~node11(s26)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[2550, 238, 2547])).
% 0.82/0.99 tff(2552,plain,
% 0.82/0.99 (succ(s26, s27) <=> succ(s26, s27)),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2553,axiom,(succ(s26, s27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound27')).
% 0.82/0.99 tff(2554,plain,
% 0.82/0.99 (succ(s26, s27)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[2553, 2552])).
% 0.82/0.99 tff(2555,plain,
% 0.82/0.99 (((~![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))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2556,plain,
% 0.82/0.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s26, s27)) | trans(s26, s27))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(2557,plain,
% 0.82/0.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s26, s27)) | trans(s26, s27)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[2556, 2555])).
% 0.82/0.99 tff(2558,plain,
% 0.82/0.99 (trans(s26, s27)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[2557, 2554, 32])).
% 0.82/0.99 tff(2559,plain,
% 0.82/0.99 (((~![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))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2560,plain,
% 0.82/0.99 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s26, s27)) | node14(s26, s27))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(2561,plain,
% 0.82/0.99 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s26, s27)) | node14(s26, s27)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[2560, 2559])).
% 0.82/0.99 tff(2562,plain,
% 0.82/0.99 (node14(s26, s27)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[2561, 46, 2558])).
% 0.82/0.99 tff(2563,plain,
% 0.82/0.99 (((~![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)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2564,plain,
% 0.82/0.99 ((~![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)))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(2565,plain,
% 0.82/0.99 ((~![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))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[2564, 2563])).
% 0.82/0.99 tff(2566,plain,
% 0.82/0.99 (m_main_v_state2(s26, c_c2) | node9(s26) | node8(s26) | node10(s26) | node11(s26) | node12(s26) | node13(s26, s27)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[2565, 296, 2562])).
% 0.82/0.99 tff(2567,plain,
% 0.82/0.99 (node13(s26, s27)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[2566, 2551, 2508, 2504, 2500, 2496, 2479])).
% 0.82/0.99 tff(2568,plain,
% 0.82/0.99 (((~![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(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)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2569,plain,
% 0.82/0.99 (((~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)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2570,plain,
% 0.82/0.99 (((~![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))))),
% 0.82/0.99 inference(monotonicity,[status(thm)],[2569])).
% 0.82/0.99 tff(2571,plain,
% 0.82/0.99 (((~![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)))),
% 0.82/0.99 inference(transitivity,[status(thm)],[2570, 2568])).
% 0.82/0.99 tff(2572,plain,
% 0.82/0.99 ((~![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)))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(2573,plain,
% 0.82/0.99 ((~![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(s26, c_n2) | (~m_main_v_state2(s27, c_n2)) | (~node13(s26, s27))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[2572, 2571])).
% 0.82/0.99 tff(2574,plain,
% 0.82/0.99 (~m_main_v_state2(s27, c_n2)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[2573, 311, 2492, 2567])).
% 0.82/0.99 tff(2575,plain,
% 0.82/0.99 (((~![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)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2576,plain,
% 0.82/0.99 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s27, c_n2) | (~node9(s27)))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(2577,plain,
% 0.82/0.99 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s27, c_n2) | (~node9(s27))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[2576, 2575])).
% 0.82/0.99 tff(2578,plain,
% 0.82/0.99 (~node9(s27)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[2577, 88, 2574])).
% 0.82/0.99 tff(2579,plain,
% 0.82/0.99 (((~![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)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2580,plain,
% 0.82/0.99 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s27, c_n2) | (~node10(s27)))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(2581,plain,
% 0.82/0.99 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s27, c_n2) | (~node10(s27))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[2580, 2579])).
% 0.82/0.99 tff(2582,plain,
% 0.82/0.99 (~node10(s27)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[2581, 249, 2574])).
% 0.82/0.99 tff(2583,plain,
% 0.82/0.99 (((~![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(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)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2584,plain,
% 0.82/0.99 (((~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)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2585,plain,
% 0.82/0.99 (((~![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))))),
% 0.82/0.99 inference(monotonicity,[status(thm)],[2584])).
% 0.82/0.99 tff(2586,plain,
% 0.82/0.99 (((~![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)))),
% 0.82/0.99 inference(transitivity,[status(thm)],[2585, 2583])).
% 0.82/0.99 tff(2587,plain,
% 0.82/0.99 ((~![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))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(2588,plain,
% 0.82/0.99 ((~![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(s26, c_t2)) | m_main_v_state2(s27, c_t2) | (~node13(s26, s27))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[2587, 2586])).
% 0.82/0.99 tff(2589,plain,
% 0.82/0.99 (m_main_v_state2(s27, c_t2)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[2588, 518, 2488, 2567])).
% 0.82/0.99 tff(2590,plain,
% 0.82/0.99 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s26, c_t1)) | (~m_main_v_state1(s26, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s26, c_t1)) | (~m_main_v_state1(s26, c_c1)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2591,plain,
% 0.82/0.99 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s26, c_t1)) | (~m_main_v_state1(s26, c_c1)))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(2592,plain,
% 0.82/0.99 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s26, c_t1)) | (~m_main_v_state1(s26, c_c1))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[2591, 2590])).
% 0.82/0.99 tff(2593,plain,
% 0.82/0.99 (~m_main_v_state1(s26, c_t1)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[2592, 539, 2543])).
% 0.82/0.99 tff(2594,plain,
% 0.82/0.99 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s26, c_t1) | (~node5(s26)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s26, c_t1) | (~node5(s26)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2595,plain,
% 0.82/0.99 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s26, c_t1) | (~node5(s26)))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(2596,plain,
% 0.82/0.99 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s26, c_t1) | (~node5(s26))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[2595, 2594])).
% 0.82/0.99 tff(2597,plain,
% 0.82/0.99 (~node5(s26)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[2596, 550, 2593])).
% 0.82/0.99 tff(2598,plain,
% 0.82/0.99 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s26, c_n2) | (~node4(s26)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s26, c_n2) | (~node4(s26)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2599,plain,
% 0.82/0.99 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s26, c_n2) | (~node4(s26)))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(2600,plain,
% 0.82/0.99 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s26, c_n2) | (~node4(s26))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[2599, 2598])).
% 0.82/0.99 tff(2601,plain,
% 0.82/0.99 (~node4(s26)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[2600, 388, 2492])).
% 0.82/0.99 tff(2602,plain,
% 0.82/0.99 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s26, c_c2) | (~node3(s26)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s26, c_c2) | (~node3(s26)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(2603,plain,
% 0.82/0.99 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s26, c_c2) | (~node3(s26)))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(2604,plain,
% 0.82/0.99 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s26, c_c2) | (~node3(s26))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[2603, 2602])).
% 0.82/0.99 tff(2605,plain,
% 0.82/0.99 (~node3(s26)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[2604, 399, 2508])).
% 0.82/0.99 tff(2606,plain,
% 0.82/0.99 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s26, c_n2) | (~node2(s26)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s26, c_n2) | (~node2(s26)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(2607,plain,
% 0.82/1.00 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s26, c_n2) | (~node2(s26)))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(2608,plain,
% 0.82/1.00 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s26, c_n2) | (~node2(s26))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[2607, 2606])).
% 0.82/1.00 tff(2609,plain,
% 0.82/1.00 (~node2(s26)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[2608, 410, 2492])).
% 0.82/1.00 tff(2610,plain,
% 0.82/1.00 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s26, c_n1) | (~node1(s26)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s26, c_n1) | (~node1(s26)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(2611,plain,
% 0.82/1.00 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s26, c_n1) | (~node1(s26)))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(2612,plain,
% 0.82/1.00 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s26, c_n1) | (~node1(s26))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[2611, 2610])).
% 0.82/1.00 tff(2613,plain,
% 0.82/1.00 (~node1(s26)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[2612, 421, 2547])).
% 0.82/1.00 tff(2614,plain,
% 0.82/1.00 (((~![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))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(2615,plain,
% 0.82/1.00 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s26, s27)) | node7(s26, s27))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(2616,plain,
% 0.82/1.00 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s26, s27)) | node7(s26, s27)),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[2615, 2614])).
% 0.82/1.00 tff(2617,plain,
% 0.82/1.00 (node7(s26, s27)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[2616, 206, 2558])).
% 0.82/1.00 tff(2618,plain,
% 0.82/1.00 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(2619,plain,
% 0.82/1.00 (((~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)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(2620,plain,
% 0.82/1.00 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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))))),
% 0.82/1.00 inference(monotonicity,[status(thm)],[2619])).
% 0.82/1.00 tff(2621,plain,
% 0.82/1.00 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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)))),
% 0.82/1.00 inference(transitivity,[status(thm)],[2620, 2618])).
% 0.82/1.00 tff(2622,plain,
% 0.82/1.00 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(2623,plain,
% 0.82/1.00 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[2622, 2621])).
% 0.82/1.00 tff(2624,plain,
% 0.82/1.00 (m_main_v_state1(s27, c_n1) | (~m_main_v_state1(s26, c_c1)) | node1(s26) | node2(s26) | node3(s26) | node4(s26) | node5(s26)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[2623, 584, 2617])).
% 0.82/1.00 tff(2625,plain,
% 0.82/1.00 (m_main_v_state1(s27, c_n1)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[2624, 2613, 2543, 2609, 2605, 2601, 2597])).
% 0.82/1.00 tff(2626,plain,
% 0.82/1.00 (((~![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)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(2627,plain,
% 0.82/1.00 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s27, c_n2) | (~node8(s27)))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(2628,plain,
% 0.82/1.00 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s27, c_n2) | (~node8(s27))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[2627, 2626])).
% 0.82/1.00 tff(2629,plain,
% 0.82/1.00 (~node8(s27)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[2628, 271, 2574])).
% 0.82/1.00 tff(2630,plain,
% 0.82/1.00 (succ(s27, s28) <=> succ(s27, s28)),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(2631,axiom,(succ(s27, s28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound28')).
% 0.82/1.00 tff(2632,plain,
% 0.82/1.00 (succ(s27, s28)),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[2631, 2630])).
% 0.82/1.00 tff(2633,plain,
% 0.82/1.00 (((~![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))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(2634,plain,
% 0.82/1.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s27, s28)) | trans(s27, s28))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(2635,plain,
% 0.82/1.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s27, s28)) | trans(s27, s28)),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[2634, 2633])).
% 0.82/1.00 tff(2636,plain,
% 0.82/1.00 (trans(s27, s28)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[2635, 2632, 32])).
% 0.82/1.00 tff(2637,plain,
% 0.82/1.00 (((~![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))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(2638,plain,
% 0.82/1.00 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s27, s28)) | node14(s27, s28))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(2639,plain,
% 0.82/1.00 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s27, s28)) | node14(s27, s28)),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[2638, 2637])).
% 0.82/1.00 tff(2640,plain,
% 0.82/1.00 (node14(s27, s28)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[2639, 46, 2636])).
% 0.82/1.00 tff(2641,plain,
% 0.82/1.00 (((~![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))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(2642,plain,
% 0.82/1.00 ((~![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))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(2643,plain,
% 0.82/1.00 ((~![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)),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[2642, 2641])).
% 0.82/1.00 tff(2644,plain,
% 0.82/1.00 ((~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)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[2643, 617, 2640])).
% 0.82/1.00 tff(2645,plain,
% 0.82/1.00 (m_main_v_state2(s28, c_c2)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[2644, 2629, 2625, 2589, 2582, 2578])).
% 0.82/1.00 tff(2646,plain,
% 0.82/1.00 (((~![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)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(2647,plain,
% 0.82/1.00 ((~![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)))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(2648,plain,
% 0.82/1.00 ((~![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))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[2647, 2646])).
% 0.82/1.00 tff(2649,plain,
% 0.82/1.00 (~m_main_v_state2(s28, c_t2)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[2648, 260, 2645])).
% 0.82/1.00 tff(2650,plain,
% 0.82/1.00 (((~![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)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(2651,plain,
% 0.82/1.00 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s28, c_t2) | (~node12(s28)))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(2652,plain,
% 0.82/1.00 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s28, c_t2) | (~node12(s28))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[2651, 2650])).
% 0.82/1.00 tff(2653,plain,
% 0.82/1.00 (~node12(s28)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[2652, 633, 2649])).
% 0.82/1.00 tff(2654,plain,
% 0.82/1.00 (((~![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))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(2655,plain,
% 0.82/1.00 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s27, s28)) | node7(s27, s28))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(2656,plain,
% 0.82/1.00 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s27, s28)) | node7(s27, s28)),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[2655, 2654])).
% 0.82/1.00 tff(2657,plain,
% 0.82/1.00 (node7(s27, s28)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[2656, 206, 2636])).
% 0.82/1.00 tff(2658,plain,
% 0.82/1.00 (((~![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))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(2659,plain,
% 0.82/1.00 ((~![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))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(2660,plain,
% 0.82/1.00 ((~![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)),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[2659, 2658])).
% 0.82/1.00 tff(2661,plain,
% 0.82/1.00 ((~m_main_v_state1(s27, c_n1)) | (~m_main_v_state2(s27, c_t2)) | m_main_v_state1(s28, c_t1)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[2660, 651, 2657])).
% 0.82/1.00 tff(2662,plain,
% 0.82/1.00 (m_main_v_state1(s28, c_t1)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[2661, 2589, 2625])).
% 0.82/1.00 tff(2663,plain,
% 0.82/1.00 (((~![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)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(2664,plain,
% 0.82/1.00 ((~![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)))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(2665,plain,
% 0.82/1.00 ((~![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))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[2664, 2663])).
% 0.82/1.00 tff(2666,plain,
% 0.82/1.00 (~m_main_v_state1(s28, c_n1)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[2665, 10, 2662])).
% 0.82/1.00 tff(2667,plain,
% 0.82/1.00 (((~![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)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(2668,plain,
% 0.82/1.00 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s28, c_n1) | (~node11(s28)))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(2669,plain,
% 0.82/1.00 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s28, c_n1) | (~node11(s28))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[2668, 2667])).
% 0.82/1.00 tff(2670,plain,
% 0.82/1.00 (~node11(s28)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[2669, 238, 2666])).
% 0.82/1.00 tff(2671,plain,
% 0.82/1.00 (((~![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)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(2672,plain,
% 0.82/1.00 ((~![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)))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(2673,plain,
% 0.82/1.00 ((~![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))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[2672, 2671])).
% 0.82/1.00 tff(2674,plain,
% 0.82/1.00 (~m_main_v_state1(s28, c_c1)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[2673, 539, 2662])).
% 0.82/1.00 tff(2675,plain,
% 0.82/1.00 (((~![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)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(2676,plain,
% 0.82/1.00 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s28, c_c1) | (~node10(s28)))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(2677,plain,
% 0.82/1.00 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s28, c_c1) | (~node10(s28))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[2676, 2675])).
% 0.82/1.00 tff(2678,plain,
% 0.82/1.00 (~node10(s28)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[2677, 675, 2674])).
% 0.82/1.00 tff(2679,plain,
% 0.82/1.00 (((~![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)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(2680,plain,
% 0.82/1.00 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s28, c_n1) | (~node9(s28)))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(2681,plain,
% 0.82/1.00 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s28, c_n1) | (~node9(s28))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[2680, 2679])).
% 0.82/1.00 tff(2682,plain,
% 0.82/1.00 (~node9(s28)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[2681, 686, 2666])).
% 0.82/1.00 tff(2683,plain,
% 0.82/1.00 (((~![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)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(2684,plain,
% 0.82/1.00 ((~![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)))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(2685,plain,
% 0.82/1.00 ((~![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))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[2684, 2683])).
% 0.82/1.00 tff(2686,plain,
% 0.82/1.00 (~m_main_v_state2(s28, c_n2)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[2685, 697, 2645])).
% 0.82/1.00 tff(2687,plain,
% 0.82/1.00 (((~![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)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(2688,plain,
% 0.82/1.00 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s28, c_n2) | (~node8(s28)))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(2689,plain,
% 0.82/1.00 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s28, c_n2) | (~node8(s28))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[2688, 2687])).
% 0.82/1.00 tff(2690,plain,
% 0.82/1.00 (~node8(s28)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[2689, 271, 2686])).
% 0.82/1.00 tff(2691,plain,
% 0.82/1.00 (succ(s28, s29) <=> succ(s28, s29)),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(2692,axiom,(succ(s28, s29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound29')).
% 0.82/1.00 tff(2693,plain,
% 0.82/1.00 (succ(s28, s29)),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[2692, 2691])).
% 0.82/1.00 tff(2694,plain,
% 0.82/1.00 (((~![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))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(2695,plain,
% 0.82/1.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s28, s29)) | trans(s28, s29))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(2696,plain,
% 0.82/1.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s28, s29)) | trans(s28, s29)),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[2695, 2694])).
% 0.82/1.00 tff(2697,plain,
% 0.82/1.00 (trans(s28, s29)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[2696, 2693, 32])).
% 0.82/1.00 tff(2698,plain,
% 0.82/1.00 (((~![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))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(2699,plain,
% 0.82/1.00 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s28, s29)) | node14(s28, s29))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(2700,plain,
% 0.82/1.00 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s28, s29)) | node14(s28, s29)),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[2699, 2698])).
% 0.82/1.00 tff(2701,plain,
% 0.82/1.00 (node14(s28, s29)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[2700, 46, 2697])).
% 0.82/1.00 tff(2702,plain,
% 0.82/1.00 (((~![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(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)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(2703,plain,
% 0.82/1.00 (((~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)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(2704,plain,
% 0.82/1.00 (((~![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(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))))),
% 0.82/1.00 inference(monotonicity,[status(thm)],[2703])).
% 0.82/1.00 tff(2705,plain,
% 0.82/1.00 (((~![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(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)))),
% 0.82/1.00 inference(transitivity,[status(thm)],[2704, 2702])).
% 0.82/1.00 tff(2706,plain,
% 0.82/1.00 ((~![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(s28, c_c2)) | node9(s28) | node8(s28) | node10(s28) | node11(s28) | node12(s28) | (~node14(s28, s29)) | m_main_v_state2(s29, c_n2))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(2707,plain,
% 0.82/1.00 ((~![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(s29, c_n2) | node9(s28) | node8(s28) | node10(s28) | node11(s28) | node12(s28) | (~node14(s28, s29)) | (~m_main_v_state2(s28, c_c2))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[2706, 2705])).
% 0.82/1.00 tff(2708,plain,
% 0.82/1.00 (m_main_v_state2(s29, c_n2) | node9(s28) | node8(s28) | node10(s28) | node11(s28) | node12(s28) | (~m_main_v_state2(s28, c_c2))),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[2707, 726, 2701])).
% 0.82/1.00 tff(2709,plain,
% 0.82/1.00 (m_main_v_state2(s29, c_n2)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[2708, 2690, 2645, 2682, 2678, 2670, 2653])).
% 0.82/1.00 tff(2710,plain,
% 0.82/1.00 (((~![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)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(2711,plain,
% 0.82/1.00 ((~![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)))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(2712,plain,
% 0.82/1.00 ((~![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))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[2711, 2710])).
% 0.82/1.00 tff(2713,plain,
% 0.82/1.00 (~m_main_v_state2(s29, c_c2)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[2712, 697, 2709])).
% 0.82/1.00 tff(2714,plain,
% 0.82/1.00 (((~![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)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(2715,plain,
% 0.82/1.00 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s29, c_c2) | (~node3(s29)))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(2716,plain,
% 0.82/1.00 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s29, c_c2) | (~node3(s29))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[2715, 2714])).
% 0.82/1.00 tff(2717,plain,
% 0.82/1.00 (~node3(s29)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[2716, 399, 2713])).
% 0.82/1.00 tff(2718,plain,
% 0.82/1.00 (((~![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)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(2719,plain,
% 0.82/1.00 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s28, c_n1) | (~node1(s28)))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(2720,plain,
% 0.82/1.00 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s28, c_n1) | (~node1(s28))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[2719, 2718])).
% 0.82/1.00 tff(2721,plain,
% 0.82/1.00 (~node1(s28)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[2720, 421, 2666])).
% 0.82/1.00 tff(2722,plain,
% 0.82/1.00 (((~![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))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(2723,plain,
% 0.82/1.00 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s27, s28)) | node18(s27, s28))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(2724,plain,
% 0.82/1.00 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s27, s28)) | node18(s27, s28)),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[2723, 2722])).
% 0.82/1.00 tff(2725,plain,
% 0.82/1.00 (node18(s27, s28)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[2724, 125, 2636])).
% 0.82/1.00 tff(2726,plain,
% 0.82/1.00 (((~![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(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))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(2727,plain,
% 0.82/1.00 ((~![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(s27, c_n1)) | (~m_main_v_state2(s27, c_t2)) | (~node18(s27, s28)) | m_main_v_turn(s28, c_2))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(2728,plain,
% 0.82/1.00 ((~![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(s27, c_n1)) | (~m_main_v_state2(s27, c_t2)) | (~node18(s27, s28)) | m_main_v_turn(s28, c_2)),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[2727, 2726])).
% 0.82/1.00 tff(2729,plain,
% 0.82/1.00 ((~m_main_v_state1(s27, c_n1)) | (~m_main_v_state2(s27, c_t2)) | m_main_v_turn(s28, c_2)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[2728, 760, 2725])).
% 0.82/1.01 tff(2730,plain,
% 0.82/1.01 (m_main_v_turn(s28, c_2)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2729, 2589, 2625])).
% 0.82/1.01 tff(2731,plain,
% 0.82/1.01 (((~![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)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2732,plain,
% 0.82/1.01 ((~![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)))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(2733,plain,
% 0.82/1.01 ((~![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))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[2732, 2731])).
% 0.82/1.01 tff(2734,plain,
% 0.82/1.01 (~m_main_v_turn(s28, c_1)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2733, 156, 2730])).
% 0.82/1.01 tff(2735,plain,
% 0.82/1.01 (((~![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)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2736,plain,
% 0.82/1.01 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s28, c_1) | (~node5(s28)))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(2737,plain,
% 0.82/1.01 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s28, c_1) | (~node5(s28))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[2736, 2735])).
% 0.82/1.01 tff(2738,plain,
% 0.82/1.01 (~node5(s28)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2737, 776, 2734])).
% 0.82/1.01 tff(2739,plain,
% 0.82/1.01 (((~![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)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2740,plain,
% 0.82/1.01 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s28, c_n1) | (~node2(s28)))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(2741,plain,
% 0.82/1.01 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s28, c_n1) | (~node2(s28))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[2740, 2739])).
% 0.82/1.01 tff(2742,plain,
% 0.82/1.01 (~node2(s28)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2741, 787, 2666])).
% 0.82/1.01 tff(2743,plain,
% 0.82/1.01 (((~![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)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2744,plain,
% 0.82/1.01 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s28, c_n1) | (~node3(s28)))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(2745,plain,
% 0.82/1.01 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s28, c_n1) | (~node3(s28))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[2744, 2743])).
% 0.82/1.01 tff(2746,plain,
% 0.82/1.01 (~node3(s28)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2745, 798, 2666])).
% 0.82/1.01 tff(2747,plain,
% 0.82/1.01 (((~![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)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2748,plain,
% 0.82/1.01 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s28, c_n2) | (~node4(s28)))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(2749,plain,
% 0.82/1.01 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s28, c_n2) | (~node4(s28))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[2748, 2747])).
% 0.82/1.01 tff(2750,plain,
% 0.82/1.01 (~node4(s28)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2749, 388, 2686])).
% 0.82/1.01 tff(2751,plain,
% 0.82/1.01 (((~![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))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2752,plain,
% 0.82/1.01 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s28, s29)) | node7(s28, s29))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(2753,plain,
% 0.82/1.01 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s28, s29)) | node7(s28, s29)),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[2752, 2751])).
% 0.82/1.01 tff(2754,plain,
% 0.82/1.01 (node7(s28, s29)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2753, 206, 2697])).
% 0.82/1.01 tff(2755,plain,
% 0.82/1.01 (((~![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)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2756,plain,
% 0.82/1.01 ((~![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)))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(2757,plain,
% 0.82/1.01 ((~![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))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[2756, 2755])).
% 0.82/1.01 tff(2758,plain,
% 0.82/1.01 (m_main_v_state1(s28, c_c1) | node1(s28) | node2(s28) | node3(s28) | node4(s28) | node5(s28) | node6(s28, s29)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2757, 820, 2754])).
% 0.82/1.01 tff(2759,plain,
% 0.82/1.01 (node6(s28, s29)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2758, 2750, 2674, 2746, 2742, 2738, 2721])).
% 0.82/1.01 tff(2760,plain,
% 0.82/1.01 (((~![V: $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)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2761,plain,
% 0.82/1.01 (((~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)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2762,plain,
% 0.82/1.01 (((~![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))))),
% 0.82/1.01 inference(monotonicity,[status(thm)],[2761])).
% 0.82/1.01 tff(2763,plain,
% 0.82/1.01 (((~![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)))),
% 0.82/1.01 inference(transitivity,[status(thm)],[2762, 2760])).
% 0.82/1.01 tff(2764,plain,
% 0.82/1.01 ((~![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)))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(2765,plain,
% 0.82/1.01 ((~![V: $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))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[2764, 2763])).
% 0.82/1.01 tff(2766,plain,
% 0.82/1.01 (~m_main_v_state1(s29, c_n1)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2765, 835, 2666, 2759])).
% 0.82/1.01 tff(2767,plain,
% 0.82/1.01 (((~![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)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2768,plain,
% 0.82/1.01 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s29, c_n1) | (~node2(s29)))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(2769,plain,
% 0.82/1.01 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s29, c_n1) | (~node2(s29))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[2768, 2767])).
% 0.82/1.01 tff(2770,plain,
% 0.82/1.01 (~node2(s29)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2769, 787, 2766])).
% 0.82/1.01 tff(2771,plain,
% 0.82/1.01 (((~![V: $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)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2772,plain,
% 0.82/1.01 (((~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)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2773,plain,
% 0.82/1.01 (((~![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))))),
% 0.82/1.01 inference(monotonicity,[status(thm)],[2772])).
% 0.82/1.01 tff(2774,plain,
% 0.82/1.01 (((~![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)))),
% 0.82/1.01 inference(transitivity,[status(thm)],[2773, 2771])).
% 0.82/1.01 tff(2775,plain,
% 0.82/1.01 ((~![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))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(2776,plain,
% 0.82/1.01 ((~![V: $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))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[2775, 2774])).
% 0.82/1.01 tff(2777,plain,
% 0.82/1.01 (m_main_v_state1(s29, c_t1)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2776, 856, 2662, 2759])).
% 0.82/1.01 tff(2778,plain,
% 0.82/1.01 (((~![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)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2779,plain,
% 0.82/1.01 ((~![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)))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(2780,plain,
% 0.82/1.01 ((~![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))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[2779, 2778])).
% 0.82/1.01 tff(2781,plain,
% 0.82/1.01 (~m_main_v_state2(s29, c_t2)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2780, 77, 2709])).
% 0.82/1.01 tff(2782,plain,
% 0.82/1.01 (((~![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)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2783,plain,
% 0.82/1.01 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s29, c_t2) | (~node1(s29)))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(2784,plain,
% 0.82/1.01 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s29, c_t2) | (~node1(s29))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[2783, 2782])).
% 0.82/1.01 tff(2785,plain,
% 0.82/1.01 (~node1(s29)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2784, 195, 2781])).
% 0.82/1.01 tff(2786,plain,
% 0.82/1.01 (succ(s29, s30) <=> succ(s29, s30)),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2787,axiom,(succ(s29, s30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound30')).
% 0.82/1.01 tff(2788,plain,
% 0.82/1.01 (succ(s29, s30)),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[2787, 2786])).
% 0.82/1.01 tff(2789,plain,
% 0.82/1.01 (((~![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))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2790,plain,
% 0.82/1.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s29, s30)) | trans(s29, s30))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(2791,plain,
% 0.82/1.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s29, s30)) | trans(s29, s30)),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[2790, 2789])).
% 0.82/1.01 tff(2792,plain,
% 0.82/1.01 (trans(s29, s30)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2791, 2788, 32])).
% 0.82/1.01 tff(2793,plain,
% 0.82/1.01 (((~![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))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2794,plain,
% 0.82/1.01 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s29, s30)) | node7(s29, s30))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(2795,plain,
% 0.82/1.01 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s29, s30)) | node7(s29, s30)),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[2794, 2793])).
% 0.82/1.01 tff(2796,plain,
% 0.82/1.01 (node7(s29, s30)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2795, 206, 2792])).
% 0.82/1.01 tff(2797,plain,
% 0.82/1.01 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2798,plain,
% 0.82/1.01 (((~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)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2799,plain,
% 0.82/1.01 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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))))),
% 0.82/1.01 inference(monotonicity,[status(thm)],[2798])).
% 0.82/1.01 tff(2800,plain,
% 0.82/1.01 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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)))),
% 0.82/1.01 inference(transitivity,[status(thm)],[2799, 2797])).
% 0.82/1.01 tff(2801,plain,
% 0.82/1.01 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(2802,plain,
% 0.82/1.01 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[2801, 2800])).
% 0.82/1.01 tff(2803,plain,
% 0.82/1.01 ((~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)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2802, 892, 2796])).
% 0.82/1.01 tff(2804,plain,
% 0.82/1.01 (m_main_v_state1(s30, c_c1)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2803, 2785, 2709, 2777, 2770, 2717])).
% 0.82/1.01 tff(2805,plain,
% 0.82/1.01 (((~![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)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2806,plain,
% 0.82/1.01 ((~![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)))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(2807,plain,
% 0.82/1.01 ((~![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))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[2806, 2805])).
% 0.82/1.01 tff(2808,plain,
% 0.82/1.01 (~m_main_v_state1(s30, c_t1)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2807, 539, 2804])).
% 0.82/1.01 tff(2809,plain,
% 0.82/1.01 (((~![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)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2810,plain,
% 0.82/1.01 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s30, c_t1) | (~node5(s30)))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(2811,plain,
% 0.82/1.01 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s30, c_t1) | (~node5(s30))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[2810, 2809])).
% 0.82/1.01 tff(2812,plain,
% 0.82/1.01 (~node5(s30)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2811, 550, 2808])).
% 0.82/1.01 tff(2813,plain,
% 0.82/1.01 (((~![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))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2814,plain,
% 0.82/1.01 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s29, s30)) | node14(s29, s30))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(2815,plain,
% 0.82/1.01 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s29, s30)) | node14(s29, s30)),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[2814, 2813])).
% 0.82/1.01 tff(2816,plain,
% 0.82/1.01 (node14(s29, s30)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2815, 46, 2792])).
% 0.82/1.01 tff(2817,plain,
% 0.82/1.01 (((~![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(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))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2818,plain,
% 0.82/1.01 ((~![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(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | (~node14(s29, s30)) | m_main_v_state2(s30, c_t2))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(2819,plain,
% 0.82/1.01 ((~![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(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | (~node14(s29, s30)) | m_main_v_state2(s30, c_t2)),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[2818, 2817])).
% 0.82/1.01 tff(2820,plain,
% 0.82/1.01 ((~m_main_v_state1(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | m_main_v_state2(s30, c_t2)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2819, 922, 2816])).
% 0.82/1.01 tff(2821,plain,
% 0.82/1.01 (m_main_v_state2(s30, c_t2)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2820, 2777, 2709])).
% 0.82/1.01 tff(2822,plain,
% 0.82/1.01 (((~![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)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2823,plain,
% 0.82/1.01 ((~![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)))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(2824,plain,
% 0.82/1.01 ((~![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))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[2823, 2822])).
% 0.82/1.01 tff(2825,plain,
% 0.82/1.01 (~m_main_v_state2(s30, c_n2)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2824, 77, 2821])).
% 0.82/1.01 tff(2826,plain,
% 0.82/1.01 (((~![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)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2827,plain,
% 0.82/1.01 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s30, c_n2) | (~node4(s30)))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(2828,plain,
% 0.82/1.01 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s30, c_n2) | (~node4(s30))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[2827, 2826])).
% 0.82/1.01 tff(2829,plain,
% 0.82/1.01 (~node4(s30)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2828, 388, 2825])).
% 0.82/1.01 tff(2830,plain,
% 0.82/1.01 (((~![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)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2831,plain,
% 0.82/1.01 ((~![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)))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(2832,plain,
% 0.82/1.01 ((~![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))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[2831, 2830])).
% 0.82/1.01 tff(2833,plain,
% 0.82/1.01 (~m_main_v_state2(s30, c_c2)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2832, 260, 2821])).
% 0.82/1.01 tff(2834,plain,
% 0.82/1.01 (((~![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)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2835,plain,
% 0.82/1.01 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s30, c_c2) | (~node3(s30)))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(2836,plain,
% 0.82/1.01 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s30, c_c2) | (~node3(s30))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[2835, 2834])).
% 0.82/1.01 tff(2837,plain,
% 0.82/1.01 (~node3(s30)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2836, 399, 2833])).
% 0.82/1.01 tff(2838,plain,
% 0.82/1.01 (((~![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)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2839,plain,
% 0.82/1.01 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s30, c_n2) | (~node2(s30)))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(2840,plain,
% 0.82/1.01 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s30, c_n2) | (~node2(s30))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[2839, 2838])).
% 0.82/1.01 tff(2841,plain,
% 0.82/1.01 (~node2(s30)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2840, 410, 2825])).
% 0.82/1.01 tff(2842,plain,
% 0.82/1.01 (((~![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)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2843,plain,
% 0.82/1.01 ((~![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)))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(2844,plain,
% 0.82/1.01 ((~![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))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[2843, 2842])).
% 0.82/1.01 tff(2845,plain,
% 0.82/1.01 (~m_main_v_state1(s30, c_n1)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2844, 454, 2804])).
% 0.82/1.01 tff(2846,plain,
% 0.82/1.01 (((~![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)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2847,plain,
% 0.82/1.01 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s30, c_n1) | (~node1(s30)))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(2848,plain,
% 0.82/1.01 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s30, c_n1) | (~node1(s30))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[2847, 2846])).
% 0.82/1.01 tff(2849,plain,
% 0.82/1.01 (~node1(s30)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2848, 421, 2845])).
% 0.82/1.01 tff(2850,plain,
% 0.82/1.01 (succ(s30, s31) <=> succ(s30, s31)),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2851,axiom,(succ(s30, s31)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound31')).
% 0.82/1.01 tff(2852,plain,
% 0.82/1.01 (succ(s30, s31)),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[2851, 2850])).
% 0.82/1.01 tff(2853,plain,
% 0.82/1.01 (((~![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))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2854,plain,
% 0.82/1.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s30, s31)) | trans(s30, s31))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(2855,plain,
% 0.82/1.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s30, s31)) | trans(s30, s31)),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[2854, 2853])).
% 0.82/1.01 tff(2856,plain,
% 0.82/1.01 (trans(s30, s31)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2855, 2852, 32])).
% 0.82/1.01 tff(2857,plain,
% 0.82/1.01 (((~![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))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2858,plain,
% 0.82/1.01 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s30, s31)) | node7(s30, s31))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(2859,plain,
% 0.82/1.01 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s30, s31)) | node7(s30, s31)),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[2858, 2857])).
% 0.82/1.01 tff(2860,plain,
% 0.82/1.01 (node7(s30, s31)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[2859, 206, 2856])).
% 0.82/1.01 tff(2861,plain,
% 0.82/1.01 (((~![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(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)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2862,plain,
% 0.82/1.01 (((~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)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(2863,plain,
% 0.82/1.01 (((~![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(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))))),
% 0.82/1.01 inference(monotonicity,[status(thm)],[2862])).
% 0.82/1.01 tff(2864,plain,
% 0.82/1.01 (((~![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(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)))),
% 0.82/1.01 inference(transitivity,[status(thm)],[2863, 2861])).
% 0.82/1.01 tff(2865,plain,
% 0.82/1.01 ((~![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(s30, c_c1)) | node1(s30) | node2(s30) | node3(s30) | node4(s30) | node5(s30) | (~node7(s30, s31)) | m_main_v_state1(s31, c_n1))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(2866,plain,
% 0.82/1.02 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[2865, 2864])).
% 0.82/1.02 tff(2867,plain,
% 0.82/1.02 (m_main_v_state1(s31, c_n1) | (~m_main_v_state1(s30, c_c1)) | node1(s30) | node2(s30) | node3(s30) | node4(s30) | node5(s30)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2866, 584, 2860])).
% 0.82/1.02 tff(2868,plain,
% 0.82/1.02 (m_main_v_state1(s31, c_n1)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2867, 2849, 2804, 2841, 2837, 2829, 2812])).
% 0.82/1.02 tff(2869,plain,
% 0.82/1.02 (((~![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)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2870,plain,
% 0.82/1.02 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s29, c_t2) | (~node15(s29)))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(2871,plain,
% 0.82/1.02 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s29, c_t2) | (~node15(s29))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[2870, 2869])).
% 0.82/1.02 tff(2872,plain,
% 0.82/1.02 (~node15(s29)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2871, 103, 2781])).
% 0.82/1.02 tff(2873,plain,
% 0.82/1.02 (((~![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))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2874,plain,
% 0.82/1.02 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s29, s30)) | node18(s29, s30))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(2875,plain,
% 0.82/1.02 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s29, s30)) | node18(s29, s30)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[2874, 2873])).
% 0.82/1.02 tff(2876,plain,
% 0.82/1.02 (node18(s29, s30)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2875, 125, 2792])).
% 0.82/1.02 tff(2877,plain,
% 0.82/1.02 (((~![Y: $i, X: $i] : ((~m_main_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))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2878,plain,
% 0.82/1.02 (((~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))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2879,plain,
% 0.82/1.02 (((~![Y: $i, X: $i] : ((~m_main_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)))),
% 0.82/1.02 inference(monotonicity,[status(thm)],[2878])).
% 0.82/1.02 tff(2880,plain,
% 0.82/1.02 (((~![Y: $i, X: $i] : ((~m_main_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))),
% 0.82/1.02 inference(transitivity,[status(thm)],[2879, 2877])).
% 0.82/1.02 tff(2881,plain,
% 0.82/1.02 ((~![Y: $i, X: $i] : ((~m_main_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))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(2882,plain,
% 0.82/1.02 ((~![Y: $i, X: $i] : ((~m_main_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)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[2881, 2880])).
% 0.82/1.02 tff(2883,plain,
% 0.82/1.02 (node15(s29) | (~m_main_v_state1(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | m_main_v_turn(s30, c_1)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2882, 992, 2876])).
% 0.82/1.02 tff(2884,plain,
% 0.82/1.02 (m_main_v_turn(s30, c_1)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2883, 2872, 2709, 2777])).
% 0.82/1.02 tff(2885,plain,
% 0.82/1.02 (((~![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)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2886,plain,
% 0.82/1.02 ((~![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)))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(2887,plain,
% 0.82/1.02 ((~![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))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[2886, 2885])).
% 0.82/1.02 tff(2888,plain,
% 0.82/1.02 (~m_main_v_turn(s30, c_2)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2887, 156, 2884])).
% 0.82/1.02 tff(2889,plain,
% 0.82/1.02 (((~![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)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2890,plain,
% 0.82/1.02 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s30, c_2) | (~node12(s30)))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(2891,plain,
% 0.82/1.02 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s30, c_2) | (~node12(s30))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[2890, 2889])).
% 0.82/1.02 tff(2892,plain,
% 0.82/1.02 (~node12(s30)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2891, 184, 2888])).
% 0.82/1.02 tff(2893,plain,
% 0.82/1.02 (((~![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)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2894,plain,
% 0.82/1.02 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s30, c_n2) | (~node8(s30)))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(2895,plain,
% 0.82/1.02 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s30, c_n2) | (~node8(s30))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[2894, 2893])).
% 0.82/1.02 tff(2896,plain,
% 0.82/1.02 (~node8(s30)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2895, 271, 2825])).
% 0.82/1.02 tff(2897,plain,
% 0.82/1.02 (((~![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)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2898,plain,
% 0.82/1.02 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s30, c_n2) | (~node9(s30)))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(2899,plain,
% 0.82/1.02 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s30, c_n2) | (~node9(s30))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[2898, 2897])).
% 0.82/1.02 tff(2900,plain,
% 0.82/1.02 (~node9(s30)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2899, 88, 2825])).
% 0.82/1.02 tff(2901,plain,
% 0.82/1.02 (((~![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)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2902,plain,
% 0.82/1.02 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s30, c_n2) | (~node10(s30)))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(2903,plain,
% 0.82/1.02 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s30, c_n2) | (~node10(s30))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[2902, 2901])).
% 0.82/1.02 tff(2904,plain,
% 0.82/1.02 (~node10(s30)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2903, 249, 2825])).
% 0.82/1.02 tff(2905,plain,
% 0.82/1.02 (((~![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)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2906,plain,
% 0.82/1.02 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s30, c_n1) | (~node11(s30)))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(2907,plain,
% 0.82/1.02 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s30, c_n1) | (~node11(s30))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[2906, 2905])).
% 0.82/1.02 tff(2908,plain,
% 0.82/1.02 (~node11(s30)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2907, 238, 2845])).
% 0.82/1.02 tff(2909,plain,
% 0.82/1.02 (((~![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))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2910,plain,
% 0.82/1.02 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s30, s31)) | node14(s30, s31))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(2911,plain,
% 0.82/1.02 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s30, s31)) | node14(s30, s31)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[2910, 2909])).
% 0.82/1.02 tff(2912,plain,
% 0.82/1.02 (node14(s30, s31)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2911, 46, 2856])).
% 0.82/1.02 tff(2913,plain,
% 0.82/1.02 (((~![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)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2914,plain,
% 0.82/1.02 ((~![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)))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(2915,plain,
% 0.82/1.02 ((~![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))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[2914, 2913])).
% 0.82/1.02 tff(2916,plain,
% 0.82/1.02 (m_main_v_state2(s30, c_c2) | node9(s30) | node8(s30) | node10(s30) | node11(s30) | node12(s30) | node13(s30, s31)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2915, 296, 2912])).
% 0.82/1.02 tff(2917,plain,
% 0.82/1.02 (node13(s30, s31)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2916, 2908, 2833, 2904, 2900, 2896, 2892])).
% 0.82/1.02 tff(2918,plain,
% 0.82/1.02 (((~![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(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)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2919,plain,
% 0.82/1.02 (((~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)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2920,plain,
% 0.82/1.02 (((~![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))))),
% 0.82/1.02 inference(monotonicity,[status(thm)],[2919])).
% 0.82/1.02 tff(2921,plain,
% 0.82/1.02 (((~![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)))),
% 0.82/1.02 inference(transitivity,[status(thm)],[2920, 2918])).
% 0.82/1.02 tff(2922,plain,
% 0.82/1.02 ((~![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))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(2923,plain,
% 0.82/1.02 ((~![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(s30, c_t2)) | m_main_v_state2(s31, c_t2) | (~node13(s30, s31))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[2922, 2921])).
% 0.82/1.02 tff(2924,plain,
% 0.82/1.02 (m_main_v_state2(s31, c_t2)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2923, 518, 2821, 2917])).
% 0.82/1.02 tff(2925,plain,
% 0.82/1.02 (succ(s31, s32) <=> succ(s31, s32)),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2926,axiom,(succ(s31, s32)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound32')).
% 0.82/1.02 tff(2927,plain,
% 0.82/1.02 (succ(s31, s32)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[2926, 2925])).
% 0.82/1.02 tff(2928,plain,
% 0.82/1.02 (((~![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))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2929,plain,
% 0.82/1.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s31, s32)) | trans(s31, s32))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(2930,plain,
% 0.82/1.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s31, s32)) | trans(s31, s32)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[2929, 2928])).
% 0.82/1.02 tff(2931,plain,
% 0.82/1.02 (trans(s31, s32)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2930, 2927, 32])).
% 0.82/1.02 tff(2932,plain,
% 0.82/1.02 (((~![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))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2933,plain,
% 0.82/1.02 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s31, s32)) | node7(s31, s32))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(2934,plain,
% 0.82/1.02 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s31, s32)) | node7(s31, s32)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[2933, 2932])).
% 0.82/1.02 tff(2935,plain,
% 0.82/1.02 (node7(s31, s32)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2934, 206, 2931])).
% 0.82/1.02 tff(2936,plain,
% 0.82/1.02 (((~![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(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))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2937,plain,
% 0.82/1.02 ((~![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(s31, c_n1)) | (~m_main_v_state2(s31, c_t2)) | (~node7(s31, s32)) | m_main_v_state1(s32, c_t1))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(2938,plain,
% 0.82/1.02 ((~![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(s31, c_n1)) | (~m_main_v_state2(s31, c_t2)) | (~node7(s31, s32)) | m_main_v_state1(s32, c_t1)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[2937, 2936])).
% 0.82/1.02 tff(2939,plain,
% 0.82/1.02 ((~m_main_v_state1(s31, c_n1)) | (~m_main_v_state2(s31, c_t2)) | m_main_v_state1(s32, c_t1)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2938, 651, 2935])).
% 0.82/1.02 tff(2940,plain,
% 0.82/1.02 (m_main_v_state1(s32, c_t1)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2939, 2924, 2868])).
% 0.82/1.02 tff(2941,plain,
% 0.82/1.02 (((~![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)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2942,plain,
% 0.82/1.02 ((~![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)))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(2943,plain,
% 0.82/1.02 ((~![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))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[2942, 2941])).
% 0.82/1.02 tff(2944,plain,
% 0.82/1.02 (~m_main_v_state1(s32, c_n1)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2943, 10, 2940])).
% 0.82/1.02 tff(2945,plain,
% 0.82/1.02 (((~![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)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2946,plain,
% 0.82/1.02 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s32, c_n1) | (~node1(s32)))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(2947,plain,
% 0.82/1.02 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s32, c_n1) | (~node1(s32))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[2946, 2945])).
% 0.82/1.02 tff(2948,plain,
% 0.82/1.02 (~node1(s32)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2947, 421, 2944])).
% 0.82/1.02 tff(2949,plain,
% 0.82/1.02 (((~![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))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2950,plain,
% 0.82/1.02 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s31, s32)) | node18(s31, s32))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(2951,plain,
% 0.82/1.02 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s31, s32)) | node18(s31, s32)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[2950, 2949])).
% 0.82/1.02 tff(2952,plain,
% 0.82/1.02 (node18(s31, s32)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2951, 125, 2931])).
% 0.82/1.02 tff(2953,plain,
% 0.82/1.02 (((~![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(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))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2954,plain,
% 0.82/1.02 ((~![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(s31, c_n1)) | (~m_main_v_state2(s31, c_t2)) | (~node18(s31, s32)) | m_main_v_turn(s32, c_2))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(2955,plain,
% 0.82/1.02 ((~![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(s31, c_n1)) | (~m_main_v_state2(s31, c_t2)) | (~node18(s31, s32)) | m_main_v_turn(s32, c_2)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[2954, 2953])).
% 0.82/1.02 tff(2956,plain,
% 0.82/1.02 ((~m_main_v_state1(s31, c_n1)) | (~m_main_v_state2(s31, c_t2)) | m_main_v_turn(s32, c_2)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2955, 760, 2952])).
% 0.82/1.02 tff(2957,plain,
% 0.82/1.02 (m_main_v_turn(s32, c_2)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2956, 2924, 2868])).
% 0.82/1.02 tff(2958,plain,
% 0.82/1.02 (((~![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)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2959,plain,
% 0.82/1.02 ((~![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)))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(2960,plain,
% 0.82/1.02 ((~![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))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[2959, 2958])).
% 0.82/1.02 tff(2961,plain,
% 0.82/1.02 (~m_main_v_turn(s32, c_1)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2960, 156, 2957])).
% 0.82/1.02 tff(2962,plain,
% 0.82/1.02 (((~![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)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2963,plain,
% 0.82/1.02 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s32, c_1) | (~node5(s32)))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(2964,plain,
% 0.82/1.02 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s32, c_1) | (~node5(s32))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[2963, 2962])).
% 0.82/1.02 tff(2965,plain,
% 0.82/1.02 (~node5(s32)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2964, 776, 2961])).
% 0.82/1.02 tff(2966,plain,
% 0.82/1.02 (((~![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)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2967,plain,
% 0.82/1.02 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s32, c_n1) | (~node2(s32)))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(2968,plain,
% 0.82/1.02 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s32, c_n1) | (~node2(s32))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[2967, 2966])).
% 0.82/1.02 tff(2969,plain,
% 0.82/1.02 (~node2(s32)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2968, 787, 2944])).
% 0.82/1.02 tff(2970,plain,
% 0.82/1.02 (((~![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)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2971,plain,
% 0.82/1.02 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s32, c_n1) | (~node3(s32)))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(2972,plain,
% 0.82/1.02 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s32, c_n1) | (~node3(s32))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[2971, 2970])).
% 0.82/1.02 tff(2973,plain,
% 0.82/1.02 (~node3(s32)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2972, 798, 2944])).
% 0.82/1.02 tff(2974,plain,
% 0.82/1.02 (((~![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)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2975,plain,
% 0.82/1.02 ((~![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)))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(2976,plain,
% 0.82/1.02 ((~![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))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[2975, 2974])).
% 0.82/1.02 tff(2977,plain,
% 0.82/1.02 (~m_main_v_state1(s32, c_c1)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2976, 539, 2940])).
% 0.82/1.02 tff(2978,plain,
% 0.82/1.02 (((~![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(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)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2979,plain,
% 0.82/1.02 (((~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)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2980,plain,
% 0.82/1.02 (((~![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))))),
% 0.82/1.02 inference(monotonicity,[status(thm)],[2979])).
% 0.82/1.02 tff(2981,plain,
% 0.82/1.02 (((~![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)))),
% 0.82/1.02 inference(transitivity,[status(thm)],[2980, 2978])).
% 0.82/1.02 tff(2982,plain,
% 0.82/1.02 ((~![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)))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(2983,plain,
% 0.82/1.02 ((~![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(s30, c_n2) | (~m_main_v_state2(s31, c_n2)) | (~node13(s30, s31))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[2982, 2981])).
% 0.82/1.02 tff(2984,plain,
% 0.82/1.02 (~m_main_v_state2(s31, c_n2)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2983, 311, 2825, 2917])).
% 0.82/1.02 tff(2985,plain,
% 0.82/1.02 (((~![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)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2986,plain,
% 0.82/1.02 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s31, c_n2) | (~node9(s31)))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(2987,plain,
% 0.82/1.02 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s31, c_n2) | (~node9(s31))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[2986, 2985])).
% 0.82/1.02 tff(2988,plain,
% 0.82/1.02 (~node9(s31)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2987, 88, 2984])).
% 0.82/1.02 tff(2989,plain,
% 0.82/1.02 (((~![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)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2990,plain,
% 0.82/1.02 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s31, c_n2) | (~node10(s31)))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(2991,plain,
% 0.82/1.02 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s31, c_n2) | (~node10(s31))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[2990, 2989])).
% 0.82/1.02 tff(2992,plain,
% 0.82/1.02 (~node10(s31)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[2991, 249, 2984])).
% 0.82/1.02 tff(2993,plain,
% 0.82/1.02 (((~![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)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(2994,plain,
% 0.82/1.02 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s31, c_n2) | (~node8(s31)))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(2995,plain,
% 0.82/1.02 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s31, c_n2) | (~node8(s31))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[2994, 2993])).
% 0.82/1.02 tff(2996,plain,
% 0.82/1.02 (~node8(s31)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[2995, 271, 2984])).
% 0.82/1.03 tff(2997,plain,
% 0.82/1.03 (((~![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))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(2998,plain,
% 0.82/1.03 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s31, s32)) | node14(s31, s32))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(2999,plain,
% 0.82/1.03 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s31, s32)) | node14(s31, s32)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[2998, 2997])).
% 0.82/1.03 tff(3000,plain,
% 0.82/1.03 (node14(s31, s32)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[2999, 46, 2931])).
% 0.82/1.03 tff(3001,plain,
% 0.82/1.03 (((~![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))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3002,plain,
% 0.82/1.03 ((~![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))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(3003,plain,
% 0.82/1.03 ((~![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)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[3002, 3001])).
% 0.82/1.03 tff(3004,plain,
% 0.82/1.03 ((~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)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3003, 617, 3000])).
% 0.82/1.03 tff(3005,plain,
% 0.82/1.03 (m_main_v_state2(s32, c_c2)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3004, 2996, 2868, 2924, 2992, 2988])).
% 0.82/1.03 tff(3006,plain,
% 0.82/1.03 (((~![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)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3007,plain,
% 0.82/1.03 ((~![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)))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(3008,plain,
% 0.82/1.03 ((~![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))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[3007, 3006])).
% 0.82/1.03 tff(3009,plain,
% 0.82/1.03 (~m_main_v_state2(s32, c_n2)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3008, 697, 3005])).
% 0.82/1.03 tff(3010,plain,
% 0.82/1.03 (((~![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)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3011,plain,
% 0.82/1.03 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s32, c_n2) | (~node4(s32)))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(3012,plain,
% 0.82/1.03 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s32, c_n2) | (~node4(s32))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[3011, 3010])).
% 0.82/1.03 tff(3013,plain,
% 0.82/1.03 (~node4(s32)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3012, 388, 3009])).
% 0.82/1.03 tff(3014,plain,
% 0.82/1.03 (succ(s32, s33) <=> succ(s32, s33)),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3015,axiom,(succ(s32, s33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound33')).
% 0.82/1.03 tff(3016,plain,
% 0.82/1.03 (succ(s32, s33)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[3015, 3014])).
% 0.82/1.03 tff(3017,plain,
% 0.82/1.03 (((~![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))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3018,plain,
% 0.82/1.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s32, s33)) | trans(s32, s33))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(3019,plain,
% 0.82/1.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s32, s33)) | trans(s32, s33)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[3018, 3017])).
% 0.82/1.03 tff(3020,plain,
% 0.82/1.03 (trans(s32, s33)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3019, 3016, 32])).
% 0.82/1.03 tff(3021,plain,
% 0.82/1.03 (((~![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))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3022,plain,
% 0.82/1.03 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s32, s33)) | node7(s32, s33))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(3023,plain,
% 0.82/1.03 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s32, s33)) | node7(s32, s33)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[3022, 3021])).
% 0.82/1.03 tff(3024,plain,
% 0.82/1.03 (node7(s32, s33)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3023, 206, 3020])).
% 0.82/1.03 tff(3025,plain,
% 0.82/1.03 (((~![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)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3026,plain,
% 0.82/1.03 ((~![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)))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(3027,plain,
% 0.82/1.03 ((~![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))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[3026, 3025])).
% 0.82/1.03 tff(3028,plain,
% 0.82/1.03 (m_main_v_state1(s32, c_c1) | node1(s32) | node2(s32) | node3(s32) | node4(s32) | node5(s32) | node6(s32, s33)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3027, 820, 3024])).
% 0.82/1.03 tff(3029,plain,
% 0.82/1.03 (node6(s32, s33)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3028, 3013, 2977, 2973, 2969, 2965, 2948])).
% 0.82/1.03 tff(3030,plain,
% 0.82/1.03 (((~![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(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)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3031,plain,
% 0.82/1.03 (((~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)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3032,plain,
% 0.82/1.03 (((~![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))))),
% 0.82/1.03 inference(monotonicity,[status(thm)],[3031])).
% 0.82/1.03 tff(3033,plain,
% 0.82/1.03 (((~![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)))),
% 0.82/1.03 inference(transitivity,[status(thm)],[3032, 3030])).
% 0.82/1.03 tff(3034,plain,
% 0.82/1.03 ((~![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))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(3035,plain,
% 0.82/1.03 ((~![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(s32, c_t1)) | m_main_v_state1(s33, c_t1) | (~node6(s32, s33))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[3034, 3033])).
% 0.82/1.03 tff(3036,plain,
% 0.82/1.03 (m_main_v_state1(s33, c_t1)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3035, 856, 2940, 3029])).
% 0.82/1.03 tff(3037,plain,
% 0.82/1.03 (((~![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)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3038,plain,
% 0.82/1.03 ((~![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)))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(3039,plain,
% 0.82/1.03 ((~![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))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[3038, 3037])).
% 0.82/1.03 tff(3040,plain,
% 0.82/1.03 (~m_main_v_state2(s32, c_t2)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3039, 260, 3005])).
% 0.82/1.03 tff(3041,plain,
% 0.82/1.03 (((~![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)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3042,plain,
% 0.82/1.03 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s32, c_t2) | (~node12(s32)))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(3043,plain,
% 0.82/1.03 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s32, c_t2) | (~node12(s32))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[3042, 3041])).
% 0.82/1.03 tff(3044,plain,
% 0.82/1.03 (~node12(s32)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3043, 633, 3040])).
% 0.82/1.03 tff(3045,plain,
% 0.82/1.03 (((~![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)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3046,plain,
% 0.82/1.03 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s32, c_n1) | (~node11(s32)))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(3047,plain,
% 0.82/1.03 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s32, c_n1) | (~node11(s32))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[3046, 3045])).
% 0.82/1.03 tff(3048,plain,
% 0.82/1.03 (~node11(s32)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3047, 238, 2944])).
% 0.82/1.03 tff(3049,plain,
% 0.82/1.03 (((~![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)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3050,plain,
% 0.82/1.03 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s32, c_c1) | (~node10(s32)))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(3051,plain,
% 0.82/1.03 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s32, c_c1) | (~node10(s32))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[3050, 3049])).
% 0.82/1.03 tff(3052,plain,
% 0.82/1.03 (~node10(s32)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3051, 675, 2977])).
% 0.82/1.03 tff(3053,plain,
% 0.82/1.03 (((~![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)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3054,plain,
% 0.82/1.03 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s32, c_n1) | (~node9(s32)))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(3055,plain,
% 0.82/1.03 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s32, c_n1) | (~node9(s32))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[3054, 3053])).
% 0.82/1.03 tff(3056,plain,
% 0.82/1.03 (~node9(s32)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3055, 686, 2944])).
% 0.82/1.03 tff(3057,plain,
% 0.82/1.03 (((~![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)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3058,plain,
% 0.82/1.03 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s32, c_n2) | (~node8(s32)))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(3059,plain,
% 0.82/1.03 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s32, c_n2) | (~node8(s32))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[3058, 3057])).
% 0.82/1.03 tff(3060,plain,
% 0.82/1.03 (~node8(s32)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3059, 271, 3009])).
% 0.82/1.03 tff(3061,plain,
% 0.82/1.03 (((~![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))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3062,plain,
% 0.82/1.03 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s32, s33)) | node14(s32, s33))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(3063,plain,
% 0.82/1.03 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s32, s33)) | node14(s32, s33)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[3062, 3061])).
% 0.82/1.03 tff(3064,plain,
% 0.82/1.03 (node14(s32, s33)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3063, 46, 3020])).
% 0.82/1.03 tff(3065,plain,
% 0.82/1.03 (((~![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(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)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3066,plain,
% 0.82/1.03 (((~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)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3067,plain,
% 0.82/1.03 (((~![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(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))))),
% 0.82/1.03 inference(monotonicity,[status(thm)],[3066])).
% 0.82/1.03 tff(3068,plain,
% 0.82/1.03 (((~![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(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)))),
% 0.82/1.03 inference(transitivity,[status(thm)],[3067, 3065])).
% 0.82/1.03 tff(3069,plain,
% 0.82/1.03 ((~![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(s32, c_c2)) | node9(s32) | node8(s32) | node10(s32) | node11(s32) | node12(s32) | (~node14(s32, s33)) | m_main_v_state2(s33, c_n2))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(3070,plain,
% 0.82/1.03 ((~![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(s33, c_n2) | node9(s32) | node8(s32) | node10(s32) | node11(s32) | node12(s32) | (~node14(s32, s33)) | (~m_main_v_state2(s32, c_c2))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[3069, 3068])).
% 0.82/1.03 tff(3071,plain,
% 0.82/1.03 (m_main_v_state2(s33, c_n2) | node9(s32) | node8(s32) | node10(s32) | node11(s32) | node12(s32) | (~m_main_v_state2(s32, c_c2))),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3070, 726, 3064])).
% 0.82/1.03 tff(3072,plain,
% 0.82/1.03 (m_main_v_state2(s33, c_n2)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3071, 3060, 3005, 3056, 3052, 3048, 3044])).
% 0.82/1.03 tff(3073,plain,
% 0.82/1.03 (((~![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)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3074,plain,
% 0.82/1.03 ((~![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)))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(3075,plain,
% 0.82/1.03 ((~![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))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[3074, 3073])).
% 0.82/1.03 tff(3076,plain,
% 0.82/1.03 (~m_main_v_state2(s33, c_t2)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3075, 77, 3072])).
% 0.82/1.03 tff(3077,plain,
% 0.82/1.03 (((~![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)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3078,plain,
% 0.82/1.03 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s33, c_t2) | (~node15(s33)))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(3079,plain,
% 0.82/1.03 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s33, c_t2) | (~node15(s33))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[3078, 3077])).
% 0.82/1.03 tff(3080,plain,
% 0.82/1.03 (~node15(s33)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3079, 103, 3076])).
% 0.82/1.03 tff(3081,plain,
% 0.82/1.03 (succ(s33, s34) <=> succ(s33, s34)),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3082,axiom,(succ(s33, s34)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound34')).
% 0.82/1.03 tff(3083,plain,
% 0.82/1.03 (succ(s33, s34)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[3082, 3081])).
% 0.82/1.03 tff(3084,plain,
% 0.82/1.03 (((~![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))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3085,plain,
% 0.82/1.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s33, s34)) | trans(s33, s34))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(3086,plain,
% 0.82/1.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s33, s34)) | trans(s33, s34)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[3085, 3084])).
% 0.82/1.03 tff(3087,plain,
% 0.82/1.03 (trans(s33, s34)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3086, 3083, 32])).
% 0.82/1.03 tff(3088,plain,
% 0.82/1.03 (((~![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))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3089,plain,
% 0.82/1.03 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s33, s34)) | node18(s33, s34))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(3090,plain,
% 0.82/1.03 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s33, s34)) | node18(s33, s34)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[3089, 3088])).
% 0.82/1.03 tff(3091,plain,
% 0.82/1.03 (node18(s33, s34)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3090, 125, 3087])).
% 0.82/1.03 tff(3092,plain,
% 0.82/1.03 (((~![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(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))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3093,plain,
% 0.82/1.03 (((~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))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3094,plain,
% 0.82/1.03 (((~![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(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)))),
% 0.82/1.03 inference(monotonicity,[status(thm)],[3093])).
% 0.82/1.03 tff(3095,plain,
% 0.82/1.03 (((~![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(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))),
% 0.82/1.03 inference(transitivity,[status(thm)],[3094, 3092])).
% 0.82/1.03 tff(3096,plain,
% 0.82/1.03 ((~![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(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | node15(s33) | (~node18(s33, s34)) | m_main_v_turn(s34, c_1))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(3097,plain,
% 0.82/1.03 ((~![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(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)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[3096, 3095])).
% 0.82/1.03 tff(3098,plain,
% 0.82/1.03 (node15(s33) | (~m_main_v_state1(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | m_main_v_turn(s34, c_1)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3097, 992, 3091])).
% 0.82/1.03 tff(3099,plain,
% 0.82/1.03 (m_main_v_turn(s34, c_1)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3098, 3080, 3072, 3036])).
% 0.82/1.03 tff(3100,plain,
% 0.82/1.03 (((~![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)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3101,plain,
% 0.82/1.03 ((~![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)))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(3102,plain,
% 0.82/1.03 ((~![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))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[3101, 3100])).
% 0.82/1.03 tff(3103,plain,
% 0.82/1.03 (~m_main_v_turn(s34, c_2)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3102, 156, 3099])).
% 0.82/1.03 tff(3104,plain,
% 0.82/1.03 (((~![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)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3105,plain,
% 0.82/1.03 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s34, c_2) | (~node12(s34)))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(3106,plain,
% 0.82/1.03 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s34, c_2) | (~node12(s34))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[3105, 3104])).
% 0.82/1.03 tff(3107,plain,
% 0.82/1.03 (~node12(s34)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3106, 184, 3103])).
% 0.82/1.03 tff(3108,plain,
% 0.82/1.03 (((~![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))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3109,plain,
% 0.82/1.03 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s33, s34)) | node14(s33, s34))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(3110,plain,
% 0.82/1.03 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s33, s34)) | node14(s33, s34)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[3109, 3108])).
% 0.82/1.03 tff(3111,plain,
% 0.82/1.03 (node14(s33, s34)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3110, 46, 3087])).
% 0.82/1.03 tff(3112,plain,
% 0.82/1.03 (((~![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(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))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3113,plain,
% 0.82/1.03 ((~![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(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | (~node14(s33, s34)) | m_main_v_state2(s34, c_t2))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(3114,plain,
% 0.82/1.03 ((~![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(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | (~node14(s33, s34)) | m_main_v_state2(s34, c_t2)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[3113, 3112])).
% 0.82/1.03 tff(3115,plain,
% 0.82/1.03 ((~m_main_v_state1(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | m_main_v_state2(s34, c_t2)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3114, 922, 3111])).
% 0.82/1.03 tff(3116,plain,
% 0.82/1.03 (m_main_v_state2(s34, c_t2)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3115, 3036, 3072])).
% 0.82/1.03 tff(3117,plain,
% 0.82/1.03 (((~![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)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3118,plain,
% 0.82/1.03 ((~![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)))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(3119,plain,
% 0.82/1.03 ((~![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))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[3118, 3117])).
% 0.82/1.03 tff(3120,plain,
% 0.82/1.03 (~m_main_v_state2(s34, c_n2)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3119, 77, 3116])).
% 0.82/1.03 tff(3121,plain,
% 0.82/1.03 (((~![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)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3122,plain,
% 0.82/1.03 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s34, c_n2) | (~node8(s34)))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(3123,plain,
% 0.82/1.03 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s34, c_n2) | (~node8(s34))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[3122, 3121])).
% 0.82/1.03 tff(3124,plain,
% 0.82/1.03 (~node8(s34)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3123, 271, 3120])).
% 0.82/1.03 tff(3125,plain,
% 0.82/1.03 (((~![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)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3126,plain,
% 0.82/1.03 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s34, c_n2) | (~node9(s34)))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(3127,plain,
% 0.82/1.03 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s34, c_n2) | (~node9(s34))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[3126, 3125])).
% 0.82/1.03 tff(3128,plain,
% 0.82/1.03 (~node9(s34)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3127, 88, 3120])).
% 0.82/1.03 tff(3129,plain,
% 0.82/1.03 (((~![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)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(3130,plain,
% 0.82/1.03 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s34, c_n2) | (~node10(s34)))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(3131,plain,
% 0.82/1.03 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s34, c_n2) | (~node10(s34))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[3130, 3129])).
% 0.82/1.03 tff(3132,plain,
% 0.82/1.03 (~node10(s34)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3131, 249, 3120])).
% 0.82/1.04 tff(3133,plain,
% 0.82/1.04 (((~![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)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(3134,plain,
% 0.82/1.04 ((~![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)))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(3135,plain,
% 0.82/1.04 ((~![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))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[3134, 3133])).
% 0.82/1.04 tff(3136,plain,
% 0.82/1.04 (~m_main_v_state2(s34, c_c2)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[3135, 260, 3116])).
% 0.82/1.04 tff(3137,plain,
% 0.82/1.04 (((~![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)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(3138,plain,
% 0.82/1.04 ((~![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)))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(3139,plain,
% 0.82/1.04 ((~![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))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[3138, 3137])).
% 0.82/1.04 tff(3140,plain,
% 0.82/1.04 (~m_main_v_state2(s33, c_c2)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[3139, 697, 3072])).
% 0.82/1.04 tff(3141,plain,
% 0.82/1.04 (((~![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)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(3142,plain,
% 0.82/1.04 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s33, c_c2) | (~node3(s33)))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(3143,plain,
% 0.82/1.04 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s33, c_c2) | (~node3(s33))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[3142, 3141])).
% 0.82/1.04 tff(3144,plain,
% 0.82/1.04 (~node3(s33)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[3143, 399, 3140])).
% 0.82/1.04 tff(3145,plain,
% 0.82/1.04 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(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)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(3146,plain,
% 0.82/1.04 (((~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)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(3147,plain,
% 0.82/1.04 (((~![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))))),
% 0.82/1.04 inference(monotonicity,[status(thm)],[3146])).
% 0.82/1.04 tff(3148,plain,
% 0.82/1.04 (((~![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)))),
% 0.82/1.04 inference(transitivity,[status(thm)],[3147, 3145])).
% 0.82/1.04 tff(3149,plain,
% 0.82/1.04 ((~![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)))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(3150,plain,
% 0.82/1.04 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s32, c_n1) | (~m_main_v_state1(s33, c_n1)) | (~node6(s32, s33))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[3149, 3148])).
% 0.82/1.04 tff(3151,plain,
% 0.82/1.04 (~m_main_v_state1(s33, c_n1)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[3150, 835, 2944, 3029])).
% 0.82/1.04 tff(3152,plain,
% 0.82/1.04 (((~![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)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(3153,plain,
% 0.82/1.04 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s33, c_n1) | (~node2(s33)))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(3154,plain,
% 0.82/1.04 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s33, c_n1) | (~node2(s33))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[3153, 3152])).
% 0.82/1.04 tff(3155,plain,
% 0.82/1.04 (~node2(s33)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[3154, 787, 3151])).
% 0.82/1.04 tff(3156,plain,
% 0.82/1.04 (((~![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)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(3157,plain,
% 0.82/1.04 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s33, c_t2) | (~node1(s33)))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(3158,plain,
% 0.82/1.04 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s33, c_t2) | (~node1(s33))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[3157, 3156])).
% 0.82/1.04 tff(3159,plain,
% 0.82/1.04 (~node1(s33)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[3158, 195, 3076])).
% 0.82/1.04 tff(3160,plain,
% 0.82/1.04 (((~![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))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(3161,plain,
% 0.82/1.04 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s33, s34)) | node7(s33, s34))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(3162,plain,
% 0.82/1.04 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s33, s34)) | node7(s33, s34)),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[3161, 3160])).
% 0.82/1.04 tff(3163,plain,
% 0.82/1.04 (node7(s33, s34)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[3162, 206, 3087])).
% 0.82/1.04 tff(3164,plain,
% 0.82/1.04 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(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)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(3165,plain,
% 0.82/1.04 (((~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)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(3166,plain,
% 0.82/1.04 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(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))))),
% 0.82/1.04 inference(monotonicity,[status(thm)],[3165])).
% 0.82/1.04 tff(3167,plain,
% 0.82/1.04 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(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)))),
% 0.82/1.04 inference(transitivity,[status(thm)],[3166, 3164])).
% 0.82/1.04 tff(3168,plain,
% 0.82/1.04 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(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))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(3169,plain,
% 0.82/1.04 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(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))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[3168, 3167])).
% 0.82/1.04 tff(3170,plain,
% 0.82/1.04 ((~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)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[3169, 892, 3163])).
% 0.82/1.04 tff(3171,plain,
% 0.82/1.04 (m_main_v_state1(s34, c_c1)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[3170, 3159, 3072, 3036, 3155, 3144])).
% 0.82/1.04 tff(3172,plain,
% 0.82/1.04 (((~![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)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(3173,plain,
% 0.82/1.04 ((~![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)))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(3174,plain,
% 0.82/1.04 ((~![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))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[3173, 3172])).
% 0.82/1.04 tff(3175,plain,
% 0.82/1.04 (~m_main_v_state1(s34, c_n1)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[3174, 454, 3171])).
% 0.82/1.04 tff(3176,plain,
% 0.82/1.04 (((~![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)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(3177,plain,
% 0.82/1.04 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s34, c_n1) | (~node11(s34)))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(3178,plain,
% 0.82/1.04 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s34, c_n1) | (~node11(s34))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[3177, 3176])).
% 0.82/1.04 tff(3179,plain,
% 0.82/1.04 (~node11(s34)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[3178, 238, 3175])).
% 0.82/1.04 tff(3180,plain,
% 0.82/1.04 (succ(s34, s35) <=> succ(s34, s35)),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(3181,axiom,(succ(s34, s35)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound35')).
% 0.82/1.04 tff(3182,plain,
% 0.82/1.04 (succ(s34, s35)),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[3181, 3180])).
% 0.82/1.04 tff(3183,plain,
% 0.82/1.04 (((~![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))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(3184,plain,
% 0.82/1.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s34, s35)) | trans(s34, s35))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(3185,plain,
% 0.82/1.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s34, s35)) | trans(s34, s35)),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[3184, 3183])).
% 0.82/1.04 tff(3186,plain,
% 0.82/1.04 (trans(s34, s35)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[3185, 3182, 32])).
% 0.82/1.04 tff(3187,plain,
% 0.82/1.04 (((~![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))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(3188,plain,
% 0.82/1.04 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s34, s35)) | node14(s34, s35))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(3189,plain,
% 0.82/1.04 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s34, s35)) | node14(s34, s35)),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[3188, 3187])).
% 0.82/1.04 tff(3190,plain,
% 0.82/1.04 (node14(s34, s35)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[3189, 46, 3186])).
% 0.82/1.04 tff(3191,plain,
% 0.82/1.04 (((~![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(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)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(3192,plain,
% 0.82/1.04 ((~![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(s34, c_c2) | node9(s34) | node8(s34) | node10(s34) | node11(s34) | node12(s34) | node13(s34, s35) | (~node14(s34, s35)))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(3193,plain,
% 0.82/1.04 ((~![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(s34, c_c2) | node9(s34) | node8(s34) | node10(s34) | node11(s34) | node12(s34) | node13(s34, s35) | (~node14(s34, s35))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[3192, 3191])).
% 0.82/1.04 tff(3194,plain,
% 0.82/1.04 (m_main_v_state2(s34, c_c2) | node9(s34) | node8(s34) | node10(s34) | node11(s34) | node12(s34) | node13(s34, s35)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[3193, 296, 3190])).
% 0.82/1.04 tff(3195,plain,
% 0.82/1.04 (node13(s34, s35)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[3194, 3179, 3136, 3132, 3128, 3124, 3107])).
% 0.82/1.04 tff(3196,plain,
% 0.82/1.04 (((~![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(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)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(3197,plain,
% 0.82/1.04 (((~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)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(3198,plain,
% 0.82/1.04 (((~![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))))),
% 0.82/1.04 inference(monotonicity,[status(thm)],[3197])).
% 0.82/1.04 tff(3199,plain,
% 0.82/1.04 (((~![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)))),
% 0.82/1.04 inference(transitivity,[status(thm)],[3198, 3196])).
% 0.82/1.04 tff(3200,plain,
% 0.82/1.04 ((~![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)))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(3201,plain,
% 0.82/1.04 ((~![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(s34, c_n2) | (~m_main_v_state2(s35, c_n2)) | (~node13(s34, s35))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[3200, 3199])).
% 0.82/1.04 tff(3202,plain,
% 0.82/1.04 (~m_main_v_state2(s35, c_n2)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[3201, 311, 3120, 3195])).
% 0.82/1.04 tff(3203,plain,
% 0.82/1.04 (((~![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)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(3204,plain,
% 0.82/1.04 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s35, c_n2) | (~node9(s35)))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(3205,plain,
% 0.82/1.04 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s35, c_n2) | (~node9(s35))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[3204, 3203])).
% 0.82/1.04 tff(3206,plain,
% 0.82/1.04 (~node9(s35)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[3205, 88, 3202])).
% 0.82/1.04 tff(3207,plain,
% 0.82/1.04 (((~![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)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(3208,plain,
% 0.82/1.04 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s35, c_n2) | (~node10(s35)))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(3209,plain,
% 0.82/1.04 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s35, c_n2) | (~node10(s35))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[3208, 3207])).
% 0.82/1.04 tff(3210,plain,
% 0.82/1.04 (~node10(s35)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[3209, 249, 3202])).
% 0.82/1.04 tff(3211,plain,
% 0.82/1.04 (((~![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(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)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(3212,plain,
% 0.82/1.04 (((~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)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(3213,plain,
% 0.82/1.04 (((~![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))))),
% 0.82/1.04 inference(monotonicity,[status(thm)],[3212])).
% 0.82/1.04 tff(3214,plain,
% 0.82/1.04 (((~![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)))),
% 0.82/1.04 inference(transitivity,[status(thm)],[3213, 3211])).
% 0.82/1.04 tff(3215,plain,
% 0.82/1.04 ((~![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))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(3216,plain,
% 0.82/1.04 ((~![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(s34, c_t2)) | m_main_v_state2(s35, c_t2) | (~node13(s34, s35))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[3215, 3214])).
% 0.82/1.04 tff(3217,plain,
% 0.82/1.04 (m_main_v_state2(s35, c_t2)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[3216, 518, 3116, 3195])).
% 0.82/1.04 tff(3218,plain,
% 0.82/1.04 (((~![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)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(3219,plain,
% 0.82/1.04 ((~![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)))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(3220,plain,
% 0.82/1.04 ((~![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))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[3219, 3218])).
% 0.82/1.04 tff(3221,plain,
% 0.82/1.04 (~m_main_v_state1(s34, c_t1)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[3220, 539, 3171])).
% 0.82/1.04 tff(3222,plain,
% 0.82/1.04 (((~![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)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(3223,plain,
% 0.82/1.04 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s34, c_t1) | (~node5(s34)))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(3224,plain,
% 0.82/1.04 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s34, c_t1) | (~node5(s34))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[3223, 3222])).
% 0.82/1.04 tff(3225,plain,
% 0.82/1.04 (~node5(s34)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[3224, 550, 3221])).
% 0.82/1.04 tff(3226,plain,
% 0.82/1.04 (((~![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)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(3227,plain,
% 0.82/1.04 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s34, c_n2) | (~node4(s34)))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(3228,plain,
% 0.82/1.04 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s34, c_n2) | (~node4(s34))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[3227, 3226])).
% 0.82/1.04 tff(3229,plain,
% 0.82/1.04 (~node4(s34)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[3228, 388, 3120])).
% 0.82/1.04 tff(3230,plain,
% 0.82/1.04 (((~![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)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(3231,plain,
% 0.82/1.04 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s34, c_c2) | (~node3(s34)))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(3232,plain,
% 0.82/1.04 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s34, c_c2) | (~node3(s34))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[3231, 3230])).
% 0.82/1.04 tff(3233,plain,
% 0.82/1.04 (~node3(s34)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[3232, 399, 3136])).
% 0.82/1.04 tff(3234,plain,
% 0.82/1.04 (((~![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)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(3235,plain,
% 0.82/1.04 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s34, c_n2) | (~node2(s34)))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(3236,plain,
% 0.82/1.04 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s34, c_n2) | (~node2(s34))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[3235, 3234])).
% 0.82/1.04 tff(3237,plain,
% 0.82/1.04 (~node2(s34)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[3236, 410, 3120])).
% 0.82/1.04 tff(3238,plain,
% 0.82/1.04 (((~![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)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(3239,plain,
% 0.82/1.04 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s34, c_n1) | (~node1(s34)))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(3240,plain,
% 0.82/1.04 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s34, c_n1) | (~node1(s34))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[3239, 3238])).
% 0.82/1.04 tff(3241,plain,
% 0.82/1.04 (~node1(s34)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[3240, 421, 3175])).
% 0.82/1.04 tff(3242,plain,
% 0.82/1.04 (((~![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))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(3243,plain,
% 0.82/1.04 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s34, s35)) | node7(s34, s35))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(3244,plain,
% 0.82/1.04 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s34, s35)) | node7(s34, s35)),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[3243, 3242])).
% 0.82/1.04 tff(3245,plain,
% 0.82/1.04 (node7(s34, s35)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[3244, 206, 3186])).
% 0.82/1.04 tff(3246,plain,
% 0.82/1.04 (((~![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(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)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(3247,plain,
% 0.82/1.04 (((~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)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(3248,plain,
% 0.82/1.04 (((~![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(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))))),
% 0.82/1.04 inference(monotonicity,[status(thm)],[3247])).
% 0.82/1.04 tff(3249,plain,
% 0.82/1.04 (((~![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(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)))),
% 0.82/1.04 inference(transitivity,[status(thm)],[3248, 3246])).
% 0.82/1.04 tff(3250,plain,
% 0.82/1.04 ((~![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(s34, c_c1)) | node1(s34) | node2(s34) | node3(s34) | node4(s34) | node5(s34) | (~node7(s34, s35)) | m_main_v_state1(s35, c_n1))),
% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
% 0.82/1.04 tff(3251,plain,
% 0.82/1.04 ((~![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(s35, c_n1) | (~m_main_v_state1(s34, c_c1)) | node1(s34) | node2(s34) | node3(s34) | node4(s34) | node5(s34) | (~node7(s34, s35))),
% 0.82/1.04 inference(modus_ponens,[status(thm)],[3250, 3249])).
% 0.82/1.04 tff(3252,plain,
% 0.82/1.04 (m_main_v_state1(s35, c_n1) | (~m_main_v_state1(s34, c_c1)) | node1(s34) | node2(s34) | node3(s34) | node4(s34) | node5(s34)),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[3251, 584, 3245])).
% 0.82/1.05 tff(3253,plain,
% 0.82/1.05 (m_main_v_state1(s35, c_n1)),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[3252, 3241, 3171, 3237, 3233, 3229, 3225])).
% 0.82/1.05 tff(3254,plain,
% 0.82/1.05 (((~![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)))),
% 0.82/1.05 inference(rewrite,[status(thm)],[])).
% 0.82/1.05 tff(3255,plain,
% 0.82/1.05 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s35, c_n2) | (~node8(s35)))),
% 0.82/1.05 inference(quant_inst,[status(thm)],[])).
% 0.82/1.05 tff(3256,plain,
% 0.82/1.05 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s35, c_n2) | (~node8(s35))),
% 0.82/1.05 inference(modus_ponens,[status(thm)],[3255, 3254])).
% 0.82/1.05 tff(3257,plain,
% 0.82/1.05 (~node8(s35)),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[3256, 271, 3202])).
% 0.82/1.05 tff(3258,plain,
% 0.82/1.05 (succ(s35, s36) <=> succ(s35, s36)),
% 0.82/1.05 inference(rewrite,[status(thm)],[])).
% 0.82/1.05 tff(3259,axiom,(succ(s35, s36)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound36')).
% 0.82/1.05 tff(3260,plain,
% 0.82/1.05 (succ(s35, s36)),
% 0.82/1.05 inference(modus_ponens,[status(thm)],[3259, 3258])).
% 0.82/1.05 tff(3261,plain,
% 0.82/1.05 (((~![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))),
% 0.82/1.05 inference(rewrite,[status(thm)],[])).
% 0.82/1.05 tff(3262,plain,
% 0.82/1.05 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s35, s36)) | trans(s35, s36))),
% 0.82/1.05 inference(quant_inst,[status(thm)],[])).
% 0.82/1.05 tff(3263,plain,
% 0.82/1.05 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s35, s36)) | trans(s35, s36)),
% 0.82/1.05 inference(modus_ponens,[status(thm)],[3262, 3261])).
% 0.82/1.05 tff(3264,plain,
% 0.82/1.05 (trans(s35, s36)),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[3263, 3260, 32])).
% 0.82/1.05 tff(3265,plain,
% 0.82/1.05 (((~![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))),
% 0.82/1.05 inference(rewrite,[status(thm)],[])).
% 0.82/1.05 tff(3266,plain,
% 0.82/1.05 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s35, s36)) | node14(s35, s36))),
% 0.82/1.05 inference(quant_inst,[status(thm)],[])).
% 0.82/1.05 tff(3267,plain,
% 0.82/1.05 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s35, s36)) | node14(s35, s36)),
% 0.82/1.05 inference(modus_ponens,[status(thm)],[3266, 3265])).
% 0.82/1.05 tff(3268,plain,
% 0.82/1.05 (node14(s35, s36)),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[3267, 46, 3264])).
% 0.82/1.05 tff(3269,plain,
% 0.82/1.05 (((~![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))),
% 0.82/1.05 inference(rewrite,[status(thm)],[])).
% 0.82/1.05 tff(3270,plain,
% 0.82/1.05 ((~![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))),
% 0.82/1.05 inference(quant_inst,[status(thm)],[])).
% 0.82/1.05 tff(3271,plain,
% 0.82/1.05 ((~![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)),
% 0.89/1.05 inference(modus_ponens,[status(thm)],[3270, 3269])).
% 0.89/1.05 tff(3272,plain,
% 0.89/1.05 ((~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)),
% 0.89/1.05 inference(unit_resolution,[status(thm)],[3271, 617, 3268])).
% 0.89/1.05 tff(3273,plain,
% 0.89/1.05 (m_main_v_state2(s36, c_c2)),
% 0.89/1.05 inference(unit_resolution,[status(thm)],[3272, 3257, 3253, 3217, 3210, 3206])).
% 0.89/1.05 tff(3274,plain,
% 0.89/1.05 (((~![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)))),
% 0.89/1.05 inference(rewrite,[status(thm)],[])).
% 0.89/1.05 tff(3275,plain,
% 0.89/1.05 ((~![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)))),
% 0.89/1.05 inference(quant_inst,[status(thm)],[])).
% 0.89/1.05 tff(3276,plain,
% 0.89/1.05 ((~![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))),
% 0.89/1.05 inference(modus_ponens,[status(thm)],[3275, 3274])).
% 0.89/1.05 tff(3277,plain,
% 0.89/1.05 (~m_main_v_state2(s36, c_t2)),
% 0.89/1.05 inference(unit_resolution,[status(thm)],[3276, 260, 3273])).
% 0.89/1.05 tff(3278,plain,
% 0.89/1.05 (((~![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)))),
% 0.89/1.05 inference(rewrite,[status(thm)],[])).
% 0.89/1.05 tff(3279,plain,
% 0.89/1.05 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s36, c_t2) | (~node12(s36)))),
% 0.89/1.05 inference(quant_inst,[status(thm)],[])).
% 0.89/1.05 tff(3280,plain,
% 0.89/1.05 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s36, c_t2) | (~node12(s36))),
% 0.89/1.05 inference(modus_ponens,[status(thm)],[3279, 3278])).
% 0.89/1.05 tff(3281,plain,
% 0.89/1.05 (~node12(s36)),
% 0.89/1.05 inference(unit_resolution,[status(thm)],[3280, 633, 3277])).
% 0.89/1.05 tff(3282,plain,
% 0.89/1.05 (((~![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))),
% 0.89/1.05 inference(rewrite,[status(thm)],[])).
% 0.89/1.05 tff(3283,plain,
% 0.89/1.05 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s35, s36)) | node7(s35, s36))),
% 0.89/1.05 inference(quant_inst,[status(thm)],[])).
% 0.89/1.05 tff(3284,plain,
% 0.89/1.05 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s35, s36)) | node7(s35, s36)),
% 0.89/1.05 inference(modus_ponens,[status(thm)],[3283, 3282])).
% 0.89/1.05 tff(3285,plain,
% 0.89/1.05 (node7(s35, s36)),
% 0.89/1.05 inference(unit_resolution,[status(thm)],[3284, 206, 3264])).
% 0.89/1.05 tff(3286,plain,
% 0.89/1.05 (((~![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))),
% 0.89/1.05 inference(rewrite,[status(thm)],[])).
% 0.89/1.05 tff(3287,plain,
% 0.89/1.05 ((~![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))),
% 0.89/1.05 inference(quant_inst,[status(thm)],[])).
% 0.89/1.05 tff(3288,plain,
% 0.89/1.05 ((~![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)),
% 0.89/1.05 inference(modus_ponens,[status(thm)],[3287, 3286])).
% 0.89/1.05 tff(3289,plain,
% 0.89/1.05 ((~m_main_v_state1(s35, c_n1)) | (~m_main_v_state2(s35, c_t2)) | m_main_v_state1(s36, c_t1)),
% 0.89/1.05 inference(unit_resolution,[status(thm)],[3288, 651, 3285])).
% 0.89/1.05 tff(3290,plain,
% 0.89/1.05 (m_main_v_state1(s36, c_t1)),
% 0.89/1.05 inference(unit_resolution,[status(thm)],[3289, 3217, 3253])).
% 0.89/1.05 tff(3291,plain,
% 0.89/1.05 (((~![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)))),
% 0.89/1.05 inference(rewrite,[status(thm)],[])).
% 0.89/1.05 tff(3292,plain,
% 0.89/1.05 ((~![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)))),
% 0.89/1.05 inference(quant_inst,[status(thm)],[])).
% 0.89/1.05 tff(3293,plain,
% 0.89/1.05 ((~![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))),
% 0.89/1.05 inference(modus_ponens,[status(thm)],[3292, 3291])).
% 0.89/1.05 tff(3294,plain,
% 0.89/1.05 (~m_main_v_state1(s36, c_n1)),
% 0.89/1.05 inference(unit_resolution,[status(thm)],[3293, 10, 3290])).
% 0.89/1.05 tff(3295,plain,
% 0.89/1.05 (((~![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)))),
% 0.89/1.05 inference(rewrite,[status(thm)],[])).
% 0.89/1.05 tff(3296,plain,
% 0.89/1.05 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s36, c_n1) | (~node11(s36)))),
% 0.89/1.05 inference(quant_inst,[status(thm)],[])).
% 0.89/1.05 tff(3297,plain,
% 0.89/1.05 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s36, c_n1) | (~node11(s36))),
% 0.89/1.05 inference(modus_ponens,[status(thm)],[3296, 3295])).
% 0.89/1.05 tff(3298,plain,
% 0.89/1.05 (~node11(s36)),
% 0.89/1.05 inference(unit_resolution,[status(thm)],[3297, 238, 3294])).
% 0.89/1.05 tff(3299,plain,
% 0.89/1.05 (((~![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)))),
% 0.89/1.05 inference(rewrite,[status(thm)],[])).
% 0.89/1.05 tff(3300,plain,
% 0.89/1.05 ((~![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)))),
% 0.89/1.05 inference(quant_inst,[status(thm)],[])).
% 0.89/1.05 tff(3301,plain,
% 0.89/1.05 ((~![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))),
% 0.89/1.05 inference(modus_ponens,[status(thm)],[3300, 3299])).
% 0.89/1.05 tff(3302,plain,
% 0.89/1.05 (~m_main_v_state1(s36, c_c1)),
% 0.89/1.05 inference(unit_resolution,[status(thm)],[3301, 539, 3290])).
% 0.89/1.05 tff(3303,plain,
% 0.89/1.05 (((~![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)))),
% 0.89/1.05 inference(rewrite,[status(thm)],[])).
% 0.89/1.05 tff(3304,plain,
% 0.89/1.05 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s36, c_c1) | (~node10(s36)))),
% 0.89/1.05 inference(quant_inst,[status(thm)],[])).
% 0.89/1.05 tff(3305,plain,
% 0.89/1.05 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s36, c_c1) | (~node10(s36))),
% 0.89/1.05 inference(modus_ponens,[status(thm)],[3304, 3303])).
% 0.89/1.05 tff(3306,plain,
% 0.89/1.05 (~node10(s36)),
% 0.89/1.05 inference(unit_resolution,[status(thm)],[3305, 675, 3302])).
% 0.89/1.05 tff(3307,plain,
% 0.89/1.05 (((~![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)))),
% 0.89/1.05 inference(rewrite,[status(thm)],[])).
% 0.89/1.05 tff(3308,plain,
% 0.89/1.05 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s36, c_n1) | (~node9(s36)))),
% 0.89/1.05 inference(quant_inst,[status(thm)],[])).
% 0.89/1.05 tff(3309,plain,
% 0.89/1.05 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s36, c_n1) | (~node9(s36))),
% 0.89/1.05 inference(modus_ponens,[status(thm)],[3308, 3307])).
% 0.89/1.05 tff(3310,plain,
% 0.89/1.05 (~node9(s36)),
% 0.89/1.05 inference(unit_resolution,[status(thm)],[3309, 686, 3294])).
% 0.89/1.05 tff(3311,plain,
% 0.89/1.05 (((~![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)))),
% 0.89/1.05 inference(rewrite,[status(thm)],[])).
% 0.89/1.05 tff(3312,plain,
% 0.89/1.05 ((~![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)))),
% 0.89/1.05 inference(quant_inst,[status(thm)],[])).
% 0.89/1.05 tff(3313,plain,
% 0.89/1.05 ((~![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))),
% 0.89/1.05 inference(modus_ponens,[status(thm)],[3312, 3311])).
% 0.89/1.05 tff(3314,plain,
% 0.89/1.05 (~m_main_v_state2(s36, c_n2)),
% 0.89/1.05 inference(unit_resolution,[status(thm)],[3313, 697, 3273])).
% 0.89/1.05 tff(3315,plain,
% 0.89/1.05 (((~![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)))),
% 0.89/1.05 inference(rewrite,[status(thm)],[])).
% 0.89/1.05 tff(3316,plain,
% 0.89/1.05 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s36, c_n2) | (~node8(s36)))),
% 0.89/1.05 inference(quant_inst,[status(thm)],[])).
% 0.89/1.05 tff(3317,plain,
% 0.89/1.05 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s36, c_n2) | (~node8(s36))),
% 0.89/1.05 inference(modus_ponens,[status(thm)],[3316, 3315])).
% 0.89/1.05 tff(3318,plain,
% 0.89/1.05 (~node8(s36)),
% 0.89/1.05 inference(unit_resolution,[status(thm)],[3317, 271, 3314])).
% 0.89/1.05 tff(3319,plain,
% 0.89/1.05 (succ(s36, s37) <=> succ(s36, s37)),
% 0.89/1.05 inference(rewrite,[status(thm)],[])).
% 0.89/1.05 tff(3320,axiom,(succ(s36, s37)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound37')).
% 0.89/1.05 tff(3321,plain,
% 0.89/1.05 (succ(s36, s37)),
% 0.89/1.05 inference(modus_ponens,[status(thm)],[3320, 3319])).
% 0.89/1.05 tff(3322,plain,
% 0.89/1.05 (((~![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))),
% 0.89/1.05 inference(rewrite,[status(thm)],[])).
% 0.89/1.05 tff(3323,plain,
% 0.89/1.05 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s36, s37)) | trans(s36, s37))),
% 0.89/1.05 inference(quant_inst,[status(thm)],[])).
% 0.89/1.05 tff(3324,plain,
% 0.89/1.05 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s36, s37)) | trans(s36, s37)),
% 0.89/1.05 inference(modus_ponens,[status(thm)],[3323, 3322])).
% 0.89/1.05 tff(3325,plain,
% 0.89/1.05 (trans(s36, s37)),
% 0.89/1.05 inference(unit_resolution,[status(thm)],[3324, 3321, 32])).
% 0.89/1.05 tff(3326,plain,
% 0.89/1.05 (((~![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))),
% 0.89/1.05 inference(rewrite,[status(thm)],[])).
% 0.89/1.05 tff(3327,plain,
% 0.89/1.05 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s36, s37)) | node14(s36, s37))),
% 0.89/1.05 inference(quant_inst,[status(thm)],[])).
% 0.89/1.05 tff(3328,plain,
% 0.89/1.05 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s36, s37)) | node14(s36, s37)),
% 0.89/1.05 inference(modus_ponens,[status(thm)],[3327, 3326])).
% 0.89/1.05 tff(3329,plain,
% 0.89/1.05 (node14(s36, s37)),
% 0.89/1.05 inference(unit_resolution,[status(thm)],[3328, 46, 3325])).
% 0.89/1.05 tff(3330,plain,
% 0.89/1.05 (((~![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(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)))),
% 0.89/1.05 inference(rewrite,[status(thm)],[])).
% 0.89/1.05 tff(3331,plain,
% 0.89/1.05 (((~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)))),
% 0.89/1.05 inference(rewrite,[status(thm)],[])).
% 0.89/1.05 tff(3332,plain,
% 0.89/1.05 (((~![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(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))))),
% 0.89/1.05 inference(monotonicity,[status(thm)],[3331])).
% 0.89/1.05 tff(3333,plain,
% 0.89/1.05 (((~![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(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)))),
% 0.89/1.05 inference(transitivity,[status(thm)],[3332, 3330])).
% 0.89/1.05 tff(3334,plain,
% 0.89/1.05 ((~![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(s36, c_c2)) | node9(s36) | node8(s36) | node10(s36) | node11(s36) | node12(s36) | (~node14(s36, s37)) | m_main_v_state2(s37, c_n2))),
% 0.89/1.05 inference(quant_inst,[status(thm)],[])).
% 0.89/1.05 tff(3335,plain,
% 0.89/1.05 ((~![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(s37, c_n2) | node9(s36) | node8(s36) | node10(s36) | node11(s36) | node12(s36) | (~node14(s36, s37)) | (~m_main_v_state2(s36, c_c2))),
% 0.89/1.05 inference(modus_ponens,[status(thm)],[3334, 3333])).
% 0.89/1.05 tff(3336,plain,
% 0.89/1.05 (m_main_v_state2(s37, c_n2) | node9(s36) | node8(s36) | node10(s36) | node11(s36) | node12(s36) | (~m_main_v_state2(s36, c_c2))),
% 0.89/1.05 inference(unit_resolution,[status(thm)],[3335, 726, 3329])).
% 0.89/1.05 tff(3337,plain,
% 0.89/1.05 (m_main_v_state2(s37, c_n2)),
% 0.89/1.05 inference(unit_resolution,[status(thm)],[3336, 3318, 3273, 3310, 3306, 3298, 3281])).
% 0.89/1.05 tff(3338,plain,
% 0.89/1.05 (((~![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)))),
% 0.89/1.05 inference(rewrite,[status(thm)],[])).
% 0.89/1.05 tff(3339,plain,
% 0.89/1.05 ((~![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)))),
% 0.89/1.05 inference(quant_inst,[status(thm)],[])).
% 0.89/1.05 tff(3340,plain,
% 0.89/1.05 ((~![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))),
% 0.89/1.05 inference(modus_ponens,[status(thm)],[3339, 3338])).
% 0.89/1.05 tff(3341,plain,
% 0.89/1.05 (~m_main_v_state2(s37, c_c2)),
% 0.89/1.05 inference(unit_resolution,[status(thm)],[3340, 697, 3337])).
% 0.89/1.05 tff(3342,plain,
% 0.89/1.05 (((~![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)))),
% 0.89/1.05 inference(rewrite,[status(thm)],[])).
% 0.89/1.05 tff(3343,plain,
% 0.89/1.05 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s37, c_c2) | (~node3(s37)))),
% 0.89/1.05 inference(quant_inst,[status(thm)],[])).
% 0.89/1.05 tff(3344,plain,
% 0.89/1.05 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s37, c_c2) | (~node3(s37))),
% 0.89/1.05 inference(modus_ponens,[status(thm)],[3343, 3342])).
% 0.89/1.05 tff(3345,plain,
% 0.89/1.05 (~node3(s37)),
% 0.89/1.05 inference(unit_resolution,[status(thm)],[3344, 399, 3341])).
% 0.89/1.05 tff(3346,plain,
% 0.89/1.05 (((~![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)))),
% 0.89/1.05 inference(rewrite,[status(thm)],[])).
% 0.89/1.05 tff(3347,plain,
% 0.89/1.05 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s36, c_n1) | (~node1(s36)))),
% 0.89/1.05 inference(quant_inst,[status(thm)],[])).
% 0.89/1.05 tff(3348,plain,
% 0.89/1.05 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s36, c_n1) | (~node1(s36))),
% 0.89/1.05 inference(modus_ponens,[status(thm)],[3347, 3346])).
% 0.89/1.05 tff(3349,plain,
% 0.89/1.05 (~node1(s36)),
% 0.89/1.05 inference(unit_resolution,[status(thm)],[3348, 421, 3294])).
% 0.89/1.05 tff(3350,plain,
% 0.89/1.05 (((~![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))),
% 0.89/1.05 inference(rewrite,[status(thm)],[])).
% 0.89/1.05 tff(3351,plain,
% 0.89/1.05 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s35, s36)) | node18(s35, s36))),
% 0.89/1.05 inference(quant_inst,[status(thm)],[])).
% 0.89/1.05 tff(3352,plain,
% 0.89/1.05 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s35, s36)) | node18(s35, s36)),
% 0.89/1.05 inference(modus_ponens,[status(thm)],[3351, 3350])).
% 0.89/1.05 tff(3353,plain,
% 0.89/1.05 (node18(s35, s36)),
% 0.89/1.05 inference(unit_resolution,[status(thm)],[3352, 125, 3264])).
% 0.89/1.05 tff(3354,plain,
% 0.89/1.05 (((~![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(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))),
% 0.89/1.05 inference(rewrite,[status(thm)],[])).
% 0.89/1.05 tff(3355,plain,
% 0.89/1.05 ((~![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(s35, c_n1)) | (~m_main_v_state2(s35, c_t2)) | (~node18(s35, s36)) | m_main_v_turn(s36, c_2))),
% 0.89/1.05 inference(quant_inst,[status(thm)],[])).
% 0.89/1.05 tff(3356,plain,
% 0.89/1.05 ((~![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(s35, c_n1)) | (~m_main_v_state2(s35, c_t2)) | (~node18(s35, s36)) | m_main_v_turn(s36, c_2)),
% 0.89/1.05 inference(modus_ponens,[status(thm)],[3355, 3354])).
% 0.89/1.05 tff(3357,plain,
% 0.89/1.05 ((~m_main_v_state1(s35, c_n1)) | (~m_main_v_state2(s35, c_t2)) | m_main_v_turn(s36, c_2)),
% 0.89/1.05 inference(unit_resolution,[status(thm)],[3356, 760, 3353])).
% 0.89/1.05 tff(3358,plain,
% 0.89/1.05 (m_main_v_turn(s36, c_2)),
% 0.89/1.05 inference(unit_resolution,[status(thm)],[3357, 3217, 3253])).
% 0.89/1.05 tff(3359,plain,
% 0.89/1.05 (((~![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)))),
% 0.89/1.05 inference(rewrite,[status(thm)],[])).
% 0.89/1.05 tff(3360,plain,
% 0.89/1.05 ((~![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)))),
% 0.89/1.05 inference(quant_inst,[status(thm)],[])).
% 0.89/1.05 tff(3361,plain,
% 0.89/1.05 ((~![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))),
% 0.89/1.05 inference(modus_ponens,[status(thm)],[3360, 3359])).
% 0.89/1.05 tff(3362,plain,
% 0.89/1.05 (~m_main_v_turn(s36, c_1)),
% 0.89/1.05 inference(unit_resolution,[status(thm)],[3361, 156, 3358])).
% 0.89/1.05 tff(3363,plain,
% 0.89/1.05 (((~![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)))),
% 0.89/1.05 inference(rewrite,[status(thm)],[])).
% 0.89/1.05 tff(3364,plain,
% 0.89/1.05 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s36, c_1) | (~node5(s36)))),
% 0.89/1.05 inference(quant_inst,[status(thm)],[])).
% 0.89/1.05 tff(3365,plain,
% 0.89/1.05 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s36, c_1) | (~node5(s36))),
% 0.89/1.05 inference(modus_ponens,[status(thm)],[3364, 3363])).
% 0.89/1.05 tff(3366,plain,
% 0.89/1.05 (~node5(s36)),
% 0.89/1.05 inference(unit_resolution,[status(thm)],[3365, 776, 3362])).
% 0.89/1.05 tff(3367,plain,
% 0.89/1.05 (((~![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)))),
% 0.89/1.05 inference(rewrite,[status(thm)],[])).
% 0.89/1.05 tff(3368,plain,
% 0.89/1.05 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s36, c_n1) | (~node2(s36)))),
% 0.89/1.05 inference(quant_inst,[status(thm)],[])).
% 0.89/1.05 tff(3369,plain,
% 0.89/1.05 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s36, c_n1) | (~node2(s36))),
% 0.89/1.05 inference(modus_ponens,[status(thm)],[3368, 3367])).
% 0.89/1.05 tff(3370,plain,
% 0.89/1.05 (~node2(s36)),
% 0.89/1.05 inference(unit_resolution,[status(thm)],[3369, 787, 3294])).
% 0.89/1.05 tff(3371,plain,
% 0.89/1.05 (((~![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)))),
% 0.89/1.05 inference(rewrite,[status(thm)],[])).
% 0.89/1.05 tff(3372,plain,
% 0.89/1.05 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s36, c_n1) | (~node3(s36)))),
% 0.89/1.05 inference(quant_inst,[status(thm)],[])).
% 0.89/1.05 tff(3373,plain,
% 0.89/1.05 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s36, c_n1) | (~node3(s36))),
% 0.89/1.05 inference(modus_ponens,[status(thm)],[3372, 3371])).
% 0.89/1.05 tff(3374,plain,
% 0.89/1.05 (~node3(s36)),
% 0.89/1.05 inference(unit_resolution,[status(thm)],[3373, 798, 3294])).
% 0.89/1.05 tff(3375,plain,
% 0.89/1.05 (((~![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)))),
% 0.89/1.05 inference(rewrite,[status(thm)],[])).
% 0.89/1.05 tff(3376,plain,
% 0.89/1.05 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s36, c_n2) | (~node4(s36)))),
% 0.89/1.05 inference(quant_inst,[status(thm)],[])).
% 0.89/1.05 tff(3377,plain,
% 0.89/1.05 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s36, c_n2) | (~node4(s36))),
% 0.89/1.05 inference(modus_ponens,[status(thm)],[3376, 3375])).
% 0.89/1.05 tff(3378,plain,
% 0.89/1.05 (~node4(s36)),
% 0.89/1.05 inference(unit_resolution,[status(thm)],[3377, 388, 3314])).
% 0.89/1.05 tff(3379,plain,
% 0.89/1.05 (((~![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))),
% 0.89/1.05 inference(rewrite,[status(thm)],[])).
% 0.89/1.05 tff(3380,plain,
% 0.89/1.05 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s36, s37)) | node7(s36, s37))),
% 0.89/1.05 inference(quant_inst,[status(thm)],[])).
% 0.89/1.05 tff(3381,plain,
% 0.89/1.05 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s36, s37)) | node7(s36, s37)),
% 0.89/1.05 inference(modus_ponens,[status(thm)],[3380, 3379])).
% 0.89/1.05 tff(3382,plain,
% 0.89/1.05 (node7(s36, s37)),
% 0.89/1.05 inference(unit_resolution,[status(thm)],[3381, 206, 3325])).
% 0.89/1.05 tff(3383,plain,
% 0.89/1.05 (((~![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(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)))),
% 0.89/1.05 inference(rewrite,[status(thm)],[])).
% 0.89/1.06 tff(3384,plain,
% 0.89/1.06 ((~![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)))),
% 0.89/1.06 inference(quant_inst,[status(thm)],[])).
% 0.89/1.06 tff(3385,plain,
% 0.89/1.06 ((~![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))),
% 0.89/1.06 inference(modus_ponens,[status(thm)],[3384, 3383])).
% 0.89/1.06 tff(3386,plain,
% 0.89/1.06 (m_main_v_state1(s36, c_c1) | node1(s36) | node2(s36) | node3(s36) | node4(s36) | node5(s36) | node6(s36, s37)),
% 0.89/1.06 inference(unit_resolution,[status(thm)],[3385, 820, 3382])).
% 0.89/1.06 tff(3387,plain,
% 0.89/1.06 (node6(s36, s37)),
% 0.89/1.06 inference(unit_resolution,[status(thm)],[3386, 3378, 3302, 3374, 3370, 3366, 3349])).
% 0.89/1.06 tff(3388,plain,
% 0.89/1.06 (((~![V: $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)))),
% 0.89/1.06 inference(rewrite,[status(thm)],[])).
% 0.89/1.06 tff(3389,plain,
% 0.89/1.06 (((~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)))),
% 0.89/1.06 inference(rewrite,[status(thm)],[])).
% 0.89/1.06 tff(3390,plain,
% 0.89/1.06 (((~![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))))),
% 0.89/1.06 inference(monotonicity,[status(thm)],[3389])).
% 0.89/1.06 tff(3391,plain,
% 0.89/1.06 (((~![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)))),
% 0.89/1.06 inference(transitivity,[status(thm)],[3390, 3388])).
% 0.89/1.06 tff(3392,plain,
% 0.89/1.06 ((~![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)))),
% 0.89/1.06 inference(quant_inst,[status(thm)],[])).
% 0.89/1.06 tff(3393,plain,
% 0.89/1.06 ((~![V: $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))),
% 0.89/1.06 inference(modus_ponens,[status(thm)],[3392, 3391])).
% 0.89/1.06 tff(3394,plain,
% 0.89/1.06 (~m_main_v_state1(s37, c_n1)),
% 0.89/1.06 inference(unit_resolution,[status(thm)],[3393, 835, 3294, 3387])).
% 0.89/1.06 tff(3395,plain,
% 0.89/1.06 (((~![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)))),
% 0.89/1.06 inference(rewrite,[status(thm)],[])).
% 0.89/1.06 tff(3396,plain,
% 0.89/1.06 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s37, c_n1) | (~node2(s37)))),
% 0.89/1.06 inference(quant_inst,[status(thm)],[])).
% 0.89/1.06 tff(3397,plain,
% 0.89/1.06 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s37, c_n1) | (~node2(s37))),
% 0.89/1.06 inference(modus_ponens,[status(thm)],[3396, 3395])).
% 0.89/1.06 tff(3398,plain,
% 0.89/1.06 (~node2(s37)),
% 0.89/1.06 inference(unit_resolution,[status(thm)],[3397, 787, 3394])).
% 0.89/1.06 tff(3399,plain,
% 0.89/1.06 (((~![V: $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)))),
% 0.89/1.06 inference(rewrite,[status(thm)],[])).
% 0.89/1.06 tff(3400,plain,
% 0.89/1.06 (((~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)))),
% 0.89/1.06 inference(rewrite,[status(thm)],[])).
% 0.89/1.06 tff(3401,plain,
% 0.89/1.06 (((~![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))))),
% 0.89/1.06 inference(monotonicity,[status(thm)],[3400])).
% 0.89/1.06 tff(3402,plain,
% 0.89/1.06 (((~![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)))),
% 0.89/1.06 inference(transitivity,[status(thm)],[3401, 3399])).
% 0.89/1.06 tff(3403,plain,
% 0.89/1.06 ((~![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))),
% 0.89/1.06 inference(quant_inst,[status(thm)],[])).
% 0.89/1.06 tff(3404,plain,
% 0.89/1.06 ((~![V: $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))),
% 0.89/1.06 inference(modus_ponens,[status(thm)],[3403, 3402])).
% 0.89/1.06 tff(3405,plain,
% 0.89/1.06 (m_main_v_state1(s37, c_t1)),
% 0.89/1.06 inference(unit_resolution,[status(thm)],[3404, 856, 3290, 3387])).
% 0.89/1.06 tff(3406,plain,
% 0.89/1.06 (((~![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)))),
% 0.89/1.06 inference(rewrite,[status(thm)],[])).
% 0.89/1.06 tff(3407,plain,
% 0.89/1.06 ((~![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)))),
% 0.89/1.06 inference(quant_inst,[status(thm)],[])).
% 0.89/1.06 tff(3408,plain,
% 0.89/1.06 ((~![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))),
% 0.89/1.06 inference(modus_ponens,[status(thm)],[3407, 3406])).
% 0.89/1.06 tff(3409,plain,
% 0.89/1.06 (~m_main_v_state2(s37, c_t2)),
% 0.89/1.06 inference(unit_resolution,[status(thm)],[3408, 77, 3337])).
% 0.89/1.06 tff(3410,plain,
% 0.89/1.06 (((~![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)))),
% 0.89/1.06 inference(rewrite,[status(thm)],[])).
% 0.89/1.06 tff(3411,plain,
% 0.89/1.06 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s37, c_t2) | (~node1(s37)))),
% 0.89/1.06 inference(quant_inst,[status(thm)],[])).
% 0.89/1.06 tff(3412,plain,
% 0.89/1.06 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s37, c_t2) | (~node1(s37))),
% 0.89/1.06 inference(modus_ponens,[status(thm)],[3411, 3410])).
% 0.89/1.06 tff(3413,plain,
% 0.89/1.06 (~node1(s37)),
% 0.89/1.06 inference(unit_resolution,[status(thm)],[3412, 195, 3409])).
% 0.89/1.06 tff(3414,plain,
% 0.89/1.06 (succ(s37, s38) <=> succ(s37, s38)),
% 0.89/1.06 inference(rewrite,[status(thm)],[])).
% 0.89/1.06 tff(3415,axiom,(succ(s37, s38)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound38')).
% 0.89/1.06 tff(3416,plain,
% 0.89/1.06 (succ(s37, s38)),
% 0.89/1.06 inference(modus_ponens,[status(thm)],[3415, 3414])).
% 0.89/1.06 tff(3417,plain,
% 0.89/1.06 (((~![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))),
% 0.89/1.06 inference(rewrite,[status(thm)],[])).
% 0.89/1.06 tff(3418,plain,
% 0.89/1.06 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s37, s38)) | trans(s37, s38))),
% 0.89/1.06 inference(quant_inst,[status(thm)],[])).
% 0.89/1.06 tff(3419,plain,
% 0.89/1.06 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s37, s38)) | trans(s37, s38)),
% 0.89/1.06 inference(modus_ponens,[status(thm)],[3418, 3417])).
% 0.89/1.06 tff(3420,plain,
% 0.89/1.06 (trans(s37, s38)),
% 0.89/1.06 inference(unit_resolution,[status(thm)],[3419, 3416, 32])).
% 0.89/1.06 tff(3421,plain,
% 0.89/1.06 (((~![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))),
% 0.89/1.06 inference(rewrite,[status(thm)],[])).
% 0.89/1.06 tff(3422,plain,
% 0.89/1.06 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s37, s38)) | node7(s37, s38))),
% 0.89/1.06 inference(quant_inst,[status(thm)],[])).
% 0.89/1.06 tff(3423,plain,
% 0.89/1.06 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s37, s38)) | node7(s37, s38)),
% 0.89/1.06 inference(modus_ponens,[status(thm)],[3422, 3421])).
% 0.89/1.06 tff(3424,plain,
% 0.89/1.06 (node7(s37, s38)),
% 0.89/1.06 inference(unit_resolution,[status(thm)],[3423, 206, 3420])).
% 0.89/1.06 tff(3425,plain,
% 0.89/1.06 (((~![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(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)))),
% 0.89/1.06 inference(rewrite,[status(thm)],[])).
% 0.89/1.06 tff(3426,plain,
% 0.89/1.06 (((~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)))),
% 0.89/1.06 inference(rewrite,[status(thm)],[])).
% 0.89/1.06 tff(3427,plain,
% 0.89/1.06 (((~![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(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))))),
% 0.89/1.06 inference(monotonicity,[status(thm)],[3426])).
% 0.89/1.06 tff(3428,plain,
% 0.89/1.06 (((~![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(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)))),
% 0.89/1.06 inference(transitivity,[status(thm)],[3427, 3425])).
% 0.89/1.06 tff(3429,plain,
% 0.89/1.06 ((~![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(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))),
% 0.89/1.06 inference(quant_inst,[status(thm)],[])).
% 0.89/1.06 tff(3430,plain,
% 0.89/1.06 ((~![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(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))),
% 0.89/1.06 inference(modus_ponens,[status(thm)],[3429, 3428])).
% 0.89/1.06 tff(3431,plain,
% 0.89/1.06 ((~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)),
% 0.89/1.06 inference(unit_resolution,[status(thm)],[3430, 892, 3424])).
% 0.89/1.06 tff(3432,plain,
% 0.89/1.06 (m_main_v_state1(s38, c_c1)),
% 0.89/1.06 inference(unit_resolution,[status(thm)],[3431, 3413, 3337, 3405, 3398, 3345])).
% 0.89/1.06 tff(3433,plain,
% 0.89/1.06 (((~![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)))),
% 0.89/1.06 inference(rewrite,[status(thm)],[])).
% 0.89/1.06 tff(3434,plain,
% 0.89/1.06 ((~![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)))),
% 0.89/1.06 inference(quant_inst,[status(thm)],[])).
% 0.89/1.06 tff(3435,plain,
% 0.89/1.06 ((~![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))),
% 0.89/1.06 inference(modus_ponens,[status(thm)],[3434, 3433])).
% 0.89/1.06 tff(3436,plain,
% 0.89/1.06 (~m_main_v_state1(s38, c_t1)),
% 0.89/1.06 inference(unit_resolution,[status(thm)],[3435, 539, 3432])).
% 0.89/1.06 tff(3437,plain,
% 0.89/1.06 (((~![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)))),
% 0.89/1.06 inference(rewrite,[status(thm)],[])).
% 0.89/1.06 tff(3438,plain,
% 0.89/1.06 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s38, c_t1) | (~node5(s38)))),
% 0.89/1.06 inference(quant_inst,[status(thm)],[])).
% 0.89/1.06 tff(3439,plain,
% 0.89/1.06 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s38, c_t1) | (~node5(s38))),
% 0.89/1.06 inference(modus_ponens,[status(thm)],[3438, 3437])).
% 0.89/1.06 tff(3440,plain,
% 0.89/1.06 (~node5(s38)),
% 0.89/1.06 inference(unit_resolution,[status(thm)],[3439, 550, 3436])).
% 0.89/1.06 tff(3441,plain,
% 0.89/1.06 (((~![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))),
% 0.89/1.06 inference(rewrite,[status(thm)],[])).
% 0.89/1.06 tff(3442,plain,
% 0.89/1.06 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s37, s38)) | node14(s37, s38))),
% 0.89/1.06 inference(quant_inst,[status(thm)],[])).
% 0.89/1.06 tff(3443,plain,
% 0.89/1.06 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s37, s38)) | node14(s37, s38)),
% 0.89/1.06 inference(modus_ponens,[status(thm)],[3442, 3441])).
% 0.89/1.06 tff(3444,plain,
% 0.89/1.06 (node14(s37, s38)),
% 0.89/1.06 inference(unit_resolution,[status(thm)],[3443, 46, 3420])).
% 0.89/1.06 tff(3445,plain,
% 0.89/1.06 (((~![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(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))),
% 0.89/1.06 inference(rewrite,[status(thm)],[])).
% 0.89/1.06 tff(3446,plain,
% 0.89/1.06 ((~![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(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | (~node14(s37, s38)) | m_main_v_state2(s38, c_t2))),
% 0.89/1.06 inference(quant_inst,[status(thm)],[])).
% 0.89/1.06 tff(3447,plain,
% 0.89/1.06 ((~![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(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | (~node14(s37, s38)) | m_main_v_state2(s38, c_t2)),
% 0.89/1.06 inference(modus_ponens,[status(thm)],[3446, 3445])).
% 0.89/1.06 tff(3448,plain,
% 0.89/1.06 ((~m_main_v_state1(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | m_main_v_state2(s38, c_t2)),
% 0.89/1.06 inference(unit_resolution,[status(thm)],[3447, 922, 3444])).
% 0.89/1.06 tff(3449,plain,
% 0.89/1.06 (m_main_v_state2(s38, c_t2)),
% 0.89/1.06 inference(unit_resolution,[status(thm)],[3448, 3405, 3337])).
% 0.89/1.06 tff(3450,plain,
% 0.89/1.06 (((~![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)))),
% 0.89/1.06 inference(rewrite,[status(thm)],[])).
% 0.89/1.06 tff(3451,plain,
% 0.89/1.06 ((~![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)))),
% 0.89/1.06 inference(quant_inst,[status(thm)],[])).
% 0.89/1.06 tff(3452,plain,
% 0.89/1.06 ((~![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))),
% 0.89/1.06 inference(modus_ponens,[status(thm)],[3451, 3450])).
% 0.89/1.06 tff(3453,plain,
% 0.89/1.06 (~m_main_v_state2(s38, c_n2)),
% 0.89/1.06 inference(unit_resolution,[status(thm)],[3452, 77, 3449])).
% 0.89/1.06 tff(3454,plain,
% 0.89/1.06 (((~![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)))),
% 0.89/1.06 inference(rewrite,[status(thm)],[])).
% 0.89/1.06 tff(3455,plain,
% 0.89/1.06 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s38, c_n2) | (~node4(s38)))),
% 0.89/1.06 inference(quant_inst,[status(thm)],[])).
% 0.89/1.06 tff(3456,plain,
% 0.89/1.06 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s38, c_n2) | (~node4(s38))),
% 0.89/1.06 inference(modus_ponens,[status(thm)],[3455, 3454])).
% 0.89/1.06 tff(3457,plain,
% 0.89/1.06 (~node4(s38)),
% 0.89/1.06 inference(unit_resolution,[status(thm)],[3456, 388, 3453])).
% 0.89/1.06 tff(3458,plain,
% 0.89/1.06 (((~![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)))),
% 0.89/1.06 inference(rewrite,[status(thm)],[])).
% 0.89/1.06 tff(3459,plain,
% 0.89/1.06 ((~![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)))),
% 0.89/1.06 inference(quant_inst,[status(thm)],[])).
% 0.89/1.06 tff(3460,plain,
% 0.89/1.06 ((~![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))),
% 0.89/1.06 inference(modus_ponens,[status(thm)],[3459, 3458])).
% 0.89/1.06 tff(3461,plain,
% 0.89/1.06 (~m_main_v_state2(s38, c_c2)),
% 0.89/1.06 inference(unit_resolution,[status(thm)],[3460, 260, 3449])).
% 0.89/1.06 tff(3462,plain,
% 0.89/1.06 (((~![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)))),
% 0.89/1.06 inference(rewrite,[status(thm)],[])).
% 0.89/1.06 tff(3463,plain,
% 0.89/1.06 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s38, c_c2) | (~node3(s38)))),
% 0.89/1.06 inference(quant_inst,[status(thm)],[])).
% 0.89/1.06 tff(3464,plain,
% 0.89/1.06 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s38, c_c2) | (~node3(s38))),
% 0.89/1.06 inference(modus_ponens,[status(thm)],[3463, 3462])).
% 0.89/1.06 tff(3465,plain,
% 0.89/1.06 (~node3(s38)),
% 0.89/1.06 inference(unit_resolution,[status(thm)],[3464, 399, 3461])).
% 0.89/1.06 tff(3466,plain,
% 0.89/1.06 (((~![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)))),
% 0.89/1.06 inference(rewrite,[status(thm)],[])).
% 0.89/1.06 tff(3467,plain,
% 0.89/1.06 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s38, c_n2) | (~node2(s38)))),
% 0.89/1.06 inference(quant_inst,[status(thm)],[])).
% 0.89/1.06 tff(3468,plain,
% 0.89/1.06 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s38, c_n2) | (~node2(s38))),
% 0.89/1.06 inference(modus_ponens,[status(thm)],[3467, 3466])).
% 0.89/1.06 tff(3469,plain,
% 0.89/1.06 (~node2(s38)),
% 0.89/1.06 inference(unit_resolution,[status(thm)],[3468, 410, 3453])).
% 0.89/1.06 tff(3470,plain,
% 0.89/1.06 (((~![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)))),
% 0.89/1.06 inference(rewrite,[status(thm)],[])).
% 0.89/1.06 tff(3471,plain,
% 0.89/1.06 ((~![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)))),
% 0.89/1.06 inference(quant_inst,[status(thm)],[])).
% 0.89/1.06 tff(3472,plain,
% 0.89/1.06 ((~![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))),
% 0.89/1.06 inference(modus_ponens,[status(thm)],[3471, 3470])).
% 0.89/1.06 tff(3473,plain,
% 0.89/1.06 (~m_main_v_state1(s38, c_n1)),
% 0.89/1.06 inference(unit_resolution,[status(thm)],[3472, 454, 3432])).
% 0.89/1.06 tff(3474,plain,
% 0.89/1.06 (((~![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)))),
% 0.89/1.06 inference(rewrite,[status(thm)],[])).
% 0.89/1.06 tff(3475,plain,
% 0.89/1.06 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s38, c_n1) | (~node1(s38)))),
% 0.89/1.06 inference(quant_inst,[status(thm)],[])).
% 0.89/1.06 tff(3476,plain,
% 0.89/1.06 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s38, c_n1) | (~node1(s38))),
% 0.89/1.06 inference(modus_ponens,[status(thm)],[3475, 3474])).
% 0.89/1.06 tff(3477,plain,
% 0.89/1.06 (~node1(s38)),
% 0.89/1.06 inference(unit_resolution,[status(thm)],[3476, 421, 3473])).
% 0.89/1.06 tff(3478,plain,
% 0.89/1.06 (succ(s38, s39) <=> succ(s38, s39)),
% 0.89/1.06 inference(rewrite,[status(thm)],[])).
% 0.89/1.06 tff(3479,axiom,(succ(s38, s39)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound39')).
% 0.89/1.06 tff(3480,plain,
% 0.89/1.06 (succ(s38, s39)),
% 0.89/1.06 inference(modus_ponens,[status(thm)],[3479, 3478])).
% 0.89/1.06 tff(3481,plain,
% 0.89/1.06 (((~![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))),
% 0.89/1.06 inference(rewrite,[status(thm)],[])).
% 0.89/1.06 tff(3482,plain,
% 0.89/1.06 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s38, s39)) | trans(s38, s39))),
% 0.89/1.06 inference(quant_inst,[status(thm)],[])).
% 0.89/1.06 tff(3483,plain,
% 0.89/1.06 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s38, s39)) | trans(s38, s39)),
% 0.89/1.06 inference(modus_ponens,[status(thm)],[3482, 3481])).
% 0.89/1.06 tff(3484,plain,
% 0.89/1.06 (trans(s38, s39)),
% 0.89/1.06 inference(unit_resolution,[status(thm)],[3483, 3480, 32])).
% 0.89/1.06 tff(3485,plain,
% 0.89/1.06 (((~![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))),
% 0.89/1.06 inference(rewrite,[status(thm)],[])).
% 0.89/1.06 tff(3486,plain,
% 0.89/1.06 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s38, s39)) | node7(s38, s39))),
% 0.89/1.06 inference(quant_inst,[status(thm)],[])).
% 0.89/1.06 tff(3487,plain,
% 0.89/1.06 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s38, s39)) | node7(s38, s39)),
% 0.89/1.06 inference(modus_ponens,[status(thm)],[3486, 3485])).
% 0.89/1.06 tff(3488,plain,
% 0.89/1.06 (node7(s38, s39)),
% 0.89/1.06 inference(unit_resolution,[status(thm)],[3487, 206, 3484])).
% 0.89/1.06 tff(3489,plain,
% 0.89/1.06 (((~![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(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)))),
% 0.89/1.06 inference(rewrite,[status(thm)],[])).
% 0.89/1.06 tff(3490,plain,
% 0.89/1.06 (((~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)))),
% 0.89/1.06 inference(rewrite,[status(thm)],[])).
% 0.89/1.06 tff(3491,plain,
% 0.89/1.06 (((~![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(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))))),
% 0.89/1.06 inference(monotonicity,[status(thm)],[3490])).
% 0.89/1.06 tff(3492,plain,
% 0.89/1.06 (((~![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(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)))),
% 0.89/1.06 inference(transitivity,[status(thm)],[3491, 3489])).
% 0.89/1.06 tff(3493,plain,
% 0.89/1.06 ((~![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(s38, c_c1)) | node1(s38) | node2(s38) | node3(s38) | node4(s38) | node5(s38) | (~node7(s38, s39)) | m_main_v_state1(s39, c_n1))),
% 0.89/1.06 inference(quant_inst,[status(thm)],[])).
% 0.89/1.06 tff(3494,plain,
% 0.89/1.06 ((~![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(s39, c_n1) | (~m_main_v_state1(s38, c_c1)) | node1(s38) | node2(s38) | node3(s38) | node4(s38) | node5(s38) | (~node7(s38, s39))),
% 0.89/1.06 inference(modus_ponens,[status(thm)],[3493, 3492])).
% 0.89/1.06 tff(3495,plain,
% 0.89/1.06 (m_main_v_state1(s39, c_n1) | (~m_main_v_state1(s38, c_c1)) | node1(s38) | node2(s38) | node3(s38) | node4(s38) | node5(s38)),
% 0.89/1.06 inference(unit_resolution,[status(thm)],[3494, 584, 3488])).
% 0.89/1.06 tff(3496,plain,
% 0.89/1.06 (m_main_v_state1(s39, c_n1)),
% 0.89/1.06 inference(unit_resolution,[status(thm)],[3495, 3477, 3432, 3469, 3465, 3457, 3440])).
% 0.89/1.06 tff(3497,plain,
% 0.89/1.06 (((~![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)))),
% 0.89/1.06 inference(rewrite,[status(thm)],[])).
% 0.89/1.06 tff(3498,plain,
% 0.89/1.06 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s37, c_t2) | (~node15(s37)))),
% 0.89/1.06 inference(quant_inst,[status(thm)],[])).
% 0.89/1.06 tff(3499,plain,
% 0.89/1.06 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s37, c_t2) | (~node15(s37))),
% 0.89/1.06 inference(modus_ponens,[status(thm)],[3498, 3497])).
% 0.89/1.06 tff(3500,plain,
% 0.89/1.06 (~node15(s37)),
% 0.89/1.06 inference(unit_resolution,[status(thm)],[3499, 103, 3409])).
% 0.89/1.06 tff(3501,plain,
% 0.89/1.06 (((~![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))),
% 0.89/1.06 inference(rewrite,[status(thm)],[])).
% 0.89/1.06 tff(3502,plain,
% 0.89/1.06 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s37, s38)) | node18(s37, s38))),
% 0.89/1.07 inference(quant_inst,[status(thm)],[])).
% 0.89/1.07 tff(3503,plain,
% 0.89/1.07 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s37, s38)) | node18(s37, s38)),
% 0.89/1.07 inference(modus_ponens,[status(thm)],[3502, 3501])).
% 0.89/1.07 tff(3504,plain,
% 0.89/1.07 (node18(s37, s38)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3503, 125, 3420])).
% 0.89/1.07 tff(3505,plain,
% 0.89/1.07 (((~![Y: $i, X: $i] : ((~m_main_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))),
% 0.89/1.07 inference(rewrite,[status(thm)],[])).
% 0.89/1.07 tff(3506,plain,
% 0.89/1.07 (((~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))),
% 0.89/1.07 inference(rewrite,[status(thm)],[])).
% 0.89/1.07 tff(3507,plain,
% 0.89/1.07 (((~![Y: $i, X: $i] : ((~m_main_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)))),
% 0.89/1.07 inference(monotonicity,[status(thm)],[3506])).
% 0.89/1.07 tff(3508,plain,
% 0.89/1.07 (((~![Y: $i, X: $i] : ((~m_main_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))),
% 0.89/1.07 inference(transitivity,[status(thm)],[3507, 3505])).
% 0.89/1.07 tff(3509,plain,
% 0.89/1.07 ((~![Y: $i, X: $i] : ((~m_main_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))),
% 0.89/1.07 inference(quant_inst,[status(thm)],[])).
% 0.89/1.07 tff(3510,plain,
% 0.89/1.07 ((~![Y: $i, X: $i] : ((~m_main_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)),
% 0.89/1.07 inference(modus_ponens,[status(thm)],[3509, 3508])).
% 0.89/1.07 tff(3511,plain,
% 0.89/1.07 (node15(s37) | (~m_main_v_state1(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | m_main_v_turn(s38, c_1)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3510, 992, 3504])).
% 0.89/1.07 tff(3512,plain,
% 0.89/1.07 (m_main_v_turn(s38, c_1)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3511, 3500, 3337, 3405])).
% 0.89/1.07 tff(3513,plain,
% 0.89/1.07 (((~![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)))),
% 0.89/1.07 inference(rewrite,[status(thm)],[])).
% 0.89/1.07 tff(3514,plain,
% 0.89/1.07 ((~![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)))),
% 0.89/1.07 inference(quant_inst,[status(thm)],[])).
% 0.89/1.07 tff(3515,plain,
% 0.89/1.07 ((~![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))),
% 0.89/1.07 inference(modus_ponens,[status(thm)],[3514, 3513])).
% 0.89/1.07 tff(3516,plain,
% 0.89/1.07 (~m_main_v_turn(s38, c_2)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3515, 156, 3512])).
% 0.89/1.07 tff(3517,plain,
% 0.89/1.07 (((~![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)))),
% 0.89/1.07 inference(rewrite,[status(thm)],[])).
% 0.89/1.07 tff(3518,plain,
% 0.89/1.07 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s38, c_2) | (~node12(s38)))),
% 0.89/1.07 inference(quant_inst,[status(thm)],[])).
% 0.89/1.07 tff(3519,plain,
% 0.89/1.07 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s38, c_2) | (~node12(s38))),
% 0.89/1.07 inference(modus_ponens,[status(thm)],[3518, 3517])).
% 0.89/1.07 tff(3520,plain,
% 0.89/1.07 (~node12(s38)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3519, 184, 3516])).
% 0.89/1.07 tff(3521,plain,
% 0.89/1.07 (((~![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)))),
% 0.89/1.07 inference(rewrite,[status(thm)],[])).
% 0.89/1.07 tff(3522,plain,
% 0.89/1.07 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s38, c_n2) | (~node8(s38)))),
% 0.89/1.07 inference(quant_inst,[status(thm)],[])).
% 0.89/1.07 tff(3523,plain,
% 0.89/1.07 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s38, c_n2) | (~node8(s38))),
% 0.89/1.07 inference(modus_ponens,[status(thm)],[3522, 3521])).
% 0.89/1.07 tff(3524,plain,
% 0.89/1.07 (~node8(s38)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3523, 271, 3453])).
% 0.89/1.07 tff(3525,plain,
% 0.89/1.07 (((~![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)))),
% 0.89/1.07 inference(rewrite,[status(thm)],[])).
% 0.89/1.07 tff(3526,plain,
% 0.89/1.07 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s38, c_n2) | (~node9(s38)))),
% 0.89/1.07 inference(quant_inst,[status(thm)],[])).
% 0.89/1.07 tff(3527,plain,
% 0.89/1.07 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s38, c_n2) | (~node9(s38))),
% 0.89/1.07 inference(modus_ponens,[status(thm)],[3526, 3525])).
% 0.89/1.07 tff(3528,plain,
% 0.89/1.07 (~node9(s38)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3527, 88, 3453])).
% 0.89/1.07 tff(3529,plain,
% 0.89/1.07 (((~![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)))),
% 0.89/1.07 inference(rewrite,[status(thm)],[])).
% 0.89/1.07 tff(3530,plain,
% 0.89/1.07 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s38, c_n2) | (~node10(s38)))),
% 0.89/1.07 inference(quant_inst,[status(thm)],[])).
% 0.89/1.07 tff(3531,plain,
% 0.89/1.07 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s38, c_n2) | (~node10(s38))),
% 0.89/1.07 inference(modus_ponens,[status(thm)],[3530, 3529])).
% 0.89/1.07 tff(3532,plain,
% 0.89/1.07 (~node10(s38)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3531, 249, 3453])).
% 0.89/1.07 tff(3533,plain,
% 0.89/1.07 (((~![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)))),
% 0.89/1.07 inference(rewrite,[status(thm)],[])).
% 0.89/1.07 tff(3534,plain,
% 0.89/1.07 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s38, c_n1) | (~node11(s38)))),
% 0.89/1.07 inference(quant_inst,[status(thm)],[])).
% 0.89/1.07 tff(3535,plain,
% 0.89/1.07 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s38, c_n1) | (~node11(s38))),
% 0.89/1.07 inference(modus_ponens,[status(thm)],[3534, 3533])).
% 0.89/1.07 tff(3536,plain,
% 0.89/1.07 (~node11(s38)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3535, 238, 3473])).
% 0.89/1.07 tff(3537,plain,
% 0.89/1.07 (((~![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))),
% 0.89/1.07 inference(rewrite,[status(thm)],[])).
% 0.89/1.07 tff(3538,plain,
% 0.89/1.07 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s38, s39)) | node14(s38, s39))),
% 0.89/1.07 inference(quant_inst,[status(thm)],[])).
% 0.89/1.07 tff(3539,plain,
% 0.89/1.07 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s38, s39)) | node14(s38, s39)),
% 0.89/1.07 inference(modus_ponens,[status(thm)],[3538, 3537])).
% 0.89/1.07 tff(3540,plain,
% 0.89/1.07 (node14(s38, s39)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3539, 46, 3484])).
% 0.89/1.07 tff(3541,plain,
% 0.89/1.07 (((~![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)))),
% 0.89/1.07 inference(rewrite,[status(thm)],[])).
% 0.89/1.07 tff(3542,plain,
% 0.89/1.07 ((~![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)))),
% 0.89/1.07 inference(quant_inst,[status(thm)],[])).
% 0.89/1.07 tff(3543,plain,
% 0.89/1.07 ((~![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))),
% 0.89/1.07 inference(modus_ponens,[status(thm)],[3542, 3541])).
% 0.89/1.07 tff(3544,plain,
% 0.89/1.07 (m_main_v_state2(s38, c_c2) | node9(s38) | node8(s38) | node10(s38) | node11(s38) | node12(s38) | node13(s38, s39)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3543, 296, 3540])).
% 0.89/1.07 tff(3545,plain,
% 0.89/1.07 (node13(s38, s39)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3544, 3536, 3461, 3532, 3528, 3524, 3520])).
% 0.89/1.07 tff(3546,plain,
% 0.89/1.07 (((~![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(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)))),
% 0.89/1.07 inference(rewrite,[status(thm)],[])).
% 0.89/1.07 tff(3547,plain,
% 0.89/1.07 (((~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)))),
% 0.89/1.07 inference(rewrite,[status(thm)],[])).
% 0.89/1.07 tff(3548,plain,
% 0.89/1.07 (((~![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))))),
% 0.89/1.07 inference(monotonicity,[status(thm)],[3547])).
% 0.89/1.07 tff(3549,plain,
% 0.89/1.07 (((~![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)))),
% 0.89/1.07 inference(transitivity,[status(thm)],[3548, 3546])).
% 0.89/1.07 tff(3550,plain,
% 0.89/1.07 ((~![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))),
% 0.89/1.07 inference(quant_inst,[status(thm)],[])).
% 0.89/1.07 tff(3551,plain,
% 0.89/1.07 ((~![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(s38, c_t2)) | m_main_v_state2(s39, c_t2) | (~node13(s38, s39))),
% 0.89/1.07 inference(modus_ponens,[status(thm)],[3550, 3549])).
% 0.89/1.07 tff(3552,plain,
% 0.89/1.07 (m_main_v_state2(s39, c_t2)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3551, 518, 3449, 3545])).
% 0.89/1.07 tff(3553,plain,
% 0.89/1.07 (succ(s39, s40) <=> succ(s39, s40)),
% 0.89/1.07 inference(rewrite,[status(thm)],[])).
% 0.89/1.07 tff(3554,axiom,(succ(s39, s40)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound40')).
% 0.89/1.07 tff(3555,plain,
% 0.89/1.07 (succ(s39, s40)),
% 0.89/1.07 inference(modus_ponens,[status(thm)],[3554, 3553])).
% 0.89/1.07 tff(3556,plain,
% 0.89/1.07 (((~![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))),
% 0.89/1.07 inference(rewrite,[status(thm)],[])).
% 0.89/1.07 tff(3557,plain,
% 0.89/1.07 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s39, s40)) | trans(s39, s40))),
% 0.89/1.07 inference(quant_inst,[status(thm)],[])).
% 0.89/1.07 tff(3558,plain,
% 0.89/1.07 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s39, s40)) | trans(s39, s40)),
% 0.89/1.07 inference(modus_ponens,[status(thm)],[3557, 3556])).
% 0.89/1.07 tff(3559,plain,
% 0.89/1.07 (trans(s39, s40)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3558, 3555, 32])).
% 0.89/1.07 tff(3560,plain,
% 0.89/1.07 (((~![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))),
% 0.89/1.07 inference(rewrite,[status(thm)],[])).
% 0.89/1.07 tff(3561,plain,
% 0.89/1.07 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s39, s40)) | node7(s39, s40))),
% 0.89/1.07 inference(quant_inst,[status(thm)],[])).
% 0.89/1.07 tff(3562,plain,
% 0.89/1.07 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s39, s40)) | node7(s39, s40)),
% 0.89/1.07 inference(modus_ponens,[status(thm)],[3561, 3560])).
% 0.89/1.07 tff(3563,plain,
% 0.89/1.07 (node7(s39, s40)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3562, 206, 3559])).
% 0.89/1.07 tff(3564,plain,
% 0.89/1.07 (((~![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(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))),
% 0.89/1.07 inference(rewrite,[status(thm)],[])).
% 0.89/1.07 tff(3565,plain,
% 0.89/1.07 ((~![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(s39, c_n1)) | (~m_main_v_state2(s39, c_t2)) | (~node7(s39, s40)) | m_main_v_state1(s40, c_t1))),
% 0.89/1.07 inference(quant_inst,[status(thm)],[])).
% 0.89/1.07 tff(3566,plain,
% 0.89/1.07 ((~![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(s39, c_n1)) | (~m_main_v_state2(s39, c_t2)) | (~node7(s39, s40)) | m_main_v_state1(s40, c_t1)),
% 0.89/1.07 inference(modus_ponens,[status(thm)],[3565, 3564])).
% 0.89/1.07 tff(3567,plain,
% 0.89/1.07 ((~m_main_v_state1(s39, c_n1)) | (~m_main_v_state2(s39, c_t2)) | m_main_v_state1(s40, c_t1)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3566, 651, 3563])).
% 0.89/1.07 tff(3568,plain,
% 0.89/1.07 (m_main_v_state1(s40, c_t1)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3567, 3552, 3496])).
% 0.89/1.07 tff(3569,plain,
% 0.89/1.07 (((~![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)))),
% 0.89/1.07 inference(rewrite,[status(thm)],[])).
% 0.89/1.07 tff(3570,plain,
% 0.89/1.07 ((~![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)))),
% 0.89/1.07 inference(quant_inst,[status(thm)],[])).
% 0.89/1.07 tff(3571,plain,
% 0.89/1.07 ((~![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))),
% 0.89/1.07 inference(modus_ponens,[status(thm)],[3570, 3569])).
% 0.89/1.07 tff(3572,plain,
% 0.89/1.07 (~m_main_v_state1(s40, c_n1)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3571, 10, 3568])).
% 0.89/1.07 tff(3573,plain,
% 0.89/1.07 (((~![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)))),
% 0.89/1.07 inference(rewrite,[status(thm)],[])).
% 0.89/1.07 tff(3574,plain,
% 0.89/1.07 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s40, c_n1) | (~node1(s40)))),
% 0.89/1.07 inference(quant_inst,[status(thm)],[])).
% 0.89/1.07 tff(3575,plain,
% 0.89/1.07 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s40, c_n1) | (~node1(s40))),
% 0.89/1.07 inference(modus_ponens,[status(thm)],[3574, 3573])).
% 0.89/1.07 tff(3576,plain,
% 0.89/1.07 (~node1(s40)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3575, 421, 3572])).
% 0.89/1.07 tff(3577,plain,
% 0.89/1.07 (((~![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))),
% 0.89/1.07 inference(rewrite,[status(thm)],[])).
% 0.89/1.07 tff(3578,plain,
% 0.89/1.07 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s39, s40)) | node18(s39, s40))),
% 0.89/1.07 inference(quant_inst,[status(thm)],[])).
% 0.89/1.07 tff(3579,plain,
% 0.89/1.07 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s39, s40)) | node18(s39, s40)),
% 0.89/1.07 inference(modus_ponens,[status(thm)],[3578, 3577])).
% 0.89/1.07 tff(3580,plain,
% 0.89/1.07 (node18(s39, s40)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3579, 125, 3559])).
% 0.89/1.07 tff(3581,plain,
% 0.89/1.07 (((~![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(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))),
% 0.89/1.07 inference(rewrite,[status(thm)],[])).
% 0.89/1.07 tff(3582,plain,
% 0.89/1.07 ((~![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(s39, c_n1)) | (~m_main_v_state2(s39, c_t2)) | (~node18(s39, s40)) | m_main_v_turn(s40, c_2))),
% 0.89/1.07 inference(quant_inst,[status(thm)],[])).
% 0.89/1.07 tff(3583,plain,
% 0.89/1.07 ((~![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(s39, c_n1)) | (~m_main_v_state2(s39, c_t2)) | (~node18(s39, s40)) | m_main_v_turn(s40, c_2)),
% 0.89/1.07 inference(modus_ponens,[status(thm)],[3582, 3581])).
% 0.89/1.07 tff(3584,plain,
% 0.89/1.07 ((~m_main_v_state1(s39, c_n1)) | (~m_main_v_state2(s39, c_t2)) | m_main_v_turn(s40, c_2)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3583, 760, 3580])).
% 0.89/1.07 tff(3585,plain,
% 0.89/1.07 (m_main_v_turn(s40, c_2)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3584, 3552, 3496])).
% 0.89/1.07 tff(3586,plain,
% 0.89/1.07 (((~![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)))),
% 0.89/1.07 inference(rewrite,[status(thm)],[])).
% 0.89/1.07 tff(3587,plain,
% 0.89/1.07 ((~![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)))),
% 0.89/1.07 inference(quant_inst,[status(thm)],[])).
% 0.89/1.07 tff(3588,plain,
% 0.89/1.07 ((~![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))),
% 0.89/1.07 inference(modus_ponens,[status(thm)],[3587, 3586])).
% 0.89/1.07 tff(3589,plain,
% 0.89/1.07 (~m_main_v_turn(s40, c_1)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3588, 156, 3585])).
% 0.89/1.07 tff(3590,plain,
% 0.89/1.07 (((~![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)))),
% 0.89/1.07 inference(rewrite,[status(thm)],[])).
% 0.89/1.07 tff(3591,plain,
% 0.89/1.07 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s40, c_1) | (~node5(s40)))),
% 0.89/1.07 inference(quant_inst,[status(thm)],[])).
% 0.89/1.07 tff(3592,plain,
% 0.89/1.07 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s40, c_1) | (~node5(s40))),
% 0.89/1.07 inference(modus_ponens,[status(thm)],[3591, 3590])).
% 0.89/1.07 tff(3593,plain,
% 0.89/1.07 (~node5(s40)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3592, 776, 3589])).
% 0.89/1.07 tff(3594,plain,
% 0.89/1.07 (((~![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)))),
% 0.89/1.07 inference(rewrite,[status(thm)],[])).
% 0.89/1.07 tff(3595,plain,
% 0.89/1.07 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s40, c_n1) | (~node2(s40)))),
% 0.89/1.07 inference(quant_inst,[status(thm)],[])).
% 0.89/1.07 tff(3596,plain,
% 0.89/1.07 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s40, c_n1) | (~node2(s40))),
% 0.89/1.07 inference(modus_ponens,[status(thm)],[3595, 3594])).
% 0.89/1.07 tff(3597,plain,
% 0.89/1.07 (~node2(s40)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3596, 787, 3572])).
% 0.89/1.07 tff(3598,plain,
% 0.89/1.07 (((~![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)))),
% 0.89/1.07 inference(rewrite,[status(thm)],[])).
% 0.89/1.07 tff(3599,plain,
% 0.89/1.07 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s40, c_n1) | (~node3(s40)))),
% 0.89/1.07 inference(quant_inst,[status(thm)],[])).
% 0.89/1.07 tff(3600,plain,
% 0.89/1.07 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s40, c_n1) | (~node3(s40))),
% 0.89/1.07 inference(modus_ponens,[status(thm)],[3599, 3598])).
% 0.89/1.07 tff(3601,plain,
% 0.89/1.07 (~node3(s40)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3600, 798, 3572])).
% 0.89/1.07 tff(3602,plain,
% 0.89/1.07 (((~![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)))),
% 0.89/1.07 inference(rewrite,[status(thm)],[])).
% 0.89/1.07 tff(3603,plain,
% 0.89/1.07 ((~![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)))),
% 0.89/1.07 inference(quant_inst,[status(thm)],[])).
% 0.89/1.07 tff(3604,plain,
% 0.89/1.07 ((~![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))),
% 0.89/1.07 inference(modus_ponens,[status(thm)],[3603, 3602])).
% 0.89/1.07 tff(3605,plain,
% 0.89/1.07 (~m_main_v_state1(s40, c_c1)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3604, 539, 3568])).
% 0.89/1.07 tff(3606,plain,
% 0.89/1.07 (((~![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(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)))),
% 0.89/1.07 inference(rewrite,[status(thm)],[])).
% 0.89/1.07 tff(3607,plain,
% 0.89/1.07 (((~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)))),
% 0.89/1.07 inference(rewrite,[status(thm)],[])).
% 0.89/1.07 tff(3608,plain,
% 0.89/1.07 (((~![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))))),
% 0.89/1.07 inference(monotonicity,[status(thm)],[3607])).
% 0.89/1.07 tff(3609,plain,
% 0.89/1.07 (((~![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)))),
% 0.89/1.07 inference(transitivity,[status(thm)],[3608, 3606])).
% 0.89/1.07 tff(3610,plain,
% 0.89/1.07 ((~![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)))),
% 0.89/1.07 inference(quant_inst,[status(thm)],[])).
% 0.89/1.07 tff(3611,plain,
% 0.89/1.07 ((~![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(s38, c_n2) | (~m_main_v_state2(s39, c_n2)) | (~node13(s38, s39))),
% 0.89/1.07 inference(modus_ponens,[status(thm)],[3610, 3609])).
% 0.89/1.07 tff(3612,plain,
% 0.89/1.07 (~m_main_v_state2(s39, c_n2)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3611, 311, 3453, 3545])).
% 0.89/1.07 tff(3613,plain,
% 0.89/1.07 (((~![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)))),
% 0.89/1.07 inference(rewrite,[status(thm)],[])).
% 0.89/1.07 tff(3614,plain,
% 0.89/1.07 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s39, c_n2) | (~node9(s39)))),
% 0.89/1.07 inference(quant_inst,[status(thm)],[])).
% 0.89/1.07 tff(3615,plain,
% 0.89/1.07 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s39, c_n2) | (~node9(s39))),
% 0.89/1.07 inference(modus_ponens,[status(thm)],[3614, 3613])).
% 0.89/1.07 tff(3616,plain,
% 0.89/1.07 (~node9(s39)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3615, 88, 3612])).
% 0.89/1.07 tff(3617,plain,
% 0.89/1.07 (((~![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)))),
% 0.89/1.07 inference(rewrite,[status(thm)],[])).
% 0.89/1.07 tff(3618,plain,
% 0.89/1.07 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s39, c_n2) | (~node10(s39)))),
% 0.89/1.07 inference(quant_inst,[status(thm)],[])).
% 0.89/1.07 tff(3619,plain,
% 0.89/1.07 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s39, c_n2) | (~node10(s39))),
% 0.89/1.07 inference(modus_ponens,[status(thm)],[3618, 3617])).
% 0.89/1.07 tff(3620,plain,
% 0.89/1.07 (~node10(s39)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3619, 249, 3612])).
% 0.89/1.07 tff(3621,plain,
% 0.89/1.07 (((~![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)))),
% 0.89/1.07 inference(rewrite,[status(thm)],[])).
% 0.89/1.07 tff(3622,plain,
% 0.89/1.07 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s39, c_n2) | (~node8(s39)))),
% 0.89/1.07 inference(quant_inst,[status(thm)],[])).
% 0.89/1.07 tff(3623,plain,
% 0.89/1.07 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s39, c_n2) | (~node8(s39))),
% 0.89/1.07 inference(modus_ponens,[status(thm)],[3622, 3621])).
% 0.89/1.07 tff(3624,plain,
% 0.89/1.07 (~node8(s39)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3623, 271, 3612])).
% 0.89/1.07 tff(3625,plain,
% 0.89/1.07 (((~![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))),
% 0.89/1.07 inference(rewrite,[status(thm)],[])).
% 0.89/1.07 tff(3626,plain,
% 0.89/1.07 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s39, s40)) | node14(s39, s40))),
% 0.89/1.07 inference(quant_inst,[status(thm)],[])).
% 0.89/1.07 tff(3627,plain,
% 0.89/1.07 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s39, s40)) | node14(s39, s40)),
% 0.89/1.07 inference(modus_ponens,[status(thm)],[3626, 3625])).
% 0.89/1.07 tff(3628,plain,
% 0.89/1.07 (node14(s39, s40)),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[3627, 46, 3559])).
% 0.89/1.07 tff(3629,plain,
% 0.89/1.07 (((~![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(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))),
% 0.91/1.07 inference(rewrite,[status(thm)],[])).
% 0.91/1.07 tff(3630,plain,
% 0.91/1.07 ((~![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(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))),
% 0.91/1.07 inference(quant_inst,[status(thm)],[])).
% 0.91/1.07 tff(3631,plain,
% 0.91/1.07 ((~![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(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)),
% 0.91/1.07 inference(modus_ponens,[status(thm)],[3630, 3629])).
% 0.91/1.07 tff(3632,plain,
% 0.91/1.07 ((~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)),
% 0.91/1.07 inference(unit_resolution,[status(thm)],[3631, 617, 3628])).
% 0.91/1.07 tff(3633,plain,
% 0.91/1.07 (m_main_v_state2(s40, c_c2)),
% 0.91/1.07 inference(unit_resolution,[status(thm)],[3632, 3624, 3496, 3552, 3620, 3616])).
% 0.91/1.07 tff(3634,plain,
% 0.91/1.07 (((~![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)))),
% 0.91/1.07 inference(rewrite,[status(thm)],[])).
% 0.91/1.07 tff(3635,plain,
% 0.91/1.07 ((~![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)))),
% 0.91/1.07 inference(quant_inst,[status(thm)],[])).
% 0.91/1.07 tff(3636,plain,
% 0.91/1.07 ((~![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))),
% 0.91/1.07 inference(modus_ponens,[status(thm)],[3635, 3634])).
% 0.91/1.07 tff(3637,plain,
% 0.91/1.07 (~m_main_v_state2(s40, c_n2)),
% 0.91/1.07 inference(unit_resolution,[status(thm)],[3636, 697, 3633])).
% 0.91/1.07 tff(3638,plain,
% 0.91/1.07 (((~![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)))),
% 0.91/1.07 inference(rewrite,[status(thm)],[])).
% 0.91/1.07 tff(3639,plain,
% 0.91/1.07 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s40, c_n2) | (~node4(s40)))),
% 0.91/1.07 inference(quant_inst,[status(thm)],[])).
% 0.91/1.07 tff(3640,plain,
% 0.91/1.07 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s40, c_n2) | (~node4(s40))),
% 0.91/1.07 inference(modus_ponens,[status(thm)],[3639, 3638])).
% 0.91/1.07 tff(3641,plain,
% 0.91/1.07 (~node4(s40)),
% 0.91/1.07 inference(unit_resolution,[status(thm)],[3640, 388, 3637])).
% 0.91/1.07 tff(3642,plain,
% 0.91/1.07 (succ(s40, s41) <=> succ(s40, s41)),
% 0.91/1.07 inference(rewrite,[status(thm)],[])).
% 0.91/1.07 tff(3643,axiom,(succ(s40, s41)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound41')).
% 0.91/1.07 tff(3644,plain,
% 0.91/1.07 (succ(s40, s41)),
% 0.91/1.07 inference(modus_ponens,[status(thm)],[3643, 3642])).
% 0.91/1.07 tff(3645,plain,
% 0.91/1.07 (((~![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))),
% 0.91/1.07 inference(rewrite,[status(thm)],[])).
% 0.91/1.07 tff(3646,plain,
% 0.91/1.07 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s40, s41)) | trans(s40, s41))),
% 0.91/1.07 inference(quant_inst,[status(thm)],[])).
% 0.91/1.07 tff(3647,plain,
% 0.91/1.07 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s40, s41)) | trans(s40, s41)),
% 0.91/1.07 inference(modus_ponens,[status(thm)],[3646, 3645])).
% 0.91/1.07 tff(3648,plain,
% 0.91/1.07 (trans(s40, s41)),
% 0.91/1.07 inference(unit_resolution,[status(thm)],[3647, 3644, 32])).
% 0.91/1.08 tff(3649,plain,
% 0.91/1.08 (((~![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))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3650,plain,
% 0.91/1.08 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s40, s41)) | node7(s40, s41))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3651,plain,
% 0.91/1.08 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s40, s41)) | node7(s40, s41)),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3650, 3649])).
% 0.91/1.08 tff(3652,plain,
% 0.91/1.08 (node7(s40, s41)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3651, 206, 3648])).
% 0.91/1.08 tff(3653,plain,
% 0.91/1.08 (((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(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)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3654,plain,
% 0.91/1.08 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s40, c_c1) | node1(s40) | node2(s40) | node3(s40) | node4(s40) | node5(s40) | node6(s40, s41) | (~node7(s40, s41)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3655,plain,
% 0.91/1.08 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s40, c_c1) | node1(s40) | node2(s40) | node3(s40) | node4(s40) | node5(s40) | node6(s40, s41) | (~node7(s40, s41))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3654, 3653])).
% 0.91/1.08 tff(3656,plain,
% 0.91/1.08 (m_main_v_state1(s40, c_c1) | node1(s40) | node2(s40) | node3(s40) | node4(s40) | node5(s40) | node6(s40, s41)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3655, 820, 3652])).
% 0.91/1.08 tff(3657,plain,
% 0.91/1.08 (node6(s40, s41)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3656, 3641, 3605, 3601, 3597, 3593, 3576])).
% 0.91/1.08 tff(3658,plain,
% 0.91/1.08 (((~![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(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)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3659,plain,
% 0.91/1.08 (((~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)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3660,plain,
% 0.91/1.08 (((~![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))))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[3659])).
% 0.91/1.08 tff(3661,plain,
% 0.91/1.08 (((~![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)))),
% 0.91/1.08 inference(transitivity,[status(thm)],[3660, 3658])).
% 0.91/1.08 tff(3662,plain,
% 0.91/1.08 ((~![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))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3663,plain,
% 0.91/1.08 ((~![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(s40, c_t1)) | m_main_v_state1(s41, c_t1) | (~node6(s40, s41))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3662, 3661])).
% 0.91/1.08 tff(3664,plain,
% 0.91/1.08 (m_main_v_state1(s41, c_t1)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3663, 856, 3568, 3657])).
% 0.91/1.08 tff(3665,plain,
% 0.91/1.08 (((~![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)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3666,plain,
% 0.91/1.08 ((~![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)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3667,plain,
% 0.91/1.08 ((~![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))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3666, 3665])).
% 0.91/1.08 tff(3668,plain,
% 0.91/1.08 (~m_main_v_state2(s40, c_t2)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3667, 260, 3633])).
% 0.91/1.08 tff(3669,plain,
% 0.91/1.08 (((~![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)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3670,plain,
% 0.91/1.08 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s40, c_t2) | (~node12(s40)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3671,plain,
% 0.91/1.08 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s40, c_t2) | (~node12(s40))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3670, 3669])).
% 0.91/1.08 tff(3672,plain,
% 0.91/1.08 (~node12(s40)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3671, 633, 3668])).
% 0.91/1.08 tff(3673,plain,
% 0.91/1.08 (((~![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)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3674,plain,
% 0.91/1.08 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s40, c_n1) | (~node11(s40)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3675,plain,
% 0.91/1.08 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s40, c_n1) | (~node11(s40))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3674, 3673])).
% 0.91/1.08 tff(3676,plain,
% 0.91/1.08 (~node11(s40)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3675, 238, 3572])).
% 0.91/1.08 tff(3677,plain,
% 0.91/1.08 (((~![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)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3678,plain,
% 0.91/1.08 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s40, c_c1) | (~node10(s40)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3679,plain,
% 0.91/1.08 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s40, c_c1) | (~node10(s40))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3678, 3677])).
% 0.91/1.08 tff(3680,plain,
% 0.91/1.08 (~node10(s40)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3679, 675, 3605])).
% 0.91/1.08 tff(3681,plain,
% 0.91/1.08 (((~![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)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3682,plain,
% 0.91/1.08 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s40, c_n1) | (~node9(s40)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3683,plain,
% 0.91/1.08 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s40, c_n1) | (~node9(s40))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3682, 3681])).
% 0.91/1.08 tff(3684,plain,
% 0.91/1.08 (~node9(s40)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3683, 686, 3572])).
% 0.91/1.08 tff(3685,plain,
% 0.91/1.08 (((~![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)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3686,plain,
% 0.91/1.08 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s40, c_n2) | (~node8(s40)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3687,plain,
% 0.91/1.08 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s40, c_n2) | (~node8(s40))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3686, 3685])).
% 0.91/1.08 tff(3688,plain,
% 0.91/1.08 (~node8(s40)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3687, 271, 3637])).
% 0.91/1.08 tff(3689,plain,
% 0.91/1.08 (((~![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))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3690,plain,
% 0.91/1.08 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s40, s41)) | node14(s40, s41))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3691,plain,
% 0.91/1.08 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s40, s41)) | node14(s40, s41)),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3690, 3689])).
% 0.91/1.08 tff(3692,plain,
% 0.91/1.08 (node14(s40, s41)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3691, 46, 3648])).
% 0.91/1.08 tff(3693,plain,
% 0.91/1.08 (((~![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(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)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3694,plain,
% 0.91/1.08 (((~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)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3695,plain,
% 0.91/1.08 (((~![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(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))))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[3694])).
% 0.91/1.08 tff(3696,plain,
% 0.91/1.08 (((~![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(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)))),
% 0.91/1.08 inference(transitivity,[status(thm)],[3695, 3693])).
% 0.91/1.08 tff(3697,plain,
% 0.91/1.08 ((~![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(s40, c_c2)) | node9(s40) | node8(s40) | node10(s40) | node11(s40) | node12(s40) | (~node14(s40, s41)) | m_main_v_state2(s41, c_n2))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3698,plain,
% 0.91/1.08 ((~![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(s41, c_n2) | node9(s40) | node8(s40) | node10(s40) | node11(s40) | node12(s40) | (~node14(s40, s41)) | (~m_main_v_state2(s40, c_c2))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3697, 3696])).
% 0.91/1.08 tff(3699,plain,
% 0.91/1.08 (m_main_v_state2(s41, c_n2) | node9(s40) | node8(s40) | node10(s40) | node11(s40) | node12(s40) | (~m_main_v_state2(s40, c_c2))),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3698, 726, 3692])).
% 0.91/1.08 tff(3700,plain,
% 0.91/1.08 (m_main_v_state2(s41, c_n2)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3699, 3688, 3633, 3684, 3680, 3676, 3672])).
% 0.91/1.08 tff(3701,plain,
% 0.91/1.08 (((~![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)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3702,plain,
% 0.91/1.08 ((~![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)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3703,plain,
% 0.91/1.08 ((~![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))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3702, 3701])).
% 0.91/1.08 tff(3704,plain,
% 0.91/1.08 (~m_main_v_state2(s41, c_t2)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3703, 77, 3700])).
% 0.91/1.08 tff(3705,plain,
% 0.91/1.08 (((~![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)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3706,plain,
% 0.91/1.08 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s41, c_t2) | (~node15(s41)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3707,plain,
% 0.91/1.08 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s41, c_t2) | (~node15(s41))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3706, 3705])).
% 0.91/1.08 tff(3708,plain,
% 0.91/1.08 (~node15(s41)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3707, 103, 3704])).
% 0.91/1.08 tff(3709,plain,
% 0.91/1.08 (succ(s41, s42) <=> succ(s41, s42)),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3710,axiom,(succ(s41, s42)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound42')).
% 0.91/1.08 tff(3711,plain,
% 0.91/1.08 (succ(s41, s42)),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3710, 3709])).
% 0.91/1.08 tff(3712,plain,
% 0.91/1.08 (((~![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))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3713,plain,
% 0.91/1.08 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s41, s42)) | trans(s41, s42))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3714,plain,
% 0.91/1.08 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s41, s42)) | trans(s41, s42)),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3713, 3712])).
% 0.91/1.08 tff(3715,plain,
% 0.91/1.08 (trans(s41, s42)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3714, 3711, 32])).
% 0.91/1.08 tff(3716,plain,
% 0.91/1.08 (((~![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))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3717,plain,
% 0.91/1.08 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s41, s42)) | node18(s41, s42))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3718,plain,
% 0.91/1.08 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s41, s42)) | node18(s41, s42)),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3717, 3716])).
% 0.91/1.08 tff(3719,plain,
% 0.91/1.08 (node18(s41, s42)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3718, 125, 3715])).
% 0.91/1.08 tff(3720,plain,
% 0.91/1.08 (((~![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(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))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3721,plain,
% 0.91/1.08 (((~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))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3722,plain,
% 0.91/1.08 (((~![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(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)))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[3721])).
% 0.91/1.08 tff(3723,plain,
% 0.91/1.08 (((~![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(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))),
% 0.91/1.08 inference(transitivity,[status(thm)],[3722, 3720])).
% 0.91/1.08 tff(3724,plain,
% 0.91/1.08 ((~![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(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | node15(s41) | (~node18(s41, s42)) | m_main_v_turn(s42, c_1))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3725,plain,
% 0.91/1.08 ((~![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(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)),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3724, 3723])).
% 0.91/1.08 tff(3726,plain,
% 0.91/1.08 (node15(s41) | (~m_main_v_state1(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | m_main_v_turn(s42, c_1)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3725, 992, 3719])).
% 0.91/1.08 tff(3727,plain,
% 0.91/1.08 (m_main_v_turn(s42, c_1)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3726, 3708, 3700, 3664])).
% 0.91/1.08 tff(3728,plain,
% 0.91/1.08 (((~![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)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3729,plain,
% 0.91/1.08 ((~![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)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3730,plain,
% 0.91/1.08 ((~![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))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3729, 3728])).
% 0.91/1.08 tff(3731,plain,
% 0.91/1.08 (~m_main_v_turn(s42, c_2)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3730, 156, 3727])).
% 0.91/1.08 tff(3732,plain,
% 0.91/1.08 (((~![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)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3733,plain,
% 0.91/1.08 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s42, c_2) | (~node12(s42)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3734,plain,
% 0.91/1.08 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s42, c_2) | (~node12(s42))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3733, 3732])).
% 0.91/1.08 tff(3735,plain,
% 0.91/1.08 (~node12(s42)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3734, 184, 3731])).
% 0.91/1.08 tff(3736,plain,
% 0.91/1.08 (((~![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))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3737,plain,
% 0.91/1.08 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s41, s42)) | node14(s41, s42))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3738,plain,
% 0.91/1.08 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s41, s42)) | node14(s41, s42)),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3737, 3736])).
% 0.91/1.08 tff(3739,plain,
% 0.91/1.08 (node14(s41, s42)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3738, 46, 3715])).
% 0.91/1.08 tff(3740,plain,
% 0.91/1.08 (((~![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(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))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3741,plain,
% 0.91/1.08 ((~![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(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | (~node14(s41, s42)) | m_main_v_state2(s42, c_t2))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3742,plain,
% 0.91/1.08 ((~![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(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | (~node14(s41, s42)) | m_main_v_state2(s42, c_t2)),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3741, 3740])).
% 0.91/1.08 tff(3743,plain,
% 0.91/1.08 ((~m_main_v_state1(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | m_main_v_state2(s42, c_t2)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3742, 922, 3739])).
% 0.91/1.08 tff(3744,plain,
% 0.91/1.08 (m_main_v_state2(s42, c_t2)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3743, 3664, 3700])).
% 0.91/1.08 tff(3745,plain,
% 0.91/1.08 (((~![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)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3746,plain,
% 0.91/1.08 ((~![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)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3747,plain,
% 0.91/1.08 ((~![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))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3746, 3745])).
% 0.91/1.08 tff(3748,plain,
% 0.91/1.08 (~m_main_v_state2(s42, c_n2)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3747, 77, 3744])).
% 0.91/1.08 tff(3749,plain,
% 0.91/1.08 (((~![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)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3750,plain,
% 0.91/1.08 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s42, c_n2) | (~node8(s42)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3751,plain,
% 0.91/1.08 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s42, c_n2) | (~node8(s42))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3750, 3749])).
% 0.91/1.08 tff(3752,plain,
% 0.91/1.08 (~node8(s42)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3751, 271, 3748])).
% 0.91/1.08 tff(3753,plain,
% 0.91/1.08 (((~![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)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3754,plain,
% 0.91/1.08 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s42, c_n2) | (~node9(s42)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3755,plain,
% 0.91/1.08 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s42, c_n2) | (~node9(s42))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3754, 3753])).
% 0.91/1.08 tff(3756,plain,
% 0.91/1.08 (~node9(s42)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3755, 88, 3748])).
% 0.91/1.08 tff(3757,plain,
% 0.91/1.08 (((~![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)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3758,plain,
% 0.91/1.08 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s42, c_n2) | (~node10(s42)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3759,plain,
% 0.91/1.08 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s42, c_n2) | (~node10(s42))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3758, 3757])).
% 0.91/1.08 tff(3760,plain,
% 0.91/1.08 (~node10(s42)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3759, 249, 3748])).
% 0.91/1.08 tff(3761,plain,
% 0.91/1.08 (((~![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)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3762,plain,
% 0.91/1.08 ((~![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)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3763,plain,
% 0.91/1.08 ((~![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))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3762, 3761])).
% 0.91/1.08 tff(3764,plain,
% 0.91/1.08 (~m_main_v_state2(s42, c_c2)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3763, 260, 3744])).
% 0.91/1.08 tff(3765,plain,
% 0.91/1.08 (((~![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)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3766,plain,
% 0.91/1.08 ((~![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)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(3767,plain,
% 0.91/1.08 ((~![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))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[3766, 3765])).
% 0.91/1.08 tff(3768,plain,
% 0.91/1.08 (~m_main_v_state2(s41, c_c2)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[3767, 697, 3700])).
% 0.91/1.08 tff(3769,plain,
% 0.91/1.08 (((~![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)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(3770,plain,
% 0.91/1.08 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s41, c_c2) | (~node3(s41)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3771,plain,
% 0.91/1.09 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s41, c_c2) | (~node3(s41))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3770, 3769])).
% 0.91/1.09 tff(3772,plain,
% 0.91/1.09 (~node3(s41)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3771, 399, 3768])).
% 0.91/1.09 tff(3773,plain,
% 0.91/1.09 (((~![V: $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)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3774,plain,
% 0.91/1.09 (((~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)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3775,plain,
% 0.91/1.09 (((~![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))))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[3774])).
% 0.91/1.09 tff(3776,plain,
% 0.91/1.09 (((~![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)))),
% 0.91/1.09 inference(transitivity,[status(thm)],[3775, 3773])).
% 0.91/1.09 tff(3777,plain,
% 0.91/1.09 ((~![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)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3778,plain,
% 0.91/1.09 ((~![V: $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))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3777, 3776])).
% 0.91/1.09 tff(3779,plain,
% 0.91/1.09 (~m_main_v_state1(s41, c_n1)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3778, 835, 3572, 3657])).
% 0.91/1.09 tff(3780,plain,
% 0.91/1.09 (((~![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)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3781,plain,
% 0.91/1.09 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s41, c_n1) | (~node2(s41)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3782,plain,
% 0.91/1.09 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s41, c_n1) | (~node2(s41))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3781, 3780])).
% 0.91/1.09 tff(3783,plain,
% 0.91/1.09 (~node2(s41)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3782, 787, 3779])).
% 0.91/1.09 tff(3784,plain,
% 0.91/1.09 (((~![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)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3785,plain,
% 0.91/1.09 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s41, c_t2) | (~node1(s41)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3786,plain,
% 0.91/1.09 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s41, c_t2) | (~node1(s41))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3785, 3784])).
% 0.91/1.09 tff(3787,plain,
% 0.91/1.09 (~node1(s41)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3786, 195, 3704])).
% 0.91/1.09 tff(3788,plain,
% 0.91/1.09 (((~![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))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3789,plain,
% 0.91/1.09 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s41, s42)) | node7(s41, s42))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3790,plain,
% 0.91/1.09 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s41, s42)) | node7(s41, s42)),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3789, 3788])).
% 0.91/1.09 tff(3791,plain,
% 0.91/1.09 (node7(s41, s42)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3790, 206, 3715])).
% 0.91/1.09 tff(3792,plain,
% 0.91/1.09 (((~![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(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)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3793,plain,
% 0.91/1.09 (((~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)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3794,plain,
% 0.91/1.09 (((~![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(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))))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[3793])).
% 0.91/1.09 tff(3795,plain,
% 0.91/1.09 (((~![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(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)))),
% 0.91/1.09 inference(transitivity,[status(thm)],[3794, 3792])).
% 0.91/1.09 tff(3796,plain,
% 0.91/1.09 ((~![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(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))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3797,plain,
% 0.91/1.09 ((~![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(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))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3796, 3795])).
% 0.91/1.09 tff(3798,plain,
% 0.91/1.09 ((~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)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3797, 892, 3791])).
% 0.91/1.09 tff(3799,plain,
% 0.91/1.09 (m_main_v_state1(s42, c_c1)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3798, 3787, 3700, 3664, 3783, 3772])).
% 0.91/1.09 tff(3800,plain,
% 0.91/1.09 (((~![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)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3801,plain,
% 0.91/1.09 ((~![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)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3802,plain,
% 0.91/1.09 ((~![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))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3801, 3800])).
% 0.91/1.09 tff(3803,plain,
% 0.91/1.09 (~m_main_v_state1(s42, c_n1)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3802, 454, 3799])).
% 0.91/1.09 tff(3804,plain,
% 0.91/1.09 (((~![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)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3805,plain,
% 0.91/1.09 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s42, c_n1) | (~node11(s42)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3806,plain,
% 0.91/1.09 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s42, c_n1) | (~node11(s42))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3805, 3804])).
% 0.91/1.09 tff(3807,plain,
% 0.91/1.09 (~node11(s42)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3806, 238, 3803])).
% 0.91/1.09 tff(3808,plain,
% 0.91/1.09 (succ(s42, s43) <=> succ(s42, s43)),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3809,axiom,(succ(s42, s43)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound43')).
% 0.91/1.09 tff(3810,plain,
% 0.91/1.09 (succ(s42, s43)),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3809, 3808])).
% 0.91/1.09 tff(3811,plain,
% 0.91/1.09 (((~![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))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3812,plain,
% 0.91/1.09 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s42, s43)) | trans(s42, s43))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3813,plain,
% 0.91/1.09 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s42, s43)) | trans(s42, s43)),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3812, 3811])).
% 0.91/1.09 tff(3814,plain,
% 0.91/1.09 (trans(s42, s43)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3813, 3810, 32])).
% 0.91/1.09 tff(3815,plain,
% 0.91/1.09 (((~![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))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3816,plain,
% 0.91/1.09 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s42, s43)) | node14(s42, s43))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3817,plain,
% 0.91/1.09 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s42, s43)) | node14(s42, s43)),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3816, 3815])).
% 0.91/1.09 tff(3818,plain,
% 0.91/1.09 (node14(s42, s43)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3817, 46, 3814])).
% 0.91/1.09 tff(3819,plain,
% 0.91/1.09 (((~![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(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)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3820,plain,
% 0.91/1.09 ((~![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(s42, c_c2) | node9(s42) | node8(s42) | node10(s42) | node11(s42) | node12(s42) | node13(s42, s43) | (~node14(s42, s43)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3821,plain,
% 0.91/1.09 ((~![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(s42, c_c2) | node9(s42) | node8(s42) | node10(s42) | node11(s42) | node12(s42) | node13(s42, s43) | (~node14(s42, s43))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3820, 3819])).
% 0.91/1.09 tff(3822,plain,
% 0.91/1.09 (m_main_v_state2(s42, c_c2) | node9(s42) | node8(s42) | node10(s42) | node11(s42) | node12(s42) | node13(s42, s43)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3821, 296, 3818])).
% 0.91/1.09 tff(3823,plain,
% 0.91/1.09 (node13(s42, s43)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3822, 3807, 3764, 3760, 3756, 3752, 3735])).
% 0.91/1.09 tff(3824,plain,
% 0.91/1.09 (((~![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(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)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3825,plain,
% 0.91/1.09 (((~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)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3826,plain,
% 0.91/1.09 (((~![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))))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[3825])).
% 0.91/1.09 tff(3827,plain,
% 0.91/1.09 (((~![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)))),
% 0.91/1.09 inference(transitivity,[status(thm)],[3826, 3824])).
% 0.91/1.09 tff(3828,plain,
% 0.91/1.09 ((~![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)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3829,plain,
% 0.91/1.09 ((~![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(s42, c_n2) | (~m_main_v_state2(s43, c_n2)) | (~node13(s42, s43))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3828, 3827])).
% 0.91/1.09 tff(3830,plain,
% 0.91/1.09 (~m_main_v_state2(s43, c_n2)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3829, 311, 3748, 3823])).
% 0.91/1.09 tff(3831,plain,
% 0.91/1.09 (((~![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)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3832,plain,
% 0.91/1.09 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s43, c_n2) | (~node9(s43)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3833,plain,
% 0.91/1.09 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s43, c_n2) | (~node9(s43))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3832, 3831])).
% 0.91/1.09 tff(3834,plain,
% 0.91/1.09 (~node9(s43)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3833, 88, 3830])).
% 0.91/1.09 tff(3835,plain,
% 0.91/1.09 (((~![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)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3836,plain,
% 0.91/1.09 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s43, c_n2) | (~node10(s43)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3837,plain,
% 0.91/1.09 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s43, c_n2) | (~node10(s43))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3836, 3835])).
% 0.91/1.09 tff(3838,plain,
% 0.91/1.09 (~node10(s43)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3837, 249, 3830])).
% 0.91/1.09 tff(3839,plain,
% 0.91/1.09 (((~![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(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)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3840,plain,
% 0.91/1.09 (((~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)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3841,plain,
% 0.91/1.09 (((~![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))))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[3840])).
% 0.91/1.09 tff(3842,plain,
% 0.91/1.09 (((~![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)))),
% 0.91/1.09 inference(transitivity,[status(thm)],[3841, 3839])).
% 0.91/1.09 tff(3843,plain,
% 0.91/1.09 ((~![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))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3844,plain,
% 0.91/1.09 ((~![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(s42, c_t2)) | m_main_v_state2(s43, c_t2) | (~node13(s42, s43))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3843, 3842])).
% 0.91/1.09 tff(3845,plain,
% 0.91/1.09 (m_main_v_state2(s43, c_t2)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3844, 518, 3744, 3823])).
% 0.91/1.09 tff(3846,plain,
% 0.91/1.09 (((~![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)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3847,plain,
% 0.91/1.09 ((~![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)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3848,plain,
% 0.91/1.09 ((~![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))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3847, 3846])).
% 0.91/1.09 tff(3849,plain,
% 0.91/1.09 (~m_main_v_state1(s42, c_t1)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3848, 539, 3799])).
% 0.91/1.09 tff(3850,plain,
% 0.91/1.09 (((~![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)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3851,plain,
% 0.91/1.09 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s42, c_t1) | (~node5(s42)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3852,plain,
% 0.91/1.09 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s42, c_t1) | (~node5(s42))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3851, 3850])).
% 0.91/1.09 tff(3853,plain,
% 0.91/1.09 (~node5(s42)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3852, 550, 3849])).
% 0.91/1.09 tff(3854,plain,
% 0.91/1.09 (((~![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)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3855,plain,
% 0.91/1.09 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s42, c_n2) | (~node4(s42)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3856,plain,
% 0.91/1.09 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s42, c_n2) | (~node4(s42))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3855, 3854])).
% 0.91/1.09 tff(3857,plain,
% 0.91/1.09 (~node4(s42)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3856, 388, 3748])).
% 0.91/1.09 tff(3858,plain,
% 0.91/1.09 (((~![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)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3859,plain,
% 0.91/1.09 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s42, c_c2) | (~node3(s42)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3860,plain,
% 0.91/1.09 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s42, c_c2) | (~node3(s42))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3859, 3858])).
% 0.91/1.09 tff(3861,plain,
% 0.91/1.09 (~node3(s42)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3860, 399, 3764])).
% 0.91/1.09 tff(3862,plain,
% 0.91/1.09 (((~![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)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3863,plain,
% 0.91/1.09 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s42, c_n2) | (~node2(s42)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3864,plain,
% 0.91/1.09 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s42, c_n2) | (~node2(s42))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3863, 3862])).
% 0.91/1.09 tff(3865,plain,
% 0.91/1.09 (~node2(s42)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3864, 410, 3748])).
% 0.91/1.09 tff(3866,plain,
% 0.91/1.09 (((~![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)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3867,plain,
% 0.91/1.09 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s42, c_n1) | (~node1(s42)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3868,plain,
% 0.91/1.09 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s42, c_n1) | (~node1(s42))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3867, 3866])).
% 0.91/1.09 tff(3869,plain,
% 0.91/1.09 (~node1(s42)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3868, 421, 3803])).
% 0.91/1.09 tff(3870,plain,
% 0.91/1.09 (((~![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))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3871,plain,
% 0.91/1.09 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s42, s43)) | node7(s42, s43))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3872,plain,
% 0.91/1.09 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s42, s43)) | node7(s42, s43)),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3871, 3870])).
% 0.91/1.09 tff(3873,plain,
% 0.91/1.09 (node7(s42, s43)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3872, 206, 3814])).
% 0.91/1.09 tff(3874,plain,
% 0.91/1.09 (((~![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(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)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3875,plain,
% 0.91/1.09 (((~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)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3876,plain,
% 0.91/1.09 (((~![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(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))))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[3875])).
% 0.91/1.09 tff(3877,plain,
% 0.91/1.09 (((~![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(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)))),
% 0.91/1.09 inference(transitivity,[status(thm)],[3876, 3874])).
% 0.91/1.09 tff(3878,plain,
% 0.91/1.09 ((~![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(s42, c_c1)) | node1(s42) | node2(s42) | node3(s42) | node4(s42) | node5(s42) | (~node7(s42, s43)) | m_main_v_state1(s43, c_n1))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3879,plain,
% 0.91/1.09 ((~![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(s43, c_n1) | (~m_main_v_state1(s42, c_c1)) | node1(s42) | node2(s42) | node3(s42) | node4(s42) | node5(s42) | (~node7(s42, s43))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3878, 3877])).
% 0.91/1.09 tff(3880,plain,
% 0.91/1.09 (m_main_v_state1(s43, c_n1) | (~m_main_v_state1(s42, c_c1)) | node1(s42) | node2(s42) | node3(s42) | node4(s42) | node5(s42)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3879, 584, 3873])).
% 0.91/1.09 tff(3881,plain,
% 0.91/1.09 (m_main_v_state1(s43, c_n1)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3880, 3869, 3799, 3865, 3861, 3857, 3853])).
% 0.91/1.09 tff(3882,plain,
% 0.91/1.09 (((~![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)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3883,plain,
% 0.91/1.09 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s43, c_n2) | (~node8(s43)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3884,plain,
% 0.91/1.09 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s43, c_n2) | (~node8(s43))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3883, 3882])).
% 0.91/1.09 tff(3885,plain,
% 0.91/1.09 (~node8(s43)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3884, 271, 3830])).
% 0.91/1.09 tff(3886,plain,
% 0.91/1.09 (succ(s43, s44) <=> succ(s43, s44)),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3887,axiom,(succ(s43, s44)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound44')).
% 0.91/1.09 tff(3888,plain,
% 0.91/1.09 (succ(s43, s44)),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3887, 3886])).
% 0.91/1.09 tff(3889,plain,
% 0.91/1.09 (((~![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))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3890,plain,
% 0.91/1.09 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s43, s44)) | trans(s43, s44))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3891,plain,
% 0.91/1.09 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s43, s44)) | trans(s43, s44)),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3890, 3889])).
% 0.91/1.09 tff(3892,plain,
% 0.91/1.09 (trans(s43, s44)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3891, 3888, 32])).
% 0.91/1.09 tff(3893,plain,
% 0.91/1.09 (((~![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))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3894,plain,
% 0.91/1.09 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s43, s44)) | node14(s43, s44))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(3895,plain,
% 0.91/1.09 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s43, s44)) | node14(s43, s44)),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[3894, 3893])).
% 0.91/1.09 tff(3896,plain,
% 0.91/1.09 (node14(s43, s44)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[3895, 46, 3892])).
% 0.91/1.09 tff(3897,plain,
% 0.91/1.09 (((~![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(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))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3898,plain,
% 0.91/1.10 ((~![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))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(3899,plain,
% 0.91/1.10 ((~![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)),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[3898, 3897])).
% 0.91/1.10 tff(3900,plain,
% 0.91/1.10 ((~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)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3899, 617, 3896])).
% 0.91/1.10 tff(3901,plain,
% 0.91/1.10 (m_main_v_state2(s44, c_c2)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3900, 3885, 3881, 3845, 3838, 3834])).
% 0.91/1.10 tff(3902,plain,
% 0.91/1.10 (^[X: $i] : refl(((~m_main_v_state2(X, c_c2)) | (~always25(X))) <=> ((~m_main_v_state2(X, c_c2)) | (~always25(X))))),
% 0.91/1.10 inference(bind,[status(th)],[])).
% 0.91/1.10 tff(3903,plain,
% 0.91/1.10 (![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X))) <=> ![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))),
% 0.91/1.10 inference(quant_intro,[status(thm)],[3902])).
% 0.91/1.10 tff(3904,plain,
% 0.91/1.10 (![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X))) <=> ![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3905,axiom,(![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty14')).
% 0.91/1.10 tff(3906,plain,
% 0.91/1.10 (![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[3905, 3904])).
% 0.91/1.10 tff(3907,plain,(
% 0.91/1.10 ![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))),
% 0.91/1.10 inference(skolemize,[status(sab)],[3906])).
% 0.91/1.10 tff(3908,plain,
% 0.91/1.10 (![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[3907, 3903])).
% 0.91/1.10 tff(3909,plain,
% 0.91/1.10 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s44)) | (~m_main_v_state2(s44, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s44)) | (~m_main_v_state2(s44, c_c2)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3910,plain,
% 0.91/1.10 (((~m_main_v_state2(s44, c_c2)) | (~always25(s44))) <=> ((~always25(s44)) | (~m_main_v_state2(s44, c_c2)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3911,plain,
% 0.91/1.10 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s44, c_c2)) | (~always25(s44)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s44)) | (~m_main_v_state2(s44, c_c2))))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[3910])).
% 0.91/1.10 tff(3912,plain,
% 0.91/1.10 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s44, c_c2)) | (~always25(s44)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s44)) | (~m_main_v_state2(s44, c_c2)))),
% 0.91/1.10 inference(transitivity,[status(thm)],[3911, 3909])).
% 0.91/1.10 tff(3913,plain,
% 0.91/1.10 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s44, c_c2)) | (~always25(s44)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(3914,plain,
% 0.91/1.10 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s44)) | (~m_main_v_state2(s44, c_c2))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[3913, 3912])).
% 0.91/1.10 tff(3915,plain,
% 0.91/1.10 (~always25(s44)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3914, 3908, 3901])).
% 0.91/1.10 tff(3916,assumption,(~always25(s99)), introduced(assumption)).
% 0.91/1.10 tff(3917,assumption,(~xuntil28(s99)), introduced(assumption)).
% 0.91/1.10 tff(3918,plain,
% 0.91/1.10 (succ(s98, s99) <=> succ(s98, s99)),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3919,axiom,(succ(s98, s99)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound99')).
% 0.91/1.10 tff(3920,plain,
% 0.91/1.10 (succ(s98, s99)),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[3919, 3918])).
% 0.91/1.10 tff(3921,plain,
% 0.91/1.10 (((~![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))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3922,plain,
% 0.91/1.10 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s98, s99)) | trans(s98, s99))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(3923,plain,
% 0.91/1.10 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s98, s99)) | trans(s98, s99)),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[3922, 3921])).
% 0.91/1.10 tff(3924,plain,
% 0.91/1.10 (trans(s98, s99)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3923, 3920, 32])).
% 0.91/1.10 tff(3925,plain,
% 0.91/1.10 (^[Y: $i, X: $i] : refl(((~trans(X, Y)) | (~always25(X)) | always25(Y)) <=> ((~trans(X, Y)) | (~always25(X)) | always25(Y)))),
% 0.91/1.10 inference(bind,[status(th)],[])).
% 0.91/1.10 tff(3926,plain,
% 0.91/1.10 (![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y)) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))),
% 0.91/1.10 inference(quant_intro,[status(thm)],[3925])).
% 0.91/1.10 tff(3927,plain,
% 0.91/1.10 (![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y)) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3928,plain,
% 0.91/1.10 (^[Y: $i, X: $i] : rewrite(((always25(Y) | (~trans(X, Y))) | (~always25(X))) <=> ((~trans(X, Y)) | (~always25(X)) | always25(Y)))),
% 0.91/1.10 inference(bind,[status(th)],[])).
% 0.91/1.10 tff(3929,plain,
% 0.91/1.10 (![Y: $i, X: $i] : ((always25(Y) | (~trans(X, Y))) | (~always25(X))) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))),
% 0.91/1.10 inference(quant_intro,[status(thm)],[3928])).
% 0.91/1.10 tff(3930,axiom,(![Y: $i, X: $i] : ((always25(Y) | (~trans(X, Y))) | (~always25(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty15')).
% 0.91/1.10 tff(3931,plain,
% 0.91/1.10 (![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[3930, 3929])).
% 0.91/1.10 tff(3932,plain,
% 0.91/1.10 (![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[3931, 3927])).
% 0.91/1.10 tff(3933,plain,(
% 0.91/1.10 ![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))),
% 0.91/1.10 inference(skolemize,[status(sab)],[3932])).
% 0.91/1.10 tff(3934,plain,
% 0.91/1.10 (![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[3933, 3926])).
% 0.91/1.10 tff(3935,plain,
% 0.91/1.10 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (always25(s99) | (~trans(s98, s99)) | (~always25(s98)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | always25(s99) | (~trans(s98, s99)) | (~always25(s98)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3936,plain,
% 0.91/1.10 (((~trans(s98, s99)) | (~always25(s98)) | always25(s99)) <=> (always25(s99) | (~trans(s98, s99)) | (~always25(s98)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3937,plain,
% 0.91/1.10 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s98, s99)) | (~always25(s98)) | always25(s99))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (always25(s99) | (~trans(s98, s99)) | (~always25(s98))))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[3936])).
% 0.91/1.10 tff(3938,plain,
% 0.91/1.10 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s98, s99)) | (~always25(s98)) | always25(s99))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | always25(s99) | (~trans(s98, s99)) | (~always25(s98)))),
% 0.91/1.10 inference(transitivity,[status(thm)],[3937, 3935])).
% 0.91/1.10 tff(3939,plain,
% 0.91/1.10 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s98, s99)) | (~always25(s98)) | always25(s99))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(3940,plain,
% 0.91/1.10 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | always25(s99) | (~trans(s98, s99)) | (~always25(s98))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[3939, 3938])).
% 0.91/1.10 tff(3941,plain,
% 0.91/1.10 (always25(s99) | (~always25(s98))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3940, 3934, 3924])).
% 0.91/1.10 tff(3942,plain,
% 0.91/1.10 (~always25(s98)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3941, 3916])).
% 0.91/1.10 tff(3943,plain,
% 0.91/1.10 (^[X: $i] : refl((always25(X) | (~node26(X))) <=> (always25(X) | (~node26(X))))),
% 0.91/1.10 inference(bind,[status(th)],[])).
% 0.91/1.10 tff(3944,plain,
% 0.91/1.10 (![X: $i] : (always25(X) | (~node26(X))) <=> ![X: $i] : (always25(X) | (~node26(X)))),
% 0.91/1.10 inference(quant_intro,[status(thm)],[3943])).
% 0.91/1.10 tff(3945,plain,
% 0.91/1.10 (![X: $i] : (always25(X) | (~node26(X))) <=> ![X: $i] : (always25(X) | (~node26(X)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3946,axiom,(![X: $i] : (always25(X) | (~node26(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty18')).
% 0.91/1.10 tff(3947,plain,
% 0.91/1.10 (![X: $i] : (always25(X) | (~node26(X)))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[3946, 3945])).
% 0.91/1.10 tff(3948,plain,(
% 0.91/1.10 ![X: $i] : (always25(X) | (~node26(X)))),
% 0.91/1.10 inference(skolemize,[status(sab)],[3947])).
% 0.91/1.10 tff(3949,plain,
% 0.91/1.10 (![X: $i] : (always25(X) | (~node26(X)))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[3948, 3944])).
% 0.91/1.10 tff(3950,plain,
% 0.91/1.10 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s98) | (~node26(s98)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s98) | (~node26(s98)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3951,plain,
% 0.91/1.10 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s98) | (~node26(s98)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(3952,plain,
% 0.91/1.10 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s98) | (~node26(s98))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[3951, 3950])).
% 0.91/1.10 tff(3953,plain,
% 0.91/1.10 (~node26(s98)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3952, 3949, 3942])).
% 0.91/1.10 tff(3954,plain,
% 0.91/1.10 (((~![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))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3955,plain,
% 0.91/1.10 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s43, s44)) | node7(s43, s44))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(3956,plain,
% 0.91/1.10 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s43, s44)) | node7(s43, s44)),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[3955, 3954])).
% 0.91/1.10 tff(3957,plain,
% 0.91/1.10 (node7(s43, s44)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3956, 206, 3892])).
% 0.91/1.10 tff(3958,plain,
% 0.91/1.10 (((~![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))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3959,plain,
% 0.91/1.10 ((~![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))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(3960,plain,
% 0.91/1.10 ((~![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)),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[3959, 3958])).
% 0.91/1.10 tff(3961,plain,
% 0.91/1.10 ((~m_main_v_state1(s43, c_n1)) | (~m_main_v_state2(s43, c_t2)) | m_main_v_state1(s44, c_t1)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3960, 651, 3957])).
% 0.91/1.10 tff(3962,plain,
% 0.91/1.10 (m_main_v_state1(s44, c_t1)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3961, 3845, 3881])).
% 0.91/1.10 tff(3963,plain,
% 0.91/1.10 (((~![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)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3964,plain,
% 0.91/1.10 ((~![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)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(3965,plain,
% 0.91/1.10 ((~![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))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[3964, 3963])).
% 0.91/1.10 tff(3966,plain,
% 0.91/1.10 (~m_main_v_state1(s44, c_n1)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3965, 10, 3962])).
% 0.91/1.10 tff(3967,plain,
% 0.91/1.10 (((~![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)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3968,plain,
% 0.91/1.10 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s44, c_n1) | (~node1(s44)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(3969,plain,
% 0.91/1.10 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s44, c_n1) | (~node1(s44))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[3968, 3967])).
% 0.91/1.10 tff(3970,plain,
% 0.91/1.10 (~node1(s44)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3969, 421, 3966])).
% 0.91/1.10 tff(3971,plain,
% 0.91/1.10 (((~![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))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3972,plain,
% 0.91/1.10 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s43, s44)) | node18(s43, s44))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(3973,plain,
% 0.91/1.10 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s43, s44)) | node18(s43, s44)),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[3972, 3971])).
% 0.91/1.10 tff(3974,plain,
% 0.91/1.10 (node18(s43, s44)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3973, 125, 3892])).
% 0.91/1.10 tff(3975,plain,
% 0.91/1.10 (((~![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(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))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3976,plain,
% 0.91/1.10 ((~![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(s43, c_n1)) | (~m_main_v_state2(s43, c_t2)) | (~node18(s43, s44)) | m_main_v_turn(s44, c_2))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(3977,plain,
% 0.91/1.10 ((~![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(s43, c_n1)) | (~m_main_v_state2(s43, c_t2)) | (~node18(s43, s44)) | m_main_v_turn(s44, c_2)),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[3976, 3975])).
% 0.91/1.10 tff(3978,plain,
% 0.91/1.10 ((~m_main_v_state1(s43, c_n1)) | (~m_main_v_state2(s43, c_t2)) | m_main_v_turn(s44, c_2)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3977, 760, 3974])).
% 0.91/1.10 tff(3979,plain,
% 0.91/1.10 (m_main_v_turn(s44, c_2)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3978, 3845, 3881])).
% 0.91/1.10 tff(3980,plain,
% 0.91/1.10 (((~![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)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3981,plain,
% 0.91/1.10 ((~![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)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(3982,plain,
% 0.91/1.10 ((~![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))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[3981, 3980])).
% 0.91/1.10 tff(3983,plain,
% 0.91/1.10 (~m_main_v_turn(s44, c_1)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3982, 156, 3979])).
% 0.91/1.10 tff(3984,plain,
% 0.91/1.10 (((~![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)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3985,plain,
% 0.91/1.10 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s44, c_1) | (~node5(s44)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(3986,plain,
% 0.91/1.10 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s44, c_1) | (~node5(s44))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[3985, 3984])).
% 0.91/1.10 tff(3987,plain,
% 0.91/1.10 (~node5(s44)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3986, 776, 3983])).
% 0.91/1.10 tff(3988,plain,
% 0.91/1.10 (((~![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)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3989,plain,
% 0.91/1.10 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s44, c_n1) | (~node2(s44)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(3990,plain,
% 0.91/1.10 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s44, c_n1) | (~node2(s44))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[3989, 3988])).
% 0.91/1.10 tff(3991,plain,
% 0.91/1.10 (~node2(s44)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3990, 787, 3966])).
% 0.91/1.10 tff(3992,plain,
% 0.91/1.10 (((~![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)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3993,plain,
% 0.91/1.10 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s44, c_n1) | (~node3(s44)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(3994,plain,
% 0.91/1.10 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s44, c_n1) | (~node3(s44))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[3993, 3992])).
% 0.91/1.10 tff(3995,plain,
% 0.91/1.10 (~node3(s44)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3994, 798, 3966])).
% 0.91/1.10 tff(3996,plain,
% 0.91/1.10 (((~![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)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(3997,plain,
% 0.91/1.10 ((~![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)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(3998,plain,
% 0.91/1.10 ((~![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))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[3997, 3996])).
% 0.91/1.10 tff(3999,plain,
% 0.91/1.10 (~m_main_v_state1(s44, c_c1)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[3998, 539, 3962])).
% 0.91/1.10 tff(4000,plain,
% 0.91/1.10 (((~![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)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(4001,plain,
% 0.91/1.10 ((~![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)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(4002,plain,
% 0.91/1.10 ((~![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))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[4001, 4000])).
% 0.91/1.10 tff(4003,plain,
% 0.91/1.10 (~m_main_v_state2(s44, c_n2)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[4002, 697, 3901])).
% 0.91/1.10 tff(4004,plain,
% 0.91/1.10 (((~![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)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(4005,plain,
% 0.91/1.10 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s44, c_n2) | (~node4(s44)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(4006,plain,
% 0.91/1.10 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s44, c_n2) | (~node4(s44))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[4005, 4004])).
% 0.91/1.10 tff(4007,plain,
% 0.91/1.10 (~node4(s44)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[4006, 388, 4003])).
% 0.91/1.10 tff(4008,plain,
% 0.91/1.10 (succ(s44, s45) <=> succ(s44, s45)),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(4009,axiom,(succ(s44, s45)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound45')).
% 0.91/1.10 tff(4010,plain,
% 0.91/1.10 (succ(s44, s45)),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[4009, 4008])).
% 0.91/1.10 tff(4011,plain,
% 0.91/1.10 (((~![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))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(4012,plain,
% 0.91/1.10 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s44, s45)) | trans(s44, s45))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(4013,plain,
% 0.91/1.10 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s44, s45)) | trans(s44, s45)),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[4012, 4011])).
% 0.91/1.10 tff(4014,plain,
% 0.91/1.10 (trans(s44, s45)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[4013, 4010, 32])).
% 0.91/1.10 tff(4015,plain,
% 0.91/1.10 (((~![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))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(4016,plain,
% 0.91/1.10 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s44, s45)) | node7(s44, s45))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(4017,plain,
% 0.91/1.10 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s44, s45)) | node7(s44, s45)),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[4016, 4015])).
% 0.91/1.10 tff(4018,plain,
% 0.91/1.10 (node7(s44, s45)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[4017, 206, 4014])).
% 0.91/1.10 tff(4019,plain,
% 0.91/1.10 (((~![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(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)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(4020,plain,
% 0.91/1.10 ((~![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(s44, c_c1) | node1(s44) | node2(s44) | node3(s44) | node4(s44) | node5(s44) | node6(s44, s45) | (~node7(s44, s45)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(4021,plain,
% 0.91/1.10 ((~![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(s44, c_c1) | node1(s44) | node2(s44) | node3(s44) | node4(s44) | node5(s44) | node6(s44, s45) | (~node7(s44, s45))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[4020, 4019])).
% 0.91/1.10 tff(4022,plain,
% 0.91/1.10 (m_main_v_state1(s44, c_c1) | node1(s44) | node2(s44) | node3(s44) | node4(s44) | node5(s44) | node6(s44, s45)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[4021, 820, 4018])).
% 0.91/1.10 tff(4023,plain,
% 0.91/1.10 (node6(s44, s45)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[4022, 4007, 3999, 3995, 3991, 3987, 3970])).
% 0.91/1.10 tff(4024,plain,
% 0.91/1.10 (((~![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(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)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(4025,plain,
% 0.91/1.10 (((~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)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(4026,plain,
% 0.91/1.10 (((~![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))))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[4025])).
% 0.91/1.10 tff(4027,plain,
% 0.91/1.10 (((~![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)))),
% 0.91/1.10 inference(transitivity,[status(thm)],[4026, 4024])).
% 0.91/1.10 tff(4028,plain,
% 0.91/1.10 ((~![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))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(4029,plain,
% 0.91/1.10 ((~![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(s44, c_t1)) | m_main_v_state1(s45, c_t1) | (~node6(s44, s45))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[4028, 4027])).
% 0.91/1.10 tff(4030,plain,
% 0.91/1.10 (m_main_v_state1(s45, c_t1)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[4029, 856, 3962, 4023])).
% 0.91/1.10 tff(4031,plain,
% 0.91/1.10 (((~![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)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(4032,plain,
% 0.91/1.10 ((~![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)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(4033,plain,
% 0.91/1.10 ((~![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))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[4032, 4031])).
% 0.91/1.10 tff(4034,plain,
% 0.91/1.10 (~m_main_v_state2(s44, c_t2)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[4033, 260, 3901])).
% 0.91/1.10 tff(4035,plain,
% 0.91/1.10 (((~![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)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(4036,plain,
% 0.91/1.10 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s44, c_t2) | (~node12(s44)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(4037,plain,
% 0.91/1.10 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s44, c_t2) | (~node12(s44))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[4036, 4035])).
% 0.91/1.10 tff(4038,plain,
% 0.91/1.10 (~node12(s44)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[4037, 633, 4034])).
% 0.91/1.10 tff(4039,plain,
% 0.91/1.10 (((~![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)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(4040,plain,
% 0.91/1.10 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s44, c_n1) | (~node11(s44)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(4041,plain,
% 0.91/1.10 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s44, c_n1) | (~node11(s44))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[4040, 4039])).
% 0.91/1.10 tff(4042,plain,
% 0.91/1.10 (~node11(s44)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[4041, 238, 3966])).
% 0.91/1.10 tff(4043,plain,
% 0.91/1.10 (((~![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)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(4044,plain,
% 0.91/1.10 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s44, c_c1) | (~node10(s44)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(4045,plain,
% 0.91/1.10 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s44, c_c1) | (~node10(s44))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[4044, 4043])).
% 0.91/1.10 tff(4046,plain,
% 0.91/1.10 (~node10(s44)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[4045, 675, 3999])).
% 0.91/1.10 tff(4047,plain,
% 0.91/1.10 (((~![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)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(4048,plain,
% 0.91/1.10 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s44, c_n1) | (~node9(s44)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(4049,plain,
% 0.91/1.11 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s44, c_n1) | (~node9(s44))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[4048, 4047])).
% 0.91/1.11 tff(4050,plain,
% 0.91/1.11 (~node9(s44)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[4049, 686, 3966])).
% 0.91/1.11 tff(4051,plain,
% 0.91/1.11 (((~![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)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(4052,plain,
% 0.91/1.11 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s44, c_n2) | (~node8(s44)))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(4053,plain,
% 0.91/1.11 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s44, c_n2) | (~node8(s44))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[4052, 4051])).
% 0.91/1.11 tff(4054,plain,
% 0.91/1.11 (~node8(s44)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[4053, 271, 4003])).
% 0.91/1.11 tff(4055,plain,
% 0.91/1.11 (((~![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))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(4056,plain,
% 0.91/1.11 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s44, s45)) | node14(s44, s45))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(4057,plain,
% 0.91/1.11 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s44, s45)) | node14(s44, s45)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[4056, 4055])).
% 0.91/1.11 tff(4058,plain,
% 0.91/1.11 (node14(s44, s45)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[4057, 46, 4014])).
% 0.91/1.11 tff(4059,plain,
% 0.91/1.11 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | 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)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(4060,plain,
% 0.91/1.11 (((~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)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(4061,plain,
% 0.91/1.11 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | 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))))),
% 0.91/1.11 inference(monotonicity,[status(thm)],[4060])).
% 0.91/1.11 tff(4062,plain,
% 0.91/1.11 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | 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)))),
% 0.91/1.11 inference(transitivity,[status(thm)],[4061, 4059])).
% 0.91/1.11 tff(4063,plain,
% 0.91/1.11 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | 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))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(4064,plain,
% 0.91/1.11 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | 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))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[4063, 4062])).
% 0.91/1.11 tff(4065,plain,
% 0.91/1.11 (m_main_v_state2(s45, c_n2) | node9(s44) | node8(s44) | node10(s44) | node11(s44) | node12(s44) | (~m_main_v_state2(s44, c_c2))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[4064, 726, 4058])).
% 0.91/1.11 tff(4066,plain,
% 0.91/1.11 (m_main_v_state2(s45, c_n2)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[4065, 4054, 3901, 4050, 4046, 4042, 4038])).
% 0.91/1.11 tff(4067,plain,
% 0.91/1.11 (((~![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)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(4068,plain,
% 0.91/1.11 ((~![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)))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(4069,plain,
% 0.91/1.11 ((~![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))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[4068, 4067])).
% 0.91/1.11 tff(4070,plain,
% 0.91/1.11 (~m_main_v_state2(s45, c_t2)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[4069, 77, 4066])).
% 0.91/1.11 tff(4071,plain,
% 0.91/1.11 (((~![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)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(4072,plain,
% 0.91/1.11 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s45, c_t2) | (~node15(s45)))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(4073,plain,
% 0.91/1.11 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s45, c_t2) | (~node15(s45))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[4072, 4071])).
% 0.91/1.11 tff(4074,plain,
% 0.91/1.11 (~node15(s45)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[4073, 103, 4070])).
% 0.91/1.11 tff(4075,plain,
% 0.91/1.11 (succ(s45, s46) <=> succ(s45, s46)),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(4076,axiom,(succ(s45, s46)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound46')).
% 0.91/1.11 tff(4077,plain,
% 0.91/1.11 (succ(s45, s46)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[4076, 4075])).
% 0.91/1.11 tff(4078,plain,
% 0.91/1.11 (((~![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))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(4079,plain,
% 0.91/1.11 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s45, s46)) | trans(s45, s46))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(4080,plain,
% 0.91/1.11 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s45, s46)) | trans(s45, s46)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[4079, 4078])).
% 0.91/1.11 tff(4081,plain,
% 0.91/1.11 (trans(s45, s46)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[4080, 4077, 32])).
% 0.91/1.11 tff(4082,plain,
% 0.91/1.11 (((~![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))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(4083,plain,
% 0.91/1.11 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s45, s46)) | node18(s45, s46))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(4084,plain,
% 0.91/1.11 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s45, s46)) | node18(s45, s46)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[4083, 4082])).
% 0.91/1.11 tff(4085,plain,
% 0.91/1.11 (node18(s45, s46)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[4084, 125, 4081])).
% 0.91/1.11 tff(4086,plain,
% 0.91/1.11 (((~![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(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))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(4087,plain,
% 0.91/1.11 (((~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))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(4088,plain,
% 0.91/1.11 (((~![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))) | ((~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)))),
% 0.91/1.11 inference(monotonicity,[status(thm)],[4087])).
% 0.91/1.11 tff(4089,plain,
% 0.91/1.11 (((~![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))) | ((~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))),
% 0.91/1.11 inference(transitivity,[status(thm)],[4088, 4086])).
% 0.91/1.11 tff(4090,plain,
% 0.91/1.11 ((~![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))) | ((~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))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(4091,plain,
% 0.91/1.11 ((~![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(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)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[4090, 4089])).
% 0.91/1.11 tff(4092,plain,
% 0.91/1.11 (node15(s45) | (~m_main_v_state1(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | m_main_v_turn(s46, c_1)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[4091, 992, 4085])).
% 0.91/1.11 tff(4093,plain,
% 0.91/1.11 (m_main_v_turn(s46, c_1)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[4092, 4074, 4066, 4030])).
% 0.91/1.11 tff(4094,plain,
% 0.91/1.11 (((~![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)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(4095,plain,
% 0.91/1.11 ((~![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)))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(4096,plain,
% 0.91/1.11 ((~![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))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[4095, 4094])).
% 0.91/1.11 tff(4097,plain,
% 0.91/1.11 (~m_main_v_turn(s46, c_2)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[4096, 156, 4093])).
% 0.91/1.11 tff(4098,plain,
% 0.91/1.11 (((~![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)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(4099,plain,
% 0.91/1.11 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s46, c_2) | (~node12(s46)))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(4100,plain,
% 0.91/1.11 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s46, c_2) | (~node12(s46))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[4099, 4098])).
% 0.91/1.11 tff(4101,plain,
% 0.91/1.11 (~node12(s46)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[4100, 184, 4097])).
% 0.91/1.11 tff(4102,plain,
% 0.91/1.11 (((~![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))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(4103,plain,
% 0.91/1.11 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s45, s46)) | node14(s45, s46))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(4104,plain,
% 0.91/1.11 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s45, s46)) | node14(s45, s46)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[4103, 4102])).
% 0.91/1.11 tff(4105,plain,
% 0.91/1.11 (node14(s45, s46)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[4104, 46, 4081])).
% 0.91/1.11 tff(4106,plain,
% 0.91/1.11 (((~![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(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))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(4107,plain,
% 0.91/1.11 ((~![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(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | (~node14(s45, s46)) | m_main_v_state2(s46, c_t2))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(4108,plain,
% 0.91/1.11 ((~![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(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | (~node14(s45, s46)) | m_main_v_state2(s46, c_t2)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[4107, 4106])).
% 0.91/1.11 tff(4109,plain,
% 0.91/1.11 ((~m_main_v_state1(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | m_main_v_state2(s46, c_t2)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[4108, 922, 4105])).
% 0.91/1.11 tff(4110,plain,
% 0.91/1.11 (m_main_v_state2(s46, c_t2)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[4109, 4030, 4066])).
% 0.91/1.11 tff(4111,plain,
% 0.91/1.11 (((~![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)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(4112,plain,
% 0.91/1.11 ((~![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)))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(4113,plain,
% 0.91/1.11 ((~![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))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[4112, 4111])).
% 0.91/1.11 tff(4114,plain,
% 0.91/1.11 (~m_main_v_state2(s46, c_n2)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[4113, 77, 4110])).
% 0.91/1.11 tff(4115,plain,
% 0.91/1.11 (((~![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)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(4116,plain,
% 0.91/1.11 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s46, c_n2) | (~node8(s46)))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(4117,plain,
% 0.91/1.11 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s46, c_n2) | (~node8(s46))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[4116, 4115])).
% 0.91/1.11 tff(4118,plain,
% 0.91/1.11 (~node8(s46)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[4117, 271, 4114])).
% 0.91/1.11 tff(4119,plain,
% 0.91/1.11 (((~![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)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(4120,plain,
% 0.91/1.11 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s46, c_n2) | (~node9(s46)))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(4121,plain,
% 0.91/1.11 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s46, c_n2) | (~node9(s46))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[4120, 4119])).
% 0.91/1.11 tff(4122,plain,
% 0.91/1.11 (~node9(s46)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[4121, 88, 4114])).
% 0.91/1.11 tff(4123,plain,
% 0.91/1.11 (((~![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)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(4124,plain,
% 0.91/1.11 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s46, c_n2) | (~node10(s46)))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(4125,plain,
% 0.91/1.11 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s46, c_n2) | (~node10(s46))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[4124, 4123])).
% 0.91/1.11 tff(4126,plain,
% 0.91/1.11 (~node10(s46)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[4125, 249, 4114])).
% 0.91/1.11 tff(4127,plain,
% 0.91/1.11 (((~![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)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(4128,plain,
% 0.91/1.11 ((~![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)))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(4129,plain,
% 0.91/1.11 ((~![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))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[4128, 4127])).
% 0.91/1.11 tff(4130,plain,
% 0.91/1.11 (~m_main_v_state2(s46, c_c2)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[4129, 260, 4110])).
% 0.91/1.11 tff(4131,plain,
% 0.91/1.11 (((~![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)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(4132,plain,
% 0.91/1.11 ((~![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)))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(4133,plain,
% 0.91/1.11 ((~![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))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[4132, 4131])).
% 0.91/1.11 tff(4134,plain,
% 0.91/1.11 (~m_main_v_state2(s45, c_c2)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[4133, 697, 4066])).
% 0.91/1.11 tff(4135,plain,
% 0.91/1.11 (((~![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)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(4136,plain,
% 0.91/1.11 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s45, c_c2) | (~node3(s45)))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(4137,plain,
% 0.91/1.11 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s45, c_c2) | (~node3(s45))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[4136, 4135])).
% 0.91/1.11 tff(4138,plain,
% 0.91/1.11 (~node3(s45)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[4137, 399, 4134])).
% 0.91/1.11 tff(4139,plain,
% 0.91/1.11 (((~![V: $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)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(4140,plain,
% 0.91/1.11 (((~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)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(4141,plain,
% 0.91/1.11 (((~![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))))),
% 0.91/1.11 inference(monotonicity,[status(thm)],[4140])).
% 0.91/1.11 tff(4142,plain,
% 0.91/1.11 (((~![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)))),
% 0.91/1.11 inference(transitivity,[status(thm)],[4141, 4139])).
% 0.91/1.11 tff(4143,plain,
% 0.91/1.11 ((~![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)))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(4144,plain,
% 0.91/1.11 ((~![V: $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))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[4143, 4142])).
% 0.91/1.11 tff(4145,plain,
% 0.91/1.11 (~m_main_v_state1(s45, c_n1)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[4144, 835, 3966, 4023])).
% 0.91/1.11 tff(4146,plain,
% 0.91/1.11 (((~![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)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(4147,plain,
% 0.91/1.11 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s45, c_n1) | (~node2(s45)))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(4148,plain,
% 0.91/1.11 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s45, c_n1) | (~node2(s45))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[4147, 4146])).
% 0.91/1.11 tff(4149,plain,
% 0.91/1.11 (~node2(s45)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[4148, 787, 4145])).
% 0.91/1.11 tff(4150,plain,
% 0.91/1.11 (((~![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)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(4151,plain,
% 0.91/1.11 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s45, c_t2) | (~node1(s45)))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(4152,plain,
% 0.91/1.11 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s45, c_t2) | (~node1(s45))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[4151, 4150])).
% 0.91/1.11 tff(4153,plain,
% 0.91/1.11 (~node1(s45)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[4152, 195, 4070])).
% 0.91/1.11 tff(4154,plain,
% 0.91/1.11 (((~![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))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(4155,plain,
% 0.91/1.11 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s45, s46)) | node7(s45, s46))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(4156,plain,
% 0.91/1.11 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s45, s46)) | node7(s45, s46)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[4155, 4154])).
% 0.91/1.11 tff(4157,plain,
% 0.91/1.11 (node7(s45, s46)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[4156, 206, 4081])).
% 0.91/1.11 tff(4158,plain,
% 0.91/1.11 (((~![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(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)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(4159,plain,
% 0.91/1.11 (((~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)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(4160,plain,
% 0.91/1.11 (((~![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(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))))),
% 0.91/1.11 inference(monotonicity,[status(thm)],[4159])).
% 0.91/1.11 tff(4161,plain,
% 0.91/1.11 (((~![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(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)))),
% 0.91/1.11 inference(transitivity,[status(thm)],[4160, 4158])).
% 0.91/1.11 tff(4162,plain,
% 0.91/1.11 ((~![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(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))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(4163,plain,
% 0.91/1.11 ((~![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(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))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[4162, 4161])).
% 0.91/1.11 tff(4164,plain,
% 0.91/1.11 ((~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)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[4163, 892, 4157])).
% 0.91/1.12 tff(4165,plain,
% 0.91/1.12 (m_main_v_state1(s46, c_c1)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[4164, 4153, 4066, 4030, 4149, 4138])).
% 0.91/1.12 tff(4166,plain,
% 0.91/1.12 (((~![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)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(4167,plain,
% 0.91/1.12 ((~![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)))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(4168,plain,
% 0.91/1.12 ((~![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))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[4167, 4166])).
% 0.91/1.12 tff(4169,plain,
% 0.91/1.12 (~m_main_v_state1(s46, c_n1)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[4168, 454, 4165])).
% 0.91/1.12 tff(4170,plain,
% 0.91/1.12 (((~![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)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(4171,plain,
% 0.91/1.12 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s46, c_n1) | (~node11(s46)))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(4172,plain,
% 0.91/1.12 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s46, c_n1) | (~node11(s46))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[4171, 4170])).
% 0.91/1.12 tff(4173,plain,
% 0.91/1.12 (~node11(s46)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[4172, 238, 4169])).
% 0.91/1.12 tff(4174,plain,
% 0.91/1.12 (succ(s46, s47) <=> succ(s46, s47)),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(4175,axiom,(succ(s46, s47)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound47')).
% 0.91/1.12 tff(4176,plain,
% 0.91/1.12 (succ(s46, s47)),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[4175, 4174])).
% 0.91/1.12 tff(4177,plain,
% 0.91/1.12 (((~![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))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(4178,plain,
% 0.91/1.12 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s46, s47)) | trans(s46, s47))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(4179,plain,
% 0.91/1.12 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s46, s47)) | trans(s46, s47)),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[4178, 4177])).
% 0.91/1.12 tff(4180,plain,
% 0.91/1.12 (trans(s46, s47)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[4179, 4176, 32])).
% 0.91/1.12 tff(4181,plain,
% 0.91/1.12 (((~![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))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(4182,plain,
% 0.91/1.12 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s46, s47)) | node14(s46, s47))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(4183,plain,
% 0.91/1.12 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s46, s47)) | node14(s46, s47)),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[4182, 4181])).
% 0.91/1.12 tff(4184,plain,
% 0.91/1.12 (node14(s46, s47)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[4183, 46, 4180])).
% 0.91/1.12 tff(4185,plain,
% 0.91/1.12 (((~![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(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)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(4186,plain,
% 0.91/1.12 ((~![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(s46, c_c2) | node9(s46) | node8(s46) | node10(s46) | node11(s46) | node12(s46) | node13(s46, s47) | (~node14(s46, s47)))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(4187,plain,
% 0.91/1.12 ((~![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(s46, c_c2) | node9(s46) | node8(s46) | node10(s46) | node11(s46) | node12(s46) | node13(s46, s47) | (~node14(s46, s47))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[4186, 4185])).
% 0.91/1.12 tff(4188,plain,
% 0.91/1.12 (m_main_v_state2(s46, c_c2) | node9(s46) | node8(s46) | node10(s46) | node11(s46) | node12(s46) | node13(s46, s47)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[4187, 296, 4184])).
% 0.91/1.12 tff(4189,plain,
% 0.91/1.12 (node13(s46, s47)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[4188, 4173, 4130, 4126, 4122, 4118, 4101])).
% 0.91/1.12 tff(4190,plain,
% 0.91/1.12 (((~![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(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)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(4191,plain,
% 0.91/1.12 (((~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)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(4192,plain,
% 0.91/1.12 (((~![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))))),
% 0.91/1.12 inference(monotonicity,[status(thm)],[4191])).
% 0.91/1.12 tff(4193,plain,
% 0.91/1.12 (((~![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)))),
% 0.91/1.12 inference(transitivity,[status(thm)],[4192, 4190])).
% 0.91/1.12 tff(4194,plain,
% 0.91/1.12 ((~![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)))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(4195,plain,
% 0.91/1.12 ((~![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(s46, c_n2) | (~m_main_v_state2(s47, c_n2)) | (~node13(s46, s47))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[4194, 4193])).
% 0.91/1.12 tff(4196,plain,
% 0.91/1.12 (~m_main_v_state2(s47, c_n2)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[4195, 311, 4114, 4189])).
% 0.91/1.12 tff(4197,plain,
% 0.91/1.12 (((~![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)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(4198,plain,
% 0.91/1.12 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s47, c_n2) | (~node9(s47)))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(4199,plain,
% 0.91/1.12 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s47, c_n2) | (~node9(s47))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[4198, 4197])).
% 0.91/1.12 tff(4200,plain,
% 0.91/1.12 (~node9(s47)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[4199, 88, 4196])).
% 0.91/1.12 tff(4201,plain,
% 0.91/1.12 (((~![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)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(4202,plain,
% 0.91/1.12 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s47, c_n2) | (~node10(s47)))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(4203,plain,
% 0.91/1.12 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s47, c_n2) | (~node10(s47))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[4202, 4201])).
% 0.91/1.12 tff(4204,plain,
% 0.91/1.12 (~node10(s47)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[4203, 249, 4196])).
% 0.91/1.12 tff(4205,plain,
% 0.91/1.12 (((~![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(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)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(4206,plain,
% 0.91/1.12 (((~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)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(4207,plain,
% 0.91/1.12 (((~![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))))),
% 0.91/1.12 inference(monotonicity,[status(thm)],[4206])).
% 0.91/1.12 tff(4208,plain,
% 0.91/1.12 (((~![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)))),
% 0.91/1.12 inference(transitivity,[status(thm)],[4207, 4205])).
% 0.91/1.12 tff(4209,plain,
% 0.91/1.12 ((~![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))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(4210,plain,
% 0.91/1.12 ((~![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(s46, c_t2)) | m_main_v_state2(s47, c_t2) | (~node13(s46, s47))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[4209, 4208])).
% 0.91/1.12 tff(4211,plain,
% 0.91/1.12 (m_main_v_state2(s47, c_t2)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[4210, 518, 4110, 4189])).
% 0.91/1.12 tff(4212,plain,
% 0.91/1.12 (((~![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)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(4213,plain,
% 0.91/1.12 ((~![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)))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(4214,plain,
% 0.91/1.12 ((~![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))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[4213, 4212])).
% 0.91/1.12 tff(4215,plain,
% 0.91/1.12 (~m_main_v_state1(s46, c_t1)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[4214, 539, 4165])).
% 0.91/1.12 tff(4216,plain,
% 0.91/1.12 (((~![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)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(4217,plain,
% 0.91/1.12 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s46, c_t1) | (~node5(s46)))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(4218,plain,
% 0.91/1.12 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s46, c_t1) | (~node5(s46))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[4217, 4216])).
% 0.91/1.12 tff(4219,plain,
% 0.91/1.12 (~node5(s46)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[4218, 550, 4215])).
% 0.91/1.12 tff(4220,plain,
% 0.91/1.12 (((~![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)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(4221,plain,
% 0.91/1.12 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s46, c_n2) | (~node4(s46)))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(4222,plain,
% 0.91/1.12 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s46, c_n2) | (~node4(s46))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[4221, 4220])).
% 0.91/1.12 tff(4223,plain,
% 0.91/1.12 (~node4(s46)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[4222, 388, 4114])).
% 0.91/1.12 tff(4224,plain,
% 0.91/1.12 (((~![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)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(4225,plain,
% 0.91/1.12 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s46, c_c2) | (~node3(s46)))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(4226,plain,
% 0.91/1.12 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s46, c_c2) | (~node3(s46))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[4225, 4224])).
% 0.91/1.12 tff(4227,plain,
% 0.91/1.12 (~node3(s46)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[4226, 399, 4130])).
% 0.91/1.12 tff(4228,plain,
% 0.91/1.12 (((~![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)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(4229,plain,
% 0.91/1.12 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s46, c_n2) | (~node2(s46)))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(4230,plain,
% 0.91/1.12 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s46, c_n2) | (~node2(s46))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[4229, 4228])).
% 0.91/1.12 tff(4231,plain,
% 0.91/1.12 (~node2(s46)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[4230, 410, 4114])).
% 0.91/1.12 tff(4232,plain,
% 0.91/1.12 (((~![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)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(4233,plain,
% 0.91/1.12 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s46, c_n1) | (~node1(s46)))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(4234,plain,
% 0.91/1.12 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s46, c_n1) | (~node1(s46))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[4233, 4232])).
% 0.91/1.12 tff(4235,plain,
% 0.91/1.12 (~node1(s46)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[4234, 421, 4169])).
% 0.91/1.12 tff(4236,plain,
% 0.91/1.12 (((~![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))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(4237,plain,
% 0.91/1.12 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s46, s47)) | node7(s46, s47))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(4238,plain,
% 0.91/1.12 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s46, s47)) | node7(s46, s47)),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[4237, 4236])).
% 0.91/1.12 tff(4239,plain,
% 0.91/1.12 (node7(s46, s47)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[4238, 206, 4180])).
% 0.91/1.12 tff(4240,plain,
% 0.91/1.12 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(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)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(4241,plain,
% 0.91/1.12 (((~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)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(4242,plain,
% 0.91/1.12 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(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))))),
% 0.91/1.12 inference(monotonicity,[status(thm)],[4241])).
% 0.91/1.12 tff(4243,plain,
% 0.91/1.12 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(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)))),
% 0.91/1.12 inference(transitivity,[status(thm)],[4242, 4240])).
% 0.91/1.12 tff(4244,plain,
% 0.91/1.12 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s46, c_c1)) | node1(s46) | node2(s46) | node3(s46) | node4(s46) | node5(s46) | (~node7(s46, s47)) | m_main_v_state1(s47, c_n1))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(4245,plain,
% 0.91/1.12 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s47, c_n1) | (~m_main_v_state1(s46, c_c1)) | node1(s46) | node2(s46) | node3(s46) | node4(s46) | node5(s46) | (~node7(s46, s47))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[4244, 4243])).
% 0.91/1.12 tff(4246,plain,
% 0.91/1.12 (m_main_v_state1(s47, c_n1) | (~m_main_v_state1(s46, c_c1)) | node1(s46) | node2(s46) | node3(s46) | node4(s46) | node5(s46)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[4245, 584, 4239])).
% 0.91/1.12 tff(4247,plain,
% 0.91/1.12 (m_main_v_state1(s47, c_n1)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[4246, 4235, 4165, 4231, 4227, 4223, 4219])).
% 0.91/1.12 tff(4248,plain,
% 0.91/1.12 (((~![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)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(4249,plain,
% 0.91/1.12 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s47, c_n2) | (~node8(s47)))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(4250,plain,
% 0.91/1.12 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s47, c_n2) | (~node8(s47))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[4249, 4248])).
% 0.91/1.12 tff(4251,plain,
% 0.91/1.12 (~node8(s47)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[4250, 271, 4196])).
% 0.91/1.12 tff(4252,plain,
% 0.91/1.12 (succ(s47, s48) <=> succ(s47, s48)),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(4253,axiom,(succ(s47, s48)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound48')).
% 0.91/1.12 tff(4254,plain,
% 0.91/1.12 (succ(s47, s48)),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[4253, 4252])).
% 0.91/1.12 tff(4255,plain,
% 0.91/1.12 (((~![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))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(4256,plain,
% 0.91/1.12 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s47, s48)) | trans(s47, s48))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(4257,plain,
% 0.91/1.12 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s47, s48)) | trans(s47, s48)),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[4256, 4255])).
% 0.91/1.12 tff(4258,plain,
% 0.91/1.12 (trans(s47, s48)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[4257, 4254, 32])).
% 0.91/1.12 tff(4259,plain,
% 0.91/1.12 (((~![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))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(4260,plain,
% 0.91/1.12 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s47, s48)) | node14(s47, s48))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(4261,plain,
% 0.91/1.12 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s47, s48)) | node14(s47, s48)),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[4260, 4259])).
% 0.91/1.12 tff(4262,plain,
% 0.91/1.12 (node14(s47, s48)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[4261, 46, 4258])).
% 0.91/1.12 tff(4263,plain,
% 0.91/1.12 (((~![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(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))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(4264,plain,
% 0.91/1.12 ((~![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(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))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(4265,plain,
% 0.91/1.12 ((~![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(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)),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[4264, 4263])).
% 0.91/1.12 tff(4266,plain,
% 0.91/1.12 ((~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)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[4265, 617, 4262])).
% 0.91/1.12 tff(4267,plain,
% 0.91/1.12 (m_main_v_state2(s48, c_c2)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[4266, 4251, 4247, 4211, 4204, 4200])).
% 0.91/1.12 tff(4268,plain,
% 0.91/1.12 (((~![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)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(4269,plain,
% 0.91/1.12 ((~![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)))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(4270,plain,
% 0.91/1.12 ((~![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))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[4269, 4268])).
% 0.91/1.12 tff(4271,plain,
% 0.91/1.12 (~m_main_v_state2(s48, c_t2)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[4270, 260, 4267])).
% 0.91/1.12 tff(4272,plain,
% 0.91/1.12 (((~![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)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(4273,plain,
% 0.91/1.12 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s48, c_t2) | (~node12(s48)))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(4274,plain,
% 0.91/1.12 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s48, c_t2) | (~node12(s48))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[4273, 4272])).
% 0.91/1.12 tff(4275,plain,
% 0.91/1.12 (~node12(s48)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[4274, 633, 4271])).
% 0.91/1.12 tff(4276,plain,
% 0.91/1.12 (((~![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))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(4277,plain,
% 0.91/1.12 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s47, s48)) | node7(s47, s48))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(4278,plain,
% 0.91/1.12 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s47, s48)) | node7(s47, s48)),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[4277, 4276])).
% 0.91/1.12 tff(4279,plain,
% 0.91/1.12 (node7(s47, s48)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[4278, 206, 4258])).
% 0.91/1.12 tff(4280,plain,
% 0.91/1.12 (((~![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(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))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(4281,plain,
% 0.91/1.12 ((~![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(s47, c_n1)) | (~m_main_v_state2(s47, c_t2)) | (~node7(s47, s48)) | m_main_v_state1(s48, c_t1))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(4282,plain,
% 0.91/1.12 ((~![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(s47, c_n1)) | (~m_main_v_state2(s47, c_t2)) | (~node7(s47, s48)) | m_main_v_state1(s48, c_t1)),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[4281, 4280])).
% 0.91/1.12 tff(4283,plain,
% 0.91/1.12 ((~m_main_v_state1(s47, c_n1)) | (~m_main_v_state2(s47, c_t2)) | m_main_v_state1(s48, c_t1)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[4282, 651, 4279])).
% 0.91/1.12 tff(4284,plain,
% 0.91/1.12 (m_main_v_state1(s48, c_t1)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[4283, 4211, 4247])).
% 0.91/1.12 tff(4285,plain,
% 0.91/1.12 (((~![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)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(4286,plain,
% 0.91/1.12 ((~![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)))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(4287,plain,
% 0.91/1.12 ((~![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))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[4286, 4285])).
% 0.91/1.12 tff(4288,plain,
% 0.96/1.13 (~m_main_v_state1(s48, c_n1)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4287, 10, 4284])).
% 0.96/1.13 tff(4289,plain,
% 0.96/1.13 (((~![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)))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4290,plain,
% 0.96/1.13 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s48, c_n1) | (~node11(s48)))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(4291,plain,
% 0.96/1.13 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s48, c_n1) | (~node11(s48))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4290, 4289])).
% 0.96/1.13 tff(4292,plain,
% 0.96/1.13 (~node11(s48)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4291, 238, 4288])).
% 0.96/1.13 tff(4293,plain,
% 0.96/1.13 (((~![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)))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4294,plain,
% 0.96/1.13 ((~![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)))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(4295,plain,
% 0.96/1.13 ((~![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))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4294, 4293])).
% 0.96/1.13 tff(4296,plain,
% 0.96/1.13 (~m_main_v_state1(s48, c_c1)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4295, 539, 4284])).
% 0.96/1.13 tff(4297,plain,
% 0.96/1.13 (((~![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)))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4298,plain,
% 0.96/1.13 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s48, c_c1) | (~node10(s48)))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(4299,plain,
% 0.96/1.13 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s48, c_c1) | (~node10(s48))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4298, 4297])).
% 0.96/1.13 tff(4300,plain,
% 0.96/1.13 (~node10(s48)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4299, 675, 4296])).
% 0.96/1.13 tff(4301,plain,
% 0.96/1.13 (((~![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)))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4302,plain,
% 0.96/1.13 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s48, c_n1) | (~node9(s48)))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(4303,plain,
% 0.96/1.13 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s48, c_n1) | (~node9(s48))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4302, 4301])).
% 0.96/1.13 tff(4304,plain,
% 0.96/1.13 (~node9(s48)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4303, 686, 4288])).
% 0.96/1.13 tff(4305,plain,
% 0.96/1.13 (((~![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)))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4306,plain,
% 0.96/1.13 ((~![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)))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(4307,plain,
% 0.96/1.13 ((~![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))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4306, 4305])).
% 0.96/1.13 tff(4308,plain,
% 0.96/1.13 (~m_main_v_state2(s48, c_n2)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4307, 697, 4267])).
% 0.96/1.13 tff(4309,plain,
% 0.96/1.13 (((~![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)))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4310,plain,
% 0.96/1.13 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s48, c_n2) | (~node8(s48)))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(4311,plain,
% 0.96/1.13 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s48, c_n2) | (~node8(s48))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4310, 4309])).
% 0.96/1.13 tff(4312,plain,
% 0.96/1.13 (~node8(s48)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4311, 271, 4308])).
% 0.96/1.13 tff(4313,plain,
% 0.96/1.13 (succ(s48, s49) <=> succ(s48, s49)),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4314,axiom,(succ(s48, s49)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound49')).
% 0.96/1.13 tff(4315,plain,
% 0.96/1.13 (succ(s48, s49)),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4314, 4313])).
% 0.96/1.13 tff(4316,plain,
% 0.96/1.13 (((~![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))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4317,plain,
% 0.96/1.13 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s48, s49)) | trans(s48, s49))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(4318,plain,
% 0.96/1.13 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s48, s49)) | trans(s48, s49)),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4317, 4316])).
% 0.96/1.13 tff(4319,plain,
% 0.96/1.13 (trans(s48, s49)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4318, 4315, 32])).
% 0.96/1.13 tff(4320,plain,
% 0.96/1.13 (((~![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))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4321,plain,
% 0.96/1.13 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s48, s49)) | node14(s48, s49))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(4322,plain,
% 0.96/1.13 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s48, s49)) | node14(s48, s49)),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4321, 4320])).
% 0.96/1.13 tff(4323,plain,
% 0.96/1.13 (node14(s48, s49)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4322, 46, 4319])).
% 0.96/1.13 tff(4324,plain,
% 0.96/1.13 (((~![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(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)))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4325,plain,
% 0.96/1.13 (((~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)))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4326,plain,
% 0.96/1.13 (((~![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(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))))),
% 0.96/1.13 inference(monotonicity,[status(thm)],[4325])).
% 0.96/1.13 tff(4327,plain,
% 0.96/1.13 (((~![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(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)))),
% 0.96/1.13 inference(transitivity,[status(thm)],[4326, 4324])).
% 0.96/1.13 tff(4328,plain,
% 0.96/1.13 ((~![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(s48, c_c2)) | node9(s48) | node8(s48) | node10(s48) | node11(s48) | node12(s48) | (~node14(s48, s49)) | m_main_v_state2(s49, c_n2))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(4329,plain,
% 0.96/1.13 ((~![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(s49, c_n2) | node9(s48) | node8(s48) | node10(s48) | node11(s48) | node12(s48) | (~node14(s48, s49)) | (~m_main_v_state2(s48, c_c2))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4328, 4327])).
% 0.96/1.13 tff(4330,plain,
% 0.96/1.13 (m_main_v_state2(s49, c_n2) | node9(s48) | node8(s48) | node10(s48) | node11(s48) | node12(s48) | (~m_main_v_state2(s48, c_c2))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4329, 726, 4323])).
% 0.96/1.13 tff(4331,plain,
% 0.96/1.13 (m_main_v_state2(s49, c_n2)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4330, 4312, 4267, 4304, 4300, 4292, 4275])).
% 0.96/1.13 tff(4332,plain,
% 0.96/1.13 (((~![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)))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4333,plain,
% 0.96/1.13 ((~![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)))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(4334,plain,
% 0.96/1.13 ((~![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))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4333, 4332])).
% 0.96/1.13 tff(4335,plain,
% 0.96/1.13 (~m_main_v_state2(s49, c_c2)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4334, 697, 4331])).
% 0.96/1.13 tff(4336,plain,
% 0.96/1.13 (((~![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)))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4337,plain,
% 0.96/1.13 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s49, c_c2) | (~node3(s49)))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(4338,plain,
% 0.96/1.13 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s49, c_c2) | (~node3(s49))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4337, 4336])).
% 0.96/1.13 tff(4339,plain,
% 0.96/1.13 (~node3(s49)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4338, 399, 4335])).
% 0.96/1.13 tff(4340,plain,
% 0.96/1.13 (((~![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)))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4341,plain,
% 0.96/1.13 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s48, c_n1) | (~node1(s48)))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(4342,plain,
% 0.96/1.13 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s48, c_n1) | (~node1(s48))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4341, 4340])).
% 0.96/1.13 tff(4343,plain,
% 0.96/1.13 (~node1(s48)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4342, 421, 4288])).
% 0.96/1.13 tff(4344,plain,
% 0.96/1.13 (((~![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))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4345,plain,
% 0.96/1.13 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s47, s48)) | node18(s47, s48))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(4346,plain,
% 0.96/1.13 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s47, s48)) | node18(s47, s48)),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4345, 4344])).
% 0.96/1.13 tff(4347,plain,
% 0.96/1.13 (node18(s47, s48)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4346, 125, 4258])).
% 0.96/1.13 tff(4348,plain,
% 0.96/1.13 (((~![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))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4349,plain,
% 0.96/1.13 ((~![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))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(4350,plain,
% 0.96/1.13 ((~![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)),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4349, 4348])).
% 0.96/1.13 tff(4351,plain,
% 0.96/1.13 ((~m_main_v_state1(s47, c_n1)) | (~m_main_v_state2(s47, c_t2)) | m_main_v_turn(s48, c_2)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4350, 760, 4347])).
% 0.96/1.13 tff(4352,plain,
% 0.96/1.13 (m_main_v_turn(s48, c_2)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4351, 4211, 4247])).
% 0.96/1.13 tff(4353,plain,
% 0.96/1.13 (((~![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)))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4354,plain,
% 0.96/1.13 ((~![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)))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(4355,plain,
% 0.96/1.13 ((~![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))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4354, 4353])).
% 0.96/1.13 tff(4356,plain,
% 0.96/1.13 (~m_main_v_turn(s48, c_1)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4355, 156, 4352])).
% 0.96/1.13 tff(4357,plain,
% 0.96/1.13 (((~![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)))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4358,plain,
% 0.96/1.13 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s48, c_1) | (~node5(s48)))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(4359,plain,
% 0.96/1.13 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s48, c_1) | (~node5(s48))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4358, 4357])).
% 0.96/1.13 tff(4360,plain,
% 0.96/1.13 (~node5(s48)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4359, 776, 4356])).
% 0.96/1.13 tff(4361,plain,
% 0.96/1.13 (((~![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)))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4362,plain,
% 0.96/1.13 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s48, c_n1) | (~node2(s48)))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(4363,plain,
% 0.96/1.13 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s48, c_n1) | (~node2(s48))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4362, 4361])).
% 0.96/1.13 tff(4364,plain,
% 0.96/1.13 (~node2(s48)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4363, 787, 4288])).
% 0.96/1.13 tff(4365,plain,
% 0.96/1.13 (((~![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)))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4366,plain,
% 0.96/1.13 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s48, c_n1) | (~node3(s48)))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(4367,plain,
% 0.96/1.13 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s48, c_n1) | (~node3(s48))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4366, 4365])).
% 0.96/1.13 tff(4368,plain,
% 0.96/1.13 (~node3(s48)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4367, 798, 4288])).
% 0.96/1.13 tff(4369,plain,
% 0.96/1.13 (((~![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)))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4370,plain,
% 0.96/1.13 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s48, c_n2) | (~node4(s48)))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(4371,plain,
% 0.96/1.13 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s48, c_n2) | (~node4(s48))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4370, 4369])).
% 0.96/1.13 tff(4372,plain,
% 0.96/1.13 (~node4(s48)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4371, 388, 4308])).
% 0.96/1.13 tff(4373,plain,
% 0.96/1.13 (((~![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))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4374,plain,
% 0.96/1.13 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s48, s49)) | node7(s48, s49))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(4375,plain,
% 0.96/1.13 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s48, s49)) | node7(s48, s49)),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4374, 4373])).
% 0.96/1.13 tff(4376,plain,
% 0.96/1.13 (node7(s48, s49)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4375, 206, 4319])).
% 0.96/1.13 tff(4377,plain,
% 0.96/1.13 (((~![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(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)))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4378,plain,
% 0.96/1.13 ((~![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(s48, c_c1) | node1(s48) | node2(s48) | node3(s48) | node4(s48) | node5(s48) | node6(s48, s49) | (~node7(s48, s49)))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(4379,plain,
% 0.96/1.13 ((~![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(s48, c_c1) | node1(s48) | node2(s48) | node3(s48) | node4(s48) | node5(s48) | node6(s48, s49) | (~node7(s48, s49))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4378, 4377])).
% 0.96/1.13 tff(4380,plain,
% 0.96/1.13 (m_main_v_state1(s48, c_c1) | node1(s48) | node2(s48) | node3(s48) | node4(s48) | node5(s48) | node6(s48, s49)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4379, 820, 4376])).
% 0.96/1.13 tff(4381,plain,
% 0.96/1.13 (node6(s48, s49)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4380, 4372, 4296, 4368, 4364, 4360, 4343])).
% 0.96/1.13 tff(4382,plain,
% 0.96/1.13 (((~![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(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)))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4383,plain,
% 0.96/1.13 (((~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)))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4384,plain,
% 0.96/1.13 (((~![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))))),
% 0.96/1.13 inference(monotonicity,[status(thm)],[4383])).
% 0.96/1.13 tff(4385,plain,
% 0.96/1.13 (((~![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)))),
% 0.96/1.13 inference(transitivity,[status(thm)],[4384, 4382])).
% 0.96/1.13 tff(4386,plain,
% 0.96/1.13 ((~![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)))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(4387,plain,
% 0.96/1.13 ((~![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(s48, c_n1) | (~m_main_v_state1(s49, c_n1)) | (~node6(s48, s49))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4386, 4385])).
% 0.96/1.13 tff(4388,plain,
% 0.96/1.13 (~m_main_v_state1(s49, c_n1)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4387, 835, 4288, 4381])).
% 0.96/1.13 tff(4389,plain,
% 0.96/1.13 (((~![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)))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4390,plain,
% 0.96/1.13 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s49, c_n1) | (~node2(s49)))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(4391,plain,
% 0.96/1.13 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s49, c_n1) | (~node2(s49))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4390, 4389])).
% 0.96/1.13 tff(4392,plain,
% 0.96/1.13 (~node2(s49)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4391, 787, 4388])).
% 0.96/1.13 tff(4393,plain,
% 0.96/1.13 (((~![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(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)))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4394,plain,
% 0.96/1.13 (((~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)))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4395,plain,
% 0.96/1.13 (((~![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))))),
% 0.96/1.13 inference(monotonicity,[status(thm)],[4394])).
% 0.96/1.13 tff(4396,plain,
% 0.96/1.13 (((~![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)))),
% 0.96/1.13 inference(transitivity,[status(thm)],[4395, 4393])).
% 0.96/1.13 tff(4397,plain,
% 0.96/1.13 ((~![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))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(4398,plain,
% 0.96/1.13 ((~![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(s48, c_t1)) | m_main_v_state1(s49, c_t1) | (~node6(s48, s49))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4397, 4396])).
% 0.96/1.13 tff(4399,plain,
% 0.96/1.13 (m_main_v_state1(s49, c_t1)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4398, 856, 4284, 4381])).
% 0.96/1.13 tff(4400,plain,
% 0.96/1.13 (((~![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)))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4401,plain,
% 0.96/1.13 ((~![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)))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(4402,plain,
% 0.96/1.13 ((~![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))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4401, 4400])).
% 0.96/1.13 tff(4403,plain,
% 0.96/1.13 (~m_main_v_state2(s49, c_t2)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4402, 77, 4331])).
% 0.96/1.13 tff(4404,plain,
% 0.96/1.13 (((~![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)))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4405,plain,
% 0.96/1.13 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s49, c_t2) | (~node1(s49)))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(4406,plain,
% 0.96/1.13 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s49, c_t2) | (~node1(s49))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4405, 4404])).
% 0.96/1.13 tff(4407,plain,
% 0.96/1.13 (~node1(s49)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4406, 195, 4403])).
% 0.96/1.13 tff(4408,plain,
% 0.96/1.13 (succ(s49, s50) <=> succ(s49, s50)),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4409,axiom,(succ(s49, s50)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound50')).
% 0.96/1.13 tff(4410,plain,
% 0.96/1.13 (succ(s49, s50)),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4409, 4408])).
% 0.96/1.13 tff(4411,plain,
% 0.96/1.13 (((~![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))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4412,plain,
% 0.96/1.13 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s49, s50)) | trans(s49, s50))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(4413,plain,
% 0.96/1.13 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s49, s50)) | trans(s49, s50)),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[4412, 4411])).
% 0.96/1.13 tff(4414,plain,
% 0.96/1.13 (trans(s49, s50)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[4413, 4410, 32])).
% 0.96/1.13 tff(4415,plain,
% 0.96/1.13 (((~![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))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(4416,plain,
% 0.96/1.13 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s49, s50)) | node7(s49, s50))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(4417,plain,
% 0.96/1.14 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s49, s50)) | node7(s49, s50)),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4416, 4415])).
% 0.96/1.14 tff(4418,plain,
% 0.96/1.14 (node7(s49, s50)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4417, 206, 4414])).
% 0.96/1.14 tff(4419,plain,
% 0.96/1.14 (((~![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(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)))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4420,plain,
% 0.96/1.14 (((~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)))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4421,plain,
% 0.96/1.14 (((~![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(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))))),
% 0.96/1.14 inference(monotonicity,[status(thm)],[4420])).
% 0.96/1.14 tff(4422,plain,
% 0.96/1.14 (((~![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(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)))),
% 0.96/1.14 inference(transitivity,[status(thm)],[4421, 4419])).
% 0.96/1.14 tff(4423,plain,
% 0.96/1.14 ((~![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(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))),
% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(4424,plain,
% 0.96/1.14 ((~![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(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))),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4423, 4422])).
% 0.96/1.14 tff(4425,plain,
% 0.96/1.14 ((~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)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4424, 892, 4418])).
% 0.96/1.14 tff(4426,plain,
% 0.96/1.14 (m_main_v_state1(s50, c_c1)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4425, 4407, 4331, 4399, 4392, 4339])).
% 0.96/1.14 tff(4427,plain,
% 0.96/1.14 (((~![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)))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4428,plain,
% 0.96/1.14 ((~![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)))),
% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(4429,plain,
% 0.96/1.14 ((~![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))),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4428, 4427])).
% 0.96/1.14 tff(4430,plain,
% 0.96/1.14 (~m_main_v_state1(s50, c_t1)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4429, 539, 4426])).
% 0.96/1.14 tff(4431,plain,
% 0.96/1.14 (((~![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)))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4432,plain,
% 0.96/1.14 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s50, c_t1) | (~node5(s50)))),
% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(4433,plain,
% 0.96/1.14 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s50, c_t1) | (~node5(s50))),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4432, 4431])).
% 0.96/1.14 tff(4434,plain,
% 0.96/1.14 (~node5(s50)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4433, 550, 4430])).
% 0.96/1.14 tff(4435,plain,
% 0.96/1.14 (((~![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))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4436,plain,
% 0.96/1.14 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s49, s50)) | node14(s49, s50))),
% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(4437,plain,
% 0.96/1.14 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s49, s50)) | node14(s49, s50)),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4436, 4435])).
% 0.96/1.14 tff(4438,plain,
% 0.96/1.14 (node14(s49, s50)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4437, 46, 4414])).
% 0.96/1.14 tff(4439,plain,
% 0.96/1.14 (((~![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))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4440,plain,
% 0.96/1.14 ((~![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))),
% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(4441,plain,
% 0.96/1.14 ((~![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)),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4440, 4439])).
% 0.96/1.14 tff(4442,plain,
% 0.96/1.14 ((~m_main_v_state1(s49, c_t1)) | (~m_main_v_state2(s49, c_n2)) | m_main_v_state2(s50, c_t2)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4441, 922, 4438])).
% 0.96/1.14 tff(4443,plain,
% 0.96/1.14 (m_main_v_state2(s50, c_t2)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4442, 4399, 4331])).
% 0.96/1.14 tff(4444,plain,
% 0.96/1.14 (((~![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)))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4445,plain,
% 0.96/1.14 ((~![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)))),
% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(4446,plain,
% 0.96/1.14 ((~![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))),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4445, 4444])).
% 0.96/1.14 tff(4447,plain,
% 0.96/1.14 (~m_main_v_state2(s50, c_n2)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4446, 77, 4443])).
% 0.96/1.14 tff(4448,plain,
% 0.96/1.14 (((~![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)))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4449,plain,
% 0.96/1.14 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s50, c_n2) | (~node4(s50)))),
% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(4450,plain,
% 0.96/1.14 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s50, c_n2) | (~node4(s50))),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4449, 4448])).
% 0.96/1.14 tff(4451,plain,
% 0.96/1.14 (~node4(s50)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4450, 388, 4447])).
% 0.96/1.14 tff(4452,plain,
% 0.96/1.14 (((~![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)))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4453,plain,
% 0.96/1.14 ((~![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)))),
% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(4454,plain,
% 0.96/1.14 ((~![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))),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4453, 4452])).
% 0.96/1.14 tff(4455,plain,
% 0.96/1.14 (~m_main_v_state2(s50, c_c2)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4454, 260, 4443])).
% 0.96/1.14 tff(4456,plain,
% 0.96/1.14 (((~![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)))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4457,plain,
% 0.96/1.14 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s50, c_c2) | (~node3(s50)))),
% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(4458,plain,
% 0.96/1.14 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s50, c_c2) | (~node3(s50))),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4457, 4456])).
% 0.96/1.14 tff(4459,plain,
% 0.96/1.14 (~node3(s50)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4458, 399, 4455])).
% 0.96/1.14 tff(4460,plain,
% 0.96/1.14 (((~![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)))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4461,plain,
% 0.96/1.14 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s50, c_n2) | (~node2(s50)))),
% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(4462,plain,
% 0.96/1.14 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s50, c_n2) | (~node2(s50))),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4461, 4460])).
% 0.96/1.14 tff(4463,plain,
% 0.96/1.14 (~node2(s50)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4462, 410, 4447])).
% 0.96/1.14 tff(4464,plain,
% 0.96/1.14 (((~![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)))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4465,plain,
% 0.96/1.14 ((~![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)))),
% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(4466,plain,
% 0.96/1.14 ((~![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))),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4465, 4464])).
% 0.96/1.14 tff(4467,plain,
% 0.96/1.14 (~m_main_v_state1(s50, c_n1)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4466, 454, 4426])).
% 0.96/1.14 tff(4468,plain,
% 0.96/1.14 (((~![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)))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4469,plain,
% 0.96/1.14 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s50, c_n1) | (~node1(s50)))),
% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(4470,plain,
% 0.96/1.14 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s50, c_n1) | (~node1(s50))),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4469, 4468])).
% 0.96/1.14 tff(4471,plain,
% 0.96/1.14 (~node1(s50)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4470, 421, 4467])).
% 0.96/1.14 tff(4472,plain,
% 0.96/1.14 (succ(s50, s51) <=> succ(s50, s51)),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4473,axiom,(succ(s50, s51)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound51')).
% 0.96/1.14 tff(4474,plain,
% 0.96/1.14 (succ(s50, s51)),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4473, 4472])).
% 0.96/1.14 tff(4475,plain,
% 0.96/1.14 (((~![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))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4476,plain,
% 0.96/1.14 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s50, s51)) | trans(s50, s51))),
% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(4477,plain,
% 0.96/1.14 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s50, s51)) | trans(s50, s51)),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4476, 4475])).
% 0.96/1.14 tff(4478,plain,
% 0.96/1.14 (trans(s50, s51)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4477, 4474, 32])).
% 0.96/1.14 tff(4479,plain,
% 0.96/1.14 (((~![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))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4480,plain,
% 0.96/1.14 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s50, s51)) | node7(s50, s51))),
% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(4481,plain,
% 0.96/1.14 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s50, s51)) | node7(s50, s51)),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4480, 4479])).
% 0.96/1.14 tff(4482,plain,
% 0.96/1.14 (node7(s50, s51)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4481, 206, 4478])).
% 0.96/1.14 tff(4483,plain,
% 0.96/1.14 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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)))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4484,plain,
% 0.96/1.14 (((~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)))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4485,plain,
% 0.96/1.14 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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))))),
% 0.96/1.14 inference(monotonicity,[status(thm)],[4484])).
% 0.96/1.14 tff(4486,plain,
% 0.96/1.14 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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)))),
% 0.96/1.14 inference(transitivity,[status(thm)],[4485, 4483])).
% 0.96/1.14 tff(4487,plain,
% 0.96/1.14 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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))),
% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(4488,plain,
% 0.96/1.14 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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))),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4487, 4486])).
% 0.96/1.14 tff(4489,plain,
% 0.96/1.14 (m_main_v_state1(s51, c_n1) | (~m_main_v_state1(s50, c_c1)) | node1(s50) | node2(s50) | node3(s50) | node4(s50) | node5(s50)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4488, 584, 4482])).
% 0.96/1.14 tff(4490,plain,
% 0.96/1.14 (m_main_v_state1(s51, c_n1)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4489, 4471, 4426, 4463, 4459, 4451, 4434])).
% 0.96/1.14 tff(4491,plain,
% 0.96/1.14 (((~![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)))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4492,plain,
% 0.96/1.14 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s49, c_t2) | (~node15(s49)))),
% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(4493,plain,
% 0.96/1.14 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s49, c_t2) | (~node15(s49))),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4492, 4491])).
% 0.96/1.14 tff(4494,plain,
% 0.96/1.14 (~node15(s49)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4493, 103, 4403])).
% 0.96/1.14 tff(4495,plain,
% 0.96/1.14 (((~![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))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4496,plain,
% 0.96/1.14 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s49, s50)) | node18(s49, s50))),
% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(4497,plain,
% 0.96/1.14 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s49, s50)) | node18(s49, s50)),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4496, 4495])).
% 0.96/1.14 tff(4498,plain,
% 0.96/1.14 (node18(s49, s50)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4497, 125, 4414])).
% 0.96/1.14 tff(4499,plain,
% 0.96/1.14 (((~![Y: $i, X: $i] : ((~m_main_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))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4500,plain,
% 0.96/1.14 (((~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))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4501,plain,
% 0.96/1.14 (((~![Y: $i, X: $i] : ((~m_main_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)))),
% 0.96/1.14 inference(monotonicity,[status(thm)],[4500])).
% 0.96/1.14 tff(4502,plain,
% 0.96/1.14 (((~![Y: $i, X: $i] : ((~m_main_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))),
% 0.96/1.14 inference(transitivity,[status(thm)],[4501, 4499])).
% 0.96/1.14 tff(4503,plain,
% 0.96/1.14 ((~![Y: $i, X: $i] : ((~m_main_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))),
% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(4504,plain,
% 0.96/1.14 ((~![Y: $i, X: $i] : ((~m_main_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)),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4503, 4502])).
% 0.96/1.14 tff(4505,plain,
% 0.96/1.14 (node15(s49) | (~m_main_v_state1(s49, c_t1)) | (~m_main_v_state2(s49, c_n2)) | m_main_v_turn(s50, c_1)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4504, 992, 4498])).
% 0.96/1.14 tff(4506,plain,
% 0.96/1.14 (m_main_v_turn(s50, c_1)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4505, 4494, 4331, 4399])).
% 0.96/1.14 tff(4507,plain,
% 0.96/1.14 (((~![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)))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4508,plain,
% 0.96/1.14 ((~![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)))),
% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(4509,plain,
% 0.96/1.14 ((~![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))),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4508, 4507])).
% 0.96/1.14 tff(4510,plain,
% 0.96/1.14 (~m_main_v_turn(s50, c_2)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4509, 156, 4506])).
% 0.96/1.14 tff(4511,plain,
% 0.96/1.14 (((~![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)))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4512,plain,
% 0.96/1.14 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s50, c_2) | (~node12(s50)))),
% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(4513,plain,
% 0.96/1.14 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s50, c_2) | (~node12(s50))),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4512, 4511])).
% 0.96/1.14 tff(4514,plain,
% 0.96/1.14 (~node12(s50)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4513, 184, 4510])).
% 0.96/1.14 tff(4515,plain,
% 0.96/1.14 (((~![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)))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4516,plain,
% 0.96/1.14 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s50, c_n2) | (~node8(s50)))),
% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(4517,plain,
% 0.96/1.14 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s50, c_n2) | (~node8(s50))),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4516, 4515])).
% 0.96/1.14 tff(4518,plain,
% 0.96/1.14 (~node8(s50)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4517, 271, 4447])).
% 0.96/1.14 tff(4519,plain,
% 0.96/1.14 (((~![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)))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4520,plain,
% 0.96/1.14 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s50, c_n2) | (~node9(s50)))),
% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(4521,plain,
% 0.96/1.14 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s50, c_n2) | (~node9(s50))),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4520, 4519])).
% 0.96/1.14 tff(4522,plain,
% 0.96/1.14 (~node9(s50)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4521, 88, 4447])).
% 0.96/1.14 tff(4523,plain,
% 0.96/1.14 (((~![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)))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4524,plain,
% 0.96/1.14 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s50, c_n2) | (~node10(s50)))),
% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(4525,plain,
% 0.96/1.14 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s50, c_n2) | (~node10(s50))),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4524, 4523])).
% 0.96/1.14 tff(4526,plain,
% 0.96/1.14 (~node10(s50)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4525, 249, 4447])).
% 0.96/1.14 tff(4527,plain,
% 0.96/1.14 (((~![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)))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4528,plain,
% 0.96/1.14 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s50, c_n1) | (~node11(s50)))),
% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(4529,plain,
% 0.96/1.14 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s50, c_n1) | (~node11(s50))),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4528, 4527])).
% 0.96/1.14 tff(4530,plain,
% 0.96/1.14 (~node11(s50)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4529, 238, 4467])).
% 0.96/1.14 tff(4531,plain,
% 0.96/1.14 (((~![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))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(4532,plain,
% 0.96/1.14 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s50, s51)) | node14(s50, s51))),
% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(4533,plain,
% 0.96/1.14 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s50, s51)) | node14(s50, s51)),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[4532, 4531])).
% 0.96/1.14 tff(4534,plain,
% 0.96/1.14 (node14(s50, s51)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[4533, 46, 4478])).
% 0.96/1.14 tff(4535,plain,
% 0.96/1.14 (((~![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(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)))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4536,plain,
% 0.96/1.15 ((~![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)))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4537,plain,
% 0.96/1.15 ((~![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))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4536, 4535])).
% 0.96/1.15 tff(4538,plain,
% 0.96/1.15 (m_main_v_state2(s50, c_c2) | node9(s50) | node8(s50) | node10(s50) | node11(s50) | node12(s50) | node13(s50, s51)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4537, 296, 4534])).
% 0.96/1.15 tff(4539,plain,
% 0.96/1.15 (node13(s50, s51)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4538, 4530, 4455, 4526, 4522, 4518, 4514])).
% 0.96/1.15 tff(4540,plain,
% 0.96/1.15 (((~![V: $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)))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4541,plain,
% 0.96/1.15 (((~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)))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4542,plain,
% 0.96/1.15 (((~![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))))),
% 0.96/1.15 inference(monotonicity,[status(thm)],[4541])).
% 0.96/1.15 tff(4543,plain,
% 0.96/1.15 (((~![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)))),
% 0.96/1.15 inference(transitivity,[status(thm)],[4542, 4540])).
% 0.96/1.15 tff(4544,plain,
% 0.96/1.15 ((~![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))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4545,plain,
% 0.96/1.15 ((~![V: $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))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4544, 4543])).
% 0.96/1.15 tff(4546,plain,
% 0.96/1.15 (m_main_v_state2(s51, c_t2)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4545, 518, 4443, 4539])).
% 0.96/1.15 tff(4547,plain,
% 0.96/1.15 (succ(s51, s52) <=> succ(s51, s52)),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4548,axiom,(succ(s51, s52)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound52')).
% 0.96/1.15 tff(4549,plain,
% 0.96/1.15 (succ(s51, s52)),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4548, 4547])).
% 0.96/1.15 tff(4550,plain,
% 0.96/1.15 (((~![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))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4551,plain,
% 0.96/1.15 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s51, s52)) | trans(s51, s52))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4552,plain,
% 0.96/1.15 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s51, s52)) | trans(s51, s52)),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4551, 4550])).
% 0.96/1.15 tff(4553,plain,
% 0.96/1.15 (trans(s51, s52)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4552, 4549, 32])).
% 0.96/1.15 tff(4554,plain,
% 0.96/1.15 (((~![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))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4555,plain,
% 0.96/1.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s51, s52)) | node7(s51, s52))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4556,plain,
% 0.96/1.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s51, s52)) | node7(s51, s52)),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4555, 4554])).
% 0.96/1.15 tff(4557,plain,
% 0.96/1.15 (node7(s51, s52)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4556, 206, 4553])).
% 0.96/1.15 tff(4558,plain,
% 0.96/1.15 (((~![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(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))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4559,plain,
% 0.96/1.15 ((~![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(s51, c_n1)) | (~m_main_v_state2(s51, c_t2)) | (~node7(s51, s52)) | m_main_v_state1(s52, c_t1))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4560,plain,
% 0.96/1.15 ((~![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(s51, c_n1)) | (~m_main_v_state2(s51, c_t2)) | (~node7(s51, s52)) | m_main_v_state1(s52, c_t1)),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4559, 4558])).
% 0.96/1.15 tff(4561,plain,
% 0.96/1.15 ((~m_main_v_state1(s51, c_n1)) | (~m_main_v_state2(s51, c_t2)) | m_main_v_state1(s52, c_t1)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4560, 651, 4557])).
% 0.96/1.15 tff(4562,plain,
% 0.96/1.15 (m_main_v_state1(s52, c_t1)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4561, 4546, 4490])).
% 0.96/1.15 tff(4563,plain,
% 0.96/1.15 (((~![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)))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4564,plain,
% 0.96/1.15 ((~![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)))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4565,plain,
% 0.96/1.15 ((~![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))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4564, 4563])).
% 0.96/1.15 tff(4566,plain,
% 0.96/1.15 (~m_main_v_state1(s52, c_n1)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4565, 10, 4562])).
% 0.96/1.15 tff(4567,plain,
% 0.96/1.15 (((~![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)))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4568,plain,
% 0.96/1.15 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s52, c_n1) | (~node1(s52)))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4569,plain,
% 0.96/1.15 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s52, c_n1) | (~node1(s52))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4568, 4567])).
% 0.96/1.15 tff(4570,plain,
% 0.96/1.15 (~node1(s52)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4569, 421, 4566])).
% 0.96/1.15 tff(4571,plain,
% 0.96/1.15 (((~![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))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4572,plain,
% 0.96/1.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s51, s52)) | node18(s51, s52))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4573,plain,
% 0.96/1.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s51, s52)) | node18(s51, s52)),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4572, 4571])).
% 0.96/1.15 tff(4574,plain,
% 0.96/1.15 (node18(s51, s52)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4573, 125, 4553])).
% 0.96/1.15 tff(4575,plain,
% 0.96/1.15 (((~![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(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))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4576,plain,
% 0.96/1.15 ((~![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(s51, c_n1)) | (~m_main_v_state2(s51, c_t2)) | (~node18(s51, s52)) | m_main_v_turn(s52, c_2))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4577,plain,
% 0.96/1.15 ((~![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(s51, c_n1)) | (~m_main_v_state2(s51, c_t2)) | (~node18(s51, s52)) | m_main_v_turn(s52, c_2)),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4576, 4575])).
% 0.96/1.15 tff(4578,plain,
% 0.96/1.15 ((~m_main_v_state1(s51, c_n1)) | (~m_main_v_state2(s51, c_t2)) | m_main_v_turn(s52, c_2)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4577, 760, 4574])).
% 0.96/1.15 tff(4579,plain,
% 0.96/1.15 (m_main_v_turn(s52, c_2)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4578, 4546, 4490])).
% 0.96/1.15 tff(4580,plain,
% 0.96/1.15 (((~![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)))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4581,plain,
% 0.96/1.15 ((~![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)))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4582,plain,
% 0.96/1.15 ((~![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))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4581, 4580])).
% 0.96/1.15 tff(4583,plain,
% 0.96/1.15 (~m_main_v_turn(s52, c_1)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4582, 156, 4579])).
% 0.96/1.15 tff(4584,plain,
% 0.96/1.15 (((~![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)))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4585,plain,
% 0.96/1.15 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s52, c_1) | (~node5(s52)))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4586,plain,
% 0.96/1.15 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s52, c_1) | (~node5(s52))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4585, 4584])).
% 0.96/1.15 tff(4587,plain,
% 0.96/1.15 (~node5(s52)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4586, 776, 4583])).
% 0.96/1.15 tff(4588,plain,
% 0.96/1.15 (((~![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)))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4589,plain,
% 0.96/1.15 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s52, c_n1) | (~node2(s52)))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4590,plain,
% 0.96/1.15 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s52, c_n1) | (~node2(s52))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4589, 4588])).
% 0.96/1.15 tff(4591,plain,
% 0.96/1.15 (~node2(s52)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4590, 787, 4566])).
% 0.96/1.15 tff(4592,plain,
% 0.96/1.15 (((~![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)))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4593,plain,
% 0.96/1.15 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s52, c_n1) | (~node3(s52)))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4594,plain,
% 0.96/1.15 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s52, c_n1) | (~node3(s52))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4593, 4592])).
% 0.96/1.15 tff(4595,plain,
% 0.96/1.15 (~node3(s52)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4594, 798, 4566])).
% 0.96/1.15 tff(4596,plain,
% 0.96/1.15 (((~![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)))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4597,plain,
% 0.96/1.15 ((~![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)))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4598,plain,
% 0.96/1.15 ((~![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))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4597, 4596])).
% 0.96/1.15 tff(4599,plain,
% 0.96/1.15 (~m_main_v_state1(s52, c_c1)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4598, 539, 4562])).
% 0.96/1.15 tff(4600,plain,
% 0.96/1.15 (((~![V: $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)))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4601,plain,
% 0.96/1.15 (((~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)))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4602,plain,
% 0.96/1.15 (((~![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))))),
% 0.96/1.15 inference(monotonicity,[status(thm)],[4601])).
% 0.96/1.15 tff(4603,plain,
% 0.96/1.15 (((~![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)))),
% 0.96/1.15 inference(transitivity,[status(thm)],[4602, 4600])).
% 0.96/1.15 tff(4604,plain,
% 0.96/1.15 ((~![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)))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4605,plain,
% 0.96/1.15 ((~![V: $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))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4604, 4603])).
% 0.96/1.15 tff(4606,plain,
% 0.96/1.15 (~m_main_v_state2(s51, c_n2)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4605, 311, 4447, 4539])).
% 0.96/1.15 tff(4607,plain,
% 0.96/1.15 (((~![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)))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4608,plain,
% 0.96/1.15 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s51, c_n2) | (~node9(s51)))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4609,plain,
% 0.96/1.15 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s51, c_n2) | (~node9(s51))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4608, 4607])).
% 0.96/1.15 tff(4610,plain,
% 0.96/1.15 (~node9(s51)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4609, 88, 4606])).
% 0.96/1.15 tff(4611,plain,
% 0.96/1.15 (((~![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)))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4612,plain,
% 0.96/1.15 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s51, c_n2) | (~node10(s51)))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4613,plain,
% 0.96/1.15 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s51, c_n2) | (~node10(s51))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4612, 4611])).
% 0.96/1.15 tff(4614,plain,
% 0.96/1.15 (~node10(s51)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4613, 249, 4606])).
% 0.96/1.15 tff(4615,plain,
% 0.96/1.15 (((~![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)))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4616,plain,
% 0.96/1.15 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s51, c_n2) | (~node8(s51)))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4617,plain,
% 0.96/1.15 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s51, c_n2) | (~node8(s51))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4616, 4615])).
% 0.96/1.15 tff(4618,plain,
% 0.96/1.15 (~node8(s51)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4617, 271, 4606])).
% 0.96/1.15 tff(4619,plain,
% 0.96/1.15 (((~![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))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4620,plain,
% 0.96/1.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s51, s52)) | node14(s51, s52))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4621,plain,
% 0.96/1.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s51, s52)) | node14(s51, s52)),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4620, 4619])).
% 0.96/1.15 tff(4622,plain,
% 0.96/1.15 (node14(s51, s52)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4621, 46, 4553])).
% 0.96/1.15 tff(4623,plain,
% 0.96/1.15 (((~![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(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))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4624,plain,
% 0.96/1.15 ((~![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(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))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4625,plain,
% 0.96/1.15 ((~![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(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)),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4624, 4623])).
% 0.96/1.15 tff(4626,plain,
% 0.96/1.15 ((~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)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4625, 617, 4622])).
% 0.96/1.15 tff(4627,plain,
% 0.96/1.15 (m_main_v_state2(s52, c_c2)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4626, 4618, 4490, 4546, 4614, 4610])).
% 0.96/1.15 tff(4628,plain,
% 0.96/1.15 (((~![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)))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4629,plain,
% 0.96/1.15 ((~![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)))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4630,plain,
% 0.96/1.15 ((~![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))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4629, 4628])).
% 0.96/1.15 tff(4631,plain,
% 0.96/1.15 (~m_main_v_state2(s52, c_n2)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4630, 697, 4627])).
% 0.96/1.15 tff(4632,plain,
% 0.96/1.15 (((~![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)))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4633,plain,
% 0.96/1.15 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s52, c_n2) | (~node4(s52)))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4634,plain,
% 0.96/1.15 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s52, c_n2) | (~node4(s52))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4633, 4632])).
% 0.96/1.15 tff(4635,plain,
% 0.96/1.15 (~node4(s52)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4634, 388, 4631])).
% 0.96/1.15 tff(4636,plain,
% 0.96/1.15 (succ(s52, s53) <=> succ(s52, s53)),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4637,axiom,(succ(s52, s53)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound53')).
% 0.96/1.15 tff(4638,plain,
% 0.96/1.15 (succ(s52, s53)),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4637, 4636])).
% 0.96/1.15 tff(4639,plain,
% 0.96/1.15 (((~![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))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4640,plain,
% 0.96/1.15 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s52, s53)) | trans(s52, s53))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4641,plain,
% 0.96/1.15 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s52, s53)) | trans(s52, s53)),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4640, 4639])).
% 0.96/1.15 tff(4642,plain,
% 0.96/1.15 (trans(s52, s53)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4641, 4638, 32])).
% 0.96/1.15 tff(4643,plain,
% 0.96/1.15 (((~![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))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4644,plain,
% 0.96/1.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s52, s53)) | node7(s52, s53))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4645,plain,
% 0.96/1.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s52, s53)) | node7(s52, s53)),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4644, 4643])).
% 0.96/1.15 tff(4646,plain,
% 0.96/1.15 (node7(s52, s53)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4645, 206, 4642])).
% 0.96/1.15 tff(4647,plain,
% 0.96/1.15 (((~![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)))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4648,plain,
% 0.96/1.15 ((~![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)))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4649,plain,
% 0.96/1.15 ((~![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))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4648, 4647])).
% 0.96/1.15 tff(4650,plain,
% 0.96/1.15 (m_main_v_state1(s52, c_c1) | node1(s52) | node2(s52) | node3(s52) | node4(s52) | node5(s52) | node6(s52, s53)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4649, 820, 4646])).
% 0.96/1.15 tff(4651,plain,
% 0.96/1.15 (node6(s52, s53)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4650, 4635, 4599, 4595, 4591, 4587, 4570])).
% 0.96/1.15 tff(4652,plain,
% 0.96/1.15 (((~![V: $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)))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4653,plain,
% 0.96/1.15 (((~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)))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4654,plain,
% 0.96/1.15 (((~![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))))),
% 0.96/1.15 inference(monotonicity,[status(thm)],[4653])).
% 0.96/1.15 tff(4655,plain,
% 0.96/1.15 (((~![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)))),
% 0.96/1.15 inference(transitivity,[status(thm)],[4654, 4652])).
% 0.96/1.15 tff(4656,plain,
% 0.96/1.15 ((~![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))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4657,plain,
% 0.96/1.15 ((~![V: $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))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4656, 4655])).
% 0.96/1.15 tff(4658,plain,
% 0.96/1.15 (m_main_v_state1(s53, c_t1)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4657, 856, 4562, 4651])).
% 0.96/1.15 tff(4659,plain,
% 0.96/1.15 (((~![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)))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4660,plain,
% 0.96/1.15 ((~![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)))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4661,plain,
% 0.96/1.15 ((~![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))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4660, 4659])).
% 0.96/1.15 tff(4662,plain,
% 0.96/1.15 (~m_main_v_state2(s52, c_t2)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4661, 260, 4627])).
% 0.96/1.15 tff(4663,plain,
% 0.96/1.15 (((~![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)))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4664,plain,
% 0.96/1.15 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s52, c_t2) | (~node12(s52)))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4665,plain,
% 0.96/1.15 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s52, c_t2) | (~node12(s52))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4664, 4663])).
% 0.96/1.15 tff(4666,plain,
% 0.96/1.15 (~node12(s52)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4665, 633, 4662])).
% 0.96/1.15 tff(4667,plain,
% 0.96/1.15 (((~![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)))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4668,plain,
% 0.96/1.15 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s52, c_n1) | (~node11(s52)))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4669,plain,
% 0.96/1.15 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s52, c_n1) | (~node11(s52))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4668, 4667])).
% 0.96/1.15 tff(4670,plain,
% 0.96/1.15 (~node11(s52)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4669, 238, 4566])).
% 0.96/1.15 tff(4671,plain,
% 0.96/1.15 (((~![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)))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4672,plain,
% 0.96/1.15 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s52, c_c1) | (~node10(s52)))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4673,plain,
% 0.96/1.15 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s52, c_c1) | (~node10(s52))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4672, 4671])).
% 0.96/1.15 tff(4674,plain,
% 0.96/1.15 (~node10(s52)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4673, 675, 4599])).
% 0.96/1.15 tff(4675,plain,
% 0.96/1.15 (((~![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)))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4676,plain,
% 0.96/1.15 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s52, c_n1) | (~node9(s52)))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4677,plain,
% 0.96/1.15 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s52, c_n1) | (~node9(s52))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4676, 4675])).
% 0.96/1.15 tff(4678,plain,
% 0.96/1.15 (~node9(s52)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4677, 686, 4566])).
% 0.96/1.15 tff(4679,plain,
% 0.96/1.15 (((~![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)))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(4680,plain,
% 0.96/1.15 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s52, c_n2) | (~node8(s52)))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(4681,plain,
% 0.96/1.15 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s52, c_n2) | (~node8(s52))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[4680, 4679])).
% 0.96/1.15 tff(4682,plain,
% 0.96/1.15 (~node8(s52)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[4681, 271, 4631])).
% 0.96/1.15 tff(4683,plain,
% 0.96/1.15 (((~![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))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(4684,plain,
% 0.96/1.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s52, s53)) | node14(s52, s53))),
% 0.96/1.16 inference(quant_inst,[status(thm)],[])).
% 0.96/1.16 tff(4685,plain,
% 0.96/1.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s52, s53)) | node14(s52, s53)),
% 0.96/1.16 inference(modus_ponens,[status(thm)],[4684, 4683])).
% 0.96/1.16 tff(4686,plain,
% 0.96/1.16 (node14(s52, s53)),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4685, 46, 4642])).
% 0.96/1.16 tff(4687,plain,
% 0.96/1.16 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | 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)))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(4688,plain,
% 0.96/1.16 (((~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)))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(4689,plain,
% 0.96/1.16 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | 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))))),
% 0.96/1.16 inference(monotonicity,[status(thm)],[4688])).
% 0.96/1.16 tff(4690,plain,
% 0.96/1.16 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | 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)))),
% 0.96/1.16 inference(transitivity,[status(thm)],[4689, 4687])).
% 0.96/1.16 tff(4691,plain,
% 0.96/1.16 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | 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))),
% 0.96/1.16 inference(quant_inst,[status(thm)],[])).
% 0.96/1.16 tff(4692,plain,
% 0.96/1.16 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | 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))),
% 0.96/1.16 inference(modus_ponens,[status(thm)],[4691, 4690])).
% 0.96/1.16 tff(4693,plain,
% 0.96/1.16 (m_main_v_state2(s53, c_n2) | node9(s52) | node8(s52) | node10(s52) | node11(s52) | node12(s52) | (~m_main_v_state2(s52, c_c2))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4692, 726, 4686])).
% 0.96/1.16 tff(4694,plain,
% 0.96/1.16 (m_main_v_state2(s53, c_n2)),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4693, 4682, 4627, 4678, 4674, 4670, 4666])).
% 0.96/1.16 tff(4695,plain,
% 0.96/1.16 (((~![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)))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(4696,plain,
% 0.96/1.16 ((~![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)))),
% 0.96/1.16 inference(quant_inst,[status(thm)],[])).
% 0.96/1.16 tff(4697,plain,
% 0.96/1.16 ((~![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))),
% 0.96/1.16 inference(modus_ponens,[status(thm)],[4696, 4695])).
% 0.96/1.16 tff(4698,plain,
% 0.96/1.16 (~m_main_v_state2(s53, c_t2)),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4697, 77, 4694])).
% 0.96/1.16 tff(4699,plain,
% 0.96/1.16 (((~![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)))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(4700,plain,
% 0.96/1.16 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s53, c_t2) | (~node15(s53)))),
% 0.96/1.16 inference(quant_inst,[status(thm)],[])).
% 0.96/1.16 tff(4701,plain,
% 0.96/1.16 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s53, c_t2) | (~node15(s53))),
% 0.96/1.16 inference(modus_ponens,[status(thm)],[4700, 4699])).
% 0.96/1.16 tff(4702,plain,
% 0.96/1.16 (~node15(s53)),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4701, 103, 4698])).
% 0.96/1.16 tff(4703,plain,
% 0.96/1.16 (succ(s53, s54) <=> succ(s53, s54)),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(4704,axiom,(succ(s53, s54)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound54')).
% 0.96/1.16 tff(4705,plain,
% 0.96/1.16 (succ(s53, s54)),
% 0.96/1.16 inference(modus_ponens,[status(thm)],[4704, 4703])).
% 0.96/1.16 tff(4706,plain,
% 0.96/1.16 (((~![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))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(4707,plain,
% 0.96/1.16 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s53, s54)) | trans(s53, s54))),
% 0.96/1.16 inference(quant_inst,[status(thm)],[])).
% 0.96/1.16 tff(4708,plain,
% 0.96/1.16 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s53, s54)) | trans(s53, s54)),
% 0.96/1.16 inference(modus_ponens,[status(thm)],[4707, 4706])).
% 0.96/1.16 tff(4709,plain,
% 0.96/1.16 (trans(s53, s54)),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4708, 4705, 32])).
% 0.96/1.16 tff(4710,plain,
% 0.96/1.16 (((~![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))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(4711,plain,
% 0.96/1.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s53, s54)) | node18(s53, s54))),
% 0.96/1.16 inference(quant_inst,[status(thm)],[])).
% 0.96/1.16 tff(4712,plain,
% 0.96/1.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s53, s54)) | node18(s53, s54)),
% 0.96/1.16 inference(modus_ponens,[status(thm)],[4711, 4710])).
% 0.96/1.16 tff(4713,plain,
% 0.96/1.16 (node18(s53, s54)),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4712, 125, 4709])).
% 0.96/1.16 tff(4714,plain,
% 0.96/1.16 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(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))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(4715,plain,
% 0.96/1.16 (((~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))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(4716,plain,
% 0.96/1.16 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(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)))),
% 0.96/1.16 inference(monotonicity,[status(thm)],[4715])).
% 0.96/1.16 tff(4717,plain,
% 0.96/1.16 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(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))),
% 0.96/1.16 inference(transitivity,[status(thm)],[4716, 4714])).
% 0.96/1.16 tff(4718,plain,
% 0.96/1.16 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | node15(s53) | (~node18(s53, s54)) | m_main_v_turn(s54, c_1))),
% 0.96/1.16 inference(quant_inst,[status(thm)],[])).
% 0.96/1.16 tff(4719,plain,
% 0.96/1.16 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(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)),
% 0.96/1.16 inference(modus_ponens,[status(thm)],[4718, 4717])).
% 0.96/1.16 tff(4720,plain,
% 0.96/1.16 (node15(s53) | (~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | m_main_v_turn(s54, c_1)),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4719, 992, 4713])).
% 0.96/1.16 tff(4721,plain,
% 0.96/1.16 (m_main_v_turn(s54, c_1)),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4720, 4702, 4694, 4658])).
% 0.96/1.16 tff(4722,plain,
% 0.96/1.16 (((~![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)))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(4723,plain,
% 0.96/1.16 ((~![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)))),
% 0.96/1.16 inference(quant_inst,[status(thm)],[])).
% 0.96/1.16 tff(4724,plain,
% 0.96/1.16 ((~![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))),
% 0.96/1.16 inference(modus_ponens,[status(thm)],[4723, 4722])).
% 0.96/1.16 tff(4725,plain,
% 0.96/1.16 (~m_main_v_turn(s54, c_2)),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4724, 156, 4721])).
% 0.96/1.16 tff(4726,plain,
% 0.96/1.16 (((~![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)))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(4727,plain,
% 0.96/1.16 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s54, c_2) | (~node12(s54)))),
% 0.96/1.16 inference(quant_inst,[status(thm)],[])).
% 0.96/1.16 tff(4728,plain,
% 0.96/1.16 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s54, c_2) | (~node12(s54))),
% 0.96/1.16 inference(modus_ponens,[status(thm)],[4727, 4726])).
% 0.96/1.16 tff(4729,plain,
% 0.96/1.16 (~node12(s54)),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4728, 184, 4725])).
% 0.96/1.16 tff(4730,plain,
% 0.96/1.16 (((~![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))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(4731,plain,
% 0.96/1.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s53, s54)) | node14(s53, s54))),
% 0.96/1.16 inference(quant_inst,[status(thm)],[])).
% 0.96/1.16 tff(4732,plain,
% 0.96/1.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s53, s54)) | node14(s53, s54)),
% 0.96/1.16 inference(modus_ponens,[status(thm)],[4731, 4730])).
% 0.96/1.16 tff(4733,plain,
% 0.96/1.16 (node14(s53, s54)),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4732, 46, 4709])).
% 0.96/1.16 tff(4734,plain,
% 0.96/1.16 (((~![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(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))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(4735,plain,
% 0.96/1.16 ((~![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(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | (~node14(s53, s54)) | m_main_v_state2(s54, c_t2))),
% 0.96/1.16 inference(quant_inst,[status(thm)],[])).
% 0.96/1.16 tff(4736,plain,
% 0.96/1.16 ((~![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(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | (~node14(s53, s54)) | m_main_v_state2(s54, c_t2)),
% 0.96/1.16 inference(modus_ponens,[status(thm)],[4735, 4734])).
% 0.96/1.16 tff(4737,plain,
% 0.96/1.16 ((~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | m_main_v_state2(s54, c_t2)),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4736, 922, 4733])).
% 0.96/1.16 tff(4738,plain,
% 0.96/1.16 (m_main_v_state2(s54, c_t2)),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4737, 4658, 4694])).
% 0.96/1.16 tff(4739,plain,
% 0.96/1.16 (((~![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)))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(4740,plain,
% 0.96/1.16 ((~![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)))),
% 0.96/1.16 inference(quant_inst,[status(thm)],[])).
% 0.96/1.16 tff(4741,plain,
% 0.96/1.16 ((~![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))),
% 0.96/1.16 inference(modus_ponens,[status(thm)],[4740, 4739])).
% 0.96/1.16 tff(4742,plain,
% 0.96/1.16 (~m_main_v_state2(s54, c_n2)),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4741, 77, 4738])).
% 0.96/1.16 tff(4743,plain,
% 0.96/1.16 (((~![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)))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(4744,plain,
% 0.96/1.16 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s54, c_n2) | (~node8(s54)))),
% 0.96/1.16 inference(quant_inst,[status(thm)],[])).
% 0.96/1.16 tff(4745,plain,
% 0.96/1.16 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s54, c_n2) | (~node8(s54))),
% 0.96/1.16 inference(modus_ponens,[status(thm)],[4744, 4743])).
% 0.96/1.16 tff(4746,plain,
% 0.96/1.16 (~node8(s54)),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4745, 271, 4742])).
% 0.96/1.16 tff(4747,plain,
% 0.96/1.16 (((~![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)))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(4748,plain,
% 0.96/1.16 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s54, c_n2) | (~node9(s54)))),
% 1.00/1.16 inference(quant_inst,[status(thm)],[])).
% 1.00/1.16 tff(4749,plain,
% 1.00/1.16 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s54, c_n2) | (~node9(s54))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[4748, 4747])).
% 1.00/1.16 tff(4750,plain,
% 1.00/1.16 (~node9(s54)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[4749, 88, 4742])).
% 1.00/1.16 tff(4751,plain,
% 1.00/1.16 (((~![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)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(4752,plain,
% 1.00/1.16 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s54, c_n2) | (~node10(s54)))),
% 1.00/1.16 inference(quant_inst,[status(thm)],[])).
% 1.00/1.16 tff(4753,plain,
% 1.00/1.16 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s54, c_n2) | (~node10(s54))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[4752, 4751])).
% 1.00/1.16 tff(4754,plain,
% 1.00/1.16 (~node10(s54)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[4753, 249, 4742])).
% 1.00/1.16 tff(4755,plain,
% 1.00/1.16 (((~![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)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(4756,plain,
% 1.00/1.16 ((~![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)))),
% 1.00/1.16 inference(quant_inst,[status(thm)],[])).
% 1.00/1.16 tff(4757,plain,
% 1.00/1.16 ((~![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))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[4756, 4755])).
% 1.00/1.16 tff(4758,plain,
% 1.00/1.16 (~m_main_v_state2(s54, c_c2)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[4757, 260, 4738])).
% 1.00/1.16 tff(4759,plain,
% 1.00/1.16 (((~![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)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(4760,plain,
% 1.00/1.16 ((~![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)))),
% 1.00/1.16 inference(quant_inst,[status(thm)],[])).
% 1.00/1.16 tff(4761,plain,
% 1.00/1.16 ((~![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))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[4760, 4759])).
% 1.00/1.16 tff(4762,plain,
% 1.00/1.16 (~m_main_v_state2(s53, c_c2)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[4761, 697, 4694])).
% 1.00/1.16 tff(4763,plain,
% 1.00/1.16 (((~![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)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(4764,plain,
% 1.00/1.16 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s53, c_c2) | (~node3(s53)))),
% 1.00/1.16 inference(quant_inst,[status(thm)],[])).
% 1.00/1.16 tff(4765,plain,
% 1.00/1.16 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s53, c_c2) | (~node3(s53))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[4764, 4763])).
% 1.00/1.16 tff(4766,plain,
% 1.00/1.16 (~node3(s53)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[4765, 399, 4762])).
% 1.00/1.16 tff(4767,plain,
% 1.00/1.16 (((~![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(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)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(4768,plain,
% 1.00/1.16 (((~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)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(4769,plain,
% 1.00/1.16 (((~![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))))),
% 1.00/1.16 inference(monotonicity,[status(thm)],[4768])).
% 1.00/1.16 tff(4770,plain,
% 1.00/1.16 (((~![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)))),
% 1.00/1.16 inference(transitivity,[status(thm)],[4769, 4767])).
% 1.00/1.16 tff(4771,plain,
% 1.00/1.16 ((~![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)))),
% 1.00/1.16 inference(quant_inst,[status(thm)],[])).
% 1.00/1.16 tff(4772,plain,
% 1.00/1.16 ((~![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(s52, c_n1) | (~m_main_v_state1(s53, c_n1)) | (~node6(s52, s53))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[4771, 4770])).
% 1.00/1.16 tff(4773,plain,
% 1.00/1.16 (~m_main_v_state1(s53, c_n1)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[4772, 835, 4566, 4651])).
% 1.00/1.16 tff(4774,plain,
% 1.00/1.16 (((~![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)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(4775,plain,
% 1.00/1.16 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s53, c_n1) | (~node2(s53)))),
% 1.00/1.16 inference(quant_inst,[status(thm)],[])).
% 1.00/1.16 tff(4776,plain,
% 1.00/1.16 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s53, c_n1) | (~node2(s53))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[4775, 4774])).
% 1.00/1.16 tff(4777,plain,
% 1.00/1.16 (~node2(s53)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[4776, 787, 4773])).
% 1.00/1.16 tff(4778,plain,
% 1.00/1.16 (((~![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)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(4779,plain,
% 1.00/1.16 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s53, c_t2) | (~node1(s53)))),
% 1.00/1.16 inference(quant_inst,[status(thm)],[])).
% 1.00/1.16 tff(4780,plain,
% 1.00/1.16 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s53, c_t2) | (~node1(s53))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[4779, 4778])).
% 1.00/1.16 tff(4781,plain,
% 1.00/1.16 (~node1(s53)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[4780, 195, 4698])).
% 1.00/1.16 tff(4782,plain,
% 1.00/1.16 (((~![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))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(4783,plain,
% 1.00/1.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s53, s54)) | node7(s53, s54))),
% 1.00/1.16 inference(quant_inst,[status(thm)],[])).
% 1.00/1.16 tff(4784,plain,
% 1.00/1.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s53, s54)) | node7(s53, s54)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[4783, 4782])).
% 1.00/1.16 tff(4785,plain,
% 1.00/1.16 (node7(s53, s54)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[4784, 206, 4709])).
% 1.00/1.16 tff(4786,plain,
% 1.00/1.16 (((~![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(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)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(4787,plain,
% 1.00/1.16 (((~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)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(4788,plain,
% 1.00/1.16 (((~![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(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))))),
% 1.00/1.16 inference(monotonicity,[status(thm)],[4787])).
% 1.00/1.16 tff(4789,plain,
% 1.00/1.16 (((~![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(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)))),
% 1.00/1.16 inference(transitivity,[status(thm)],[4788, 4786])).
% 1.00/1.16 tff(4790,plain,
% 1.00/1.16 ((~![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(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))),
% 1.00/1.16 inference(quant_inst,[status(thm)],[])).
% 1.00/1.16 tff(4791,plain,
% 1.00/1.16 ((~![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(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))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[4790, 4789])).
% 1.00/1.16 tff(4792,plain,
% 1.00/1.16 ((~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)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[4791, 892, 4785])).
% 1.00/1.16 tff(4793,plain,
% 1.00/1.16 (m_main_v_state1(s54, c_c1)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[4792, 4781, 4694, 4658, 4777, 4766])).
% 1.00/1.16 tff(4794,plain,
% 1.00/1.16 (((~![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)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(4795,plain,
% 1.00/1.16 ((~![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)))),
% 1.00/1.16 inference(quant_inst,[status(thm)],[])).
% 1.00/1.16 tff(4796,plain,
% 1.00/1.16 ((~![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))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[4795, 4794])).
% 1.00/1.17 tff(4797,plain,
% 1.00/1.17 (~m_main_v_state1(s54, c_n1)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[4796, 454, 4793])).
% 1.00/1.17 tff(4798,plain,
% 1.00/1.17 (((~![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)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(4799,plain,
% 1.00/1.17 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s54, c_n1) | (~node11(s54)))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(4800,plain,
% 1.00/1.17 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s54, c_n1) | (~node11(s54))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[4799, 4798])).
% 1.00/1.17 tff(4801,plain,
% 1.00/1.17 (~node11(s54)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[4800, 238, 4797])).
% 1.00/1.17 tff(4802,plain,
% 1.00/1.17 (succ(s54, s55) <=> succ(s54, s55)),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(4803,axiom,(succ(s54, s55)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound55')).
% 1.00/1.17 tff(4804,plain,
% 1.00/1.17 (succ(s54, s55)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[4803, 4802])).
% 1.00/1.17 tff(4805,plain,
% 1.00/1.17 (((~![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))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(4806,plain,
% 1.00/1.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s54, s55)) | trans(s54, s55))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(4807,plain,
% 1.00/1.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s54, s55)) | trans(s54, s55)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[4806, 4805])).
% 1.00/1.17 tff(4808,plain,
% 1.00/1.17 (trans(s54, s55)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[4807, 4804, 32])).
% 1.00/1.17 tff(4809,plain,
% 1.00/1.17 (((~![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))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(4810,plain,
% 1.00/1.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s54, s55)) | node14(s54, s55))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(4811,plain,
% 1.00/1.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s54, s55)) | node14(s54, s55)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[4810, 4809])).
% 1.00/1.17 tff(4812,plain,
% 1.00/1.17 (node14(s54, s55)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[4811, 46, 4808])).
% 1.00/1.17 tff(4813,plain,
% 1.00/1.17 (((~![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(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)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(4814,plain,
% 1.00/1.17 ((~![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(s54, c_c2) | node9(s54) | node8(s54) | node10(s54) | node11(s54) | node12(s54) | node13(s54, s55) | (~node14(s54, s55)))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(4815,plain,
% 1.00/1.17 ((~![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(s54, c_c2) | node9(s54) | node8(s54) | node10(s54) | node11(s54) | node12(s54) | node13(s54, s55) | (~node14(s54, s55))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[4814, 4813])).
% 1.00/1.17 tff(4816,plain,
% 1.00/1.17 (m_main_v_state2(s54, c_c2) | node9(s54) | node8(s54) | node10(s54) | node11(s54) | node12(s54) | node13(s54, s55)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[4815, 296, 4812])).
% 1.00/1.17 tff(4817,plain,
% 1.00/1.17 (node13(s54, s55)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[4816, 4801, 4758, 4754, 4750, 4746, 4729])).
% 1.00/1.17 tff(4818,plain,
% 1.00/1.17 (((~![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(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)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(4819,plain,
% 1.00/1.17 (((~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)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(4820,plain,
% 1.00/1.17 (((~![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))))),
% 1.00/1.17 inference(monotonicity,[status(thm)],[4819])).
% 1.00/1.17 tff(4821,plain,
% 1.00/1.17 (((~![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)))),
% 1.00/1.17 inference(transitivity,[status(thm)],[4820, 4818])).
% 1.00/1.17 tff(4822,plain,
% 1.00/1.17 ((~![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)))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(4823,plain,
% 1.00/1.17 ((~![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(s54, c_n2) | (~m_main_v_state2(s55, c_n2)) | (~node13(s54, s55))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[4822, 4821])).
% 1.00/1.17 tff(4824,plain,
% 1.00/1.17 (~m_main_v_state2(s55, c_n2)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[4823, 311, 4742, 4817])).
% 1.00/1.17 tff(4825,plain,
% 1.00/1.17 (((~![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)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(4826,plain,
% 1.00/1.17 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s55, c_n2) | (~node9(s55)))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(4827,plain,
% 1.00/1.17 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s55, c_n2) | (~node9(s55))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[4826, 4825])).
% 1.00/1.17 tff(4828,plain,
% 1.00/1.17 (~node9(s55)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[4827, 88, 4824])).
% 1.00/1.17 tff(4829,plain,
% 1.00/1.17 (((~![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)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(4830,plain,
% 1.00/1.17 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s55, c_n2) | (~node10(s55)))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(4831,plain,
% 1.00/1.17 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s55, c_n2) | (~node10(s55))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[4830, 4829])).
% 1.00/1.17 tff(4832,plain,
% 1.00/1.17 (~node10(s55)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[4831, 249, 4824])).
% 1.00/1.17 tff(4833,plain,
% 1.00/1.17 (((~![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(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)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(4834,plain,
% 1.00/1.17 (((~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)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(4835,plain,
% 1.00/1.17 (((~![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))))),
% 1.00/1.17 inference(monotonicity,[status(thm)],[4834])).
% 1.00/1.17 tff(4836,plain,
% 1.00/1.17 (((~![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)))),
% 1.00/1.17 inference(transitivity,[status(thm)],[4835, 4833])).
% 1.00/1.17 tff(4837,plain,
% 1.00/1.17 ((~![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))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(4838,plain,
% 1.00/1.17 ((~![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(s54, c_t2)) | m_main_v_state2(s55, c_t2) | (~node13(s54, s55))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[4837, 4836])).
% 1.00/1.17 tff(4839,plain,
% 1.00/1.17 (m_main_v_state2(s55, c_t2)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[4838, 518, 4738, 4817])).
% 1.00/1.17 tff(4840,plain,
% 1.00/1.17 (((~![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)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(4841,plain,
% 1.00/1.17 ((~![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)))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(4842,plain,
% 1.00/1.17 ((~![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))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[4841, 4840])).
% 1.00/1.17 tff(4843,plain,
% 1.00/1.17 (~m_main_v_state1(s54, c_t1)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[4842, 539, 4793])).
% 1.00/1.17 tff(4844,plain,
% 1.00/1.17 (((~![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)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(4845,plain,
% 1.00/1.17 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s54, c_t1) | (~node5(s54)))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(4846,plain,
% 1.00/1.17 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s54, c_t1) | (~node5(s54))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[4845, 4844])).
% 1.00/1.17 tff(4847,plain,
% 1.00/1.17 (~node5(s54)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[4846, 550, 4843])).
% 1.00/1.17 tff(4848,plain,
% 1.00/1.17 (((~![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)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(4849,plain,
% 1.00/1.17 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s54, c_n2) | (~node4(s54)))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(4850,plain,
% 1.00/1.17 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s54, c_n2) | (~node4(s54))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[4849, 4848])).
% 1.00/1.17 tff(4851,plain,
% 1.00/1.17 (~node4(s54)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[4850, 388, 4742])).
% 1.00/1.17 tff(4852,plain,
% 1.00/1.17 (((~![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)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(4853,plain,
% 1.00/1.17 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s54, c_c2) | (~node3(s54)))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(4854,plain,
% 1.00/1.17 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s54, c_c2) | (~node3(s54))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[4853, 4852])).
% 1.00/1.17 tff(4855,plain,
% 1.00/1.17 (~node3(s54)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[4854, 399, 4758])).
% 1.00/1.17 tff(4856,plain,
% 1.00/1.17 (((~![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)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(4857,plain,
% 1.00/1.17 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s54, c_n2) | (~node2(s54)))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(4858,plain,
% 1.00/1.17 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s54, c_n2) | (~node2(s54))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[4857, 4856])).
% 1.00/1.17 tff(4859,plain,
% 1.00/1.17 (~node2(s54)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[4858, 410, 4742])).
% 1.00/1.17 tff(4860,plain,
% 1.00/1.17 (((~![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)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(4861,plain,
% 1.00/1.17 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s54, c_n1) | (~node1(s54)))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(4862,plain,
% 1.00/1.17 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s54, c_n1) | (~node1(s54))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[4861, 4860])).
% 1.00/1.17 tff(4863,plain,
% 1.00/1.17 (~node1(s54)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[4862, 421, 4797])).
% 1.00/1.17 tff(4864,plain,
% 1.00/1.17 (((~![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))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(4865,plain,
% 1.00/1.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s54, s55)) | node7(s54, s55))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(4866,plain,
% 1.00/1.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s54, s55)) | node7(s54, s55)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[4865, 4864])).
% 1.00/1.17 tff(4867,plain,
% 1.00/1.17 (node7(s54, s55)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[4866, 206, 4808])).
% 1.00/1.17 tff(4868,plain,
% 1.00/1.17 (((~![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(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)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(4869,plain,
% 1.00/1.17 (((~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)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(4870,plain,
% 1.00/1.17 (((~![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(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))))),
% 1.00/1.17 inference(monotonicity,[status(thm)],[4869])).
% 1.00/1.17 tff(4871,plain,
% 1.00/1.17 (((~![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(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)))),
% 1.00/1.17 inference(transitivity,[status(thm)],[4870, 4868])).
% 1.00/1.17 tff(4872,plain,
% 1.00/1.17 ((~![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(s54, c_c1)) | node1(s54) | node2(s54) | node3(s54) | node4(s54) | node5(s54) | (~node7(s54, s55)) | m_main_v_state1(s55, c_n1))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(4873,plain,
% 1.00/1.17 ((~![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(s55, c_n1) | (~m_main_v_state1(s54, c_c1)) | node1(s54) | node2(s54) | node3(s54) | node4(s54) | node5(s54) | (~node7(s54, s55))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[4872, 4871])).
% 1.00/1.17 tff(4874,plain,
% 1.00/1.17 (m_main_v_state1(s55, c_n1) | (~m_main_v_state1(s54, c_c1)) | node1(s54) | node2(s54) | node3(s54) | node4(s54) | node5(s54)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[4873, 584, 4867])).
% 1.00/1.17 tff(4875,plain,
% 1.00/1.17 (m_main_v_state1(s55, c_n1)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[4874, 4863, 4793, 4859, 4855, 4851, 4847])).
% 1.00/1.17 tff(4876,plain,
% 1.00/1.17 (((~![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)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(4877,plain,
% 1.00/1.17 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s55, c_n2) | (~node8(s55)))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(4878,plain,
% 1.00/1.17 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s55, c_n2) | (~node8(s55))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[4877, 4876])).
% 1.00/1.17 tff(4879,plain,
% 1.00/1.17 (~node8(s55)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[4878, 271, 4824])).
% 1.00/1.17 tff(4880,plain,
% 1.00/1.17 (succ(s55, s56) <=> succ(s55, s56)),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(4881,axiom,(succ(s55, s56)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound56')).
% 1.00/1.17 tff(4882,plain,
% 1.00/1.17 (succ(s55, s56)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[4881, 4880])).
% 1.00/1.17 tff(4883,plain,
% 1.00/1.17 (((~![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))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(4884,plain,
% 1.00/1.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s55, s56)) | trans(s55, s56))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(4885,plain,
% 1.00/1.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s55, s56)) | trans(s55, s56)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[4884, 4883])).
% 1.00/1.17 tff(4886,plain,
% 1.00/1.17 (trans(s55, s56)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[4885, 4882, 32])).
% 1.00/1.17 tff(4887,plain,
% 1.00/1.17 (((~![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))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(4888,plain,
% 1.00/1.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s55, s56)) | node14(s55, s56))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(4889,plain,
% 1.00/1.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s55, s56)) | node14(s55, s56)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[4888, 4887])).
% 1.00/1.17 tff(4890,plain,
% 1.00/1.17 (node14(s55, s56)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[4889, 46, 4886])).
% 1.00/1.17 tff(4891,plain,
% 1.00/1.17 (((~![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))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(4892,plain,
% 1.00/1.17 ((~![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))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(4893,plain,
% 1.00/1.17 ((~![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)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[4892, 4891])).
% 1.00/1.17 tff(4894,plain,
% 1.00/1.17 ((~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)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[4893, 617, 4890])).
% 1.00/1.17 tff(4895,plain,
% 1.00/1.17 (m_main_v_state2(s56, c_c2)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[4894, 4879, 4875, 4839, 4832, 4828])).
% 1.00/1.17 tff(4896,plain,
% 1.00/1.17 (((~![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)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(4897,plain,
% 1.00/1.17 ((~![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)))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(4898,plain,
% 1.00/1.17 ((~![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))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[4897, 4896])).
% 1.00/1.17 tff(4899,plain,
% 1.00/1.17 (~m_main_v_state2(s56, c_t2)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[4898, 260, 4895])).
% 1.00/1.17 tff(4900,plain,
% 1.00/1.17 (((~![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)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(4901,plain,
% 1.00/1.17 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s56, c_t2) | (~node12(s56)))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(4902,plain,
% 1.00/1.17 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s56, c_t2) | (~node12(s56))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[4901, 4900])).
% 1.00/1.17 tff(4903,plain,
% 1.00/1.17 (~node12(s56)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[4902, 633, 4899])).
% 1.00/1.17 tff(4904,plain,
% 1.00/1.17 (((~![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))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(4905,plain,
% 1.00/1.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s55, s56)) | node7(s55, s56))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(4906,plain,
% 1.00/1.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s55, s56)) | node7(s55, s56)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[4905, 4904])).
% 1.00/1.17 tff(4907,plain,
% 1.00/1.17 (node7(s55, s56)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[4906, 206, 4886])).
% 1.00/1.17 tff(4908,plain,
% 1.00/1.17 (((~![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(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))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(4909,plain,
% 1.00/1.17 ((~![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(s55, c_n1)) | (~m_main_v_state2(s55, c_t2)) | (~node7(s55, s56)) | m_main_v_state1(s56, c_t1))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(4910,plain,
% 1.00/1.17 ((~![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(s55, c_n1)) | (~m_main_v_state2(s55, c_t2)) | (~node7(s55, s56)) | m_main_v_state1(s56, c_t1)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[4909, 4908])).
% 1.00/1.17 tff(4911,plain,
% 1.00/1.17 ((~m_main_v_state1(s55, c_n1)) | (~m_main_v_state2(s55, c_t2)) | m_main_v_state1(s56, c_t1)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[4910, 651, 4907])).
% 1.00/1.17 tff(4912,plain,
% 1.00/1.17 (m_main_v_state1(s56, c_t1)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[4911, 4839, 4875])).
% 1.00/1.17 tff(4913,plain,
% 1.00/1.17 (((~![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)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(4914,plain,
% 1.00/1.17 ((~![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)))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(4915,plain,
% 1.00/1.17 ((~![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))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[4914, 4913])).
% 1.00/1.17 tff(4916,plain,
% 1.00/1.17 (~m_main_v_state1(s56, c_n1)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[4915, 10, 4912])).
% 1.00/1.17 tff(4917,plain,
% 1.00/1.17 (((~![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)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(4918,plain,
% 1.00/1.17 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s56, c_n1) | (~node11(s56)))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(4919,plain,
% 1.00/1.17 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s56, c_n1) | (~node11(s56))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[4918, 4917])).
% 1.00/1.17 tff(4920,plain,
% 1.00/1.17 (~node11(s56)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[4919, 238, 4916])).
% 1.00/1.17 tff(4921,plain,
% 1.00/1.17 (((~![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)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(4922,plain,
% 1.00/1.18 ((~![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)))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(4923,plain,
% 1.00/1.18 ((~![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))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[4922, 4921])).
% 1.00/1.18 tff(4924,plain,
% 1.00/1.18 (~m_main_v_state1(s56, c_c1)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[4923, 539, 4912])).
% 1.00/1.18 tff(4925,plain,
% 1.00/1.18 (((~![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)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(4926,plain,
% 1.00/1.18 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s56, c_c1) | (~node10(s56)))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(4927,plain,
% 1.00/1.18 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s56, c_c1) | (~node10(s56))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[4926, 4925])).
% 1.00/1.18 tff(4928,plain,
% 1.00/1.18 (~node10(s56)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[4927, 675, 4924])).
% 1.00/1.18 tff(4929,plain,
% 1.00/1.18 (((~![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)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(4930,plain,
% 1.00/1.18 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s56, c_n1) | (~node9(s56)))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(4931,plain,
% 1.00/1.18 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s56, c_n1) | (~node9(s56))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[4930, 4929])).
% 1.00/1.18 tff(4932,plain,
% 1.00/1.18 (~node9(s56)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[4931, 686, 4916])).
% 1.00/1.18 tff(4933,plain,
% 1.00/1.18 (((~![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)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(4934,plain,
% 1.00/1.18 ((~![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)))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(4935,plain,
% 1.00/1.18 ((~![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))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[4934, 4933])).
% 1.00/1.18 tff(4936,plain,
% 1.00/1.18 (~m_main_v_state2(s56, c_n2)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[4935, 697, 4895])).
% 1.00/1.18 tff(4937,plain,
% 1.00/1.18 (((~![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)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(4938,plain,
% 1.00/1.18 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s56, c_n2) | (~node8(s56)))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(4939,plain,
% 1.00/1.18 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s56, c_n2) | (~node8(s56))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[4938, 4937])).
% 1.00/1.18 tff(4940,plain,
% 1.00/1.18 (~node8(s56)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[4939, 271, 4936])).
% 1.00/1.18 tff(4941,plain,
% 1.00/1.18 (succ(s56, s57) <=> succ(s56, s57)),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(4942,axiom,(succ(s56, s57)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound57')).
% 1.00/1.18 tff(4943,plain,
% 1.00/1.18 (succ(s56, s57)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[4942, 4941])).
% 1.00/1.18 tff(4944,plain,
% 1.00/1.18 (((~![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))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(4945,plain,
% 1.00/1.18 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s56, s57)) | trans(s56, s57))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(4946,plain,
% 1.00/1.18 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s56, s57)) | trans(s56, s57)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[4945, 4944])).
% 1.00/1.18 tff(4947,plain,
% 1.00/1.18 (trans(s56, s57)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[4946, 4943, 32])).
% 1.00/1.18 tff(4948,plain,
% 1.00/1.18 (((~![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))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(4949,plain,
% 1.00/1.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s56, s57)) | node14(s56, s57))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(4950,plain,
% 1.00/1.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s56, s57)) | node14(s56, s57)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[4949, 4948])).
% 1.00/1.18 tff(4951,plain,
% 1.00/1.18 (node14(s56, s57)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[4950, 46, 4947])).
% 1.00/1.18 tff(4952,plain,
% 1.00/1.18 (((~![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(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)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(4953,plain,
% 1.00/1.18 (((~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)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(4954,plain,
% 1.00/1.18 (((~![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(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))))),
% 1.00/1.18 inference(monotonicity,[status(thm)],[4953])).
% 1.00/1.18 tff(4955,plain,
% 1.00/1.18 (((~![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(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)))),
% 1.00/1.18 inference(transitivity,[status(thm)],[4954, 4952])).
% 1.00/1.18 tff(4956,plain,
% 1.00/1.18 ((~![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(s56, c_c2)) | node9(s56) | node8(s56) | node10(s56) | node11(s56) | node12(s56) | (~node14(s56, s57)) | m_main_v_state2(s57, c_n2))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(4957,plain,
% 1.00/1.18 ((~![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(s57, c_n2) | node9(s56) | node8(s56) | node10(s56) | node11(s56) | node12(s56) | (~node14(s56, s57)) | (~m_main_v_state2(s56, c_c2))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[4956, 4955])).
% 1.00/1.18 tff(4958,plain,
% 1.00/1.18 (m_main_v_state2(s57, c_n2) | node9(s56) | node8(s56) | node10(s56) | node11(s56) | node12(s56) | (~m_main_v_state2(s56, c_c2))),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[4957, 726, 4951])).
% 1.00/1.18 tff(4959,plain,
% 1.00/1.18 (m_main_v_state2(s57, c_n2)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[4958, 4940, 4895, 4932, 4928, 4920, 4903])).
% 1.00/1.18 tff(4960,plain,
% 1.00/1.18 (((~![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)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(4961,plain,
% 1.00/1.18 ((~![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)))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(4962,plain,
% 1.00/1.18 ((~![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))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[4961, 4960])).
% 1.00/1.18 tff(4963,plain,
% 1.00/1.18 (~m_main_v_state2(s57, c_c2)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[4962, 697, 4959])).
% 1.00/1.18 tff(4964,plain,
% 1.00/1.18 (((~![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)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(4965,plain,
% 1.00/1.18 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s57, c_c2) | (~node3(s57)))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(4966,plain,
% 1.00/1.18 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s57, c_c2) | (~node3(s57))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[4965, 4964])).
% 1.00/1.18 tff(4967,plain,
% 1.00/1.18 (~node3(s57)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[4966, 399, 4963])).
% 1.00/1.18 tff(4968,plain,
% 1.00/1.18 (((~![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)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(4969,plain,
% 1.00/1.18 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s56, c_n1) | (~node1(s56)))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(4970,plain,
% 1.00/1.18 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s56, c_n1) | (~node1(s56))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[4969, 4968])).
% 1.00/1.18 tff(4971,plain,
% 1.00/1.18 (~node1(s56)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[4970, 421, 4916])).
% 1.00/1.18 tff(4972,plain,
% 1.00/1.18 (((~![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))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(4973,plain,
% 1.00/1.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s55, s56)) | node18(s55, s56))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(4974,plain,
% 1.00/1.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s55, s56)) | node18(s55, s56)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[4973, 4972])).
% 1.00/1.18 tff(4975,plain,
% 1.00/1.18 (node18(s55, s56)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[4974, 125, 4886])).
% 1.00/1.18 tff(4976,plain,
% 1.00/1.18 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(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))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(4977,plain,
% 1.00/1.18 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s55, c_n1)) | (~m_main_v_state2(s55, c_t2)) | (~node18(s55, s56)) | m_main_v_turn(s56, c_2))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(4978,plain,
% 1.00/1.18 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s55, c_n1)) | (~m_main_v_state2(s55, c_t2)) | (~node18(s55, s56)) | m_main_v_turn(s56, c_2)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[4977, 4976])).
% 1.00/1.18 tff(4979,plain,
% 1.00/1.18 ((~m_main_v_state1(s55, c_n1)) | (~m_main_v_state2(s55, c_t2)) | m_main_v_turn(s56, c_2)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[4978, 760, 4975])).
% 1.00/1.18 tff(4980,plain,
% 1.00/1.18 (m_main_v_turn(s56, c_2)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[4979, 4839, 4875])).
% 1.00/1.18 tff(4981,plain,
% 1.00/1.18 (((~![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)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(4982,plain,
% 1.00/1.18 ((~![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)))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(4983,plain,
% 1.00/1.18 ((~![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))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[4982, 4981])).
% 1.00/1.18 tff(4984,plain,
% 1.00/1.18 (~m_main_v_turn(s56, c_1)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[4983, 156, 4980])).
% 1.00/1.18 tff(4985,plain,
% 1.00/1.18 (((~![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)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(4986,plain,
% 1.00/1.18 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s56, c_1) | (~node5(s56)))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(4987,plain,
% 1.00/1.18 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s56, c_1) | (~node5(s56))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[4986, 4985])).
% 1.00/1.18 tff(4988,plain,
% 1.00/1.18 (~node5(s56)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[4987, 776, 4984])).
% 1.00/1.18 tff(4989,plain,
% 1.00/1.18 (((~![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)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(4990,plain,
% 1.00/1.18 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s56, c_n1) | (~node2(s56)))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(4991,plain,
% 1.00/1.18 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s56, c_n1) | (~node2(s56))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[4990, 4989])).
% 1.00/1.18 tff(4992,plain,
% 1.00/1.18 (~node2(s56)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[4991, 787, 4916])).
% 1.00/1.18 tff(4993,plain,
% 1.00/1.18 (((~![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)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(4994,plain,
% 1.00/1.18 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s56, c_n1) | (~node3(s56)))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(4995,plain,
% 1.00/1.18 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s56, c_n1) | (~node3(s56))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[4994, 4993])).
% 1.00/1.18 tff(4996,plain,
% 1.00/1.18 (~node3(s56)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[4995, 798, 4916])).
% 1.00/1.18 tff(4997,plain,
% 1.00/1.18 (((~![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)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(4998,plain,
% 1.00/1.18 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s56, c_n2) | (~node4(s56)))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(4999,plain,
% 1.00/1.18 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s56, c_n2) | (~node4(s56))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[4998, 4997])).
% 1.00/1.18 tff(5000,plain,
% 1.00/1.18 (~node4(s56)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[4999, 388, 4936])).
% 1.00/1.18 tff(5001,plain,
% 1.00/1.18 (((~![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))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(5002,plain,
% 1.00/1.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s56, s57)) | node7(s56, s57))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(5003,plain,
% 1.00/1.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s56, s57)) | node7(s56, s57)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[5002, 5001])).
% 1.00/1.18 tff(5004,plain,
% 1.00/1.18 (node7(s56, s57)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[5003, 206, 4947])).
% 1.00/1.18 tff(5005,plain,
% 1.00/1.18 (((~![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(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)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(5006,plain,
% 1.00/1.18 ((~![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(s56, c_c1) | node1(s56) | node2(s56) | node3(s56) | node4(s56) | node5(s56) | node6(s56, s57) | (~node7(s56, s57)))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(5007,plain,
% 1.00/1.18 ((~![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(s56, c_c1) | node1(s56) | node2(s56) | node3(s56) | node4(s56) | node5(s56) | node6(s56, s57) | (~node7(s56, s57))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[5006, 5005])).
% 1.00/1.18 tff(5008,plain,
% 1.00/1.18 (m_main_v_state1(s56, c_c1) | node1(s56) | node2(s56) | node3(s56) | node4(s56) | node5(s56) | node6(s56, s57)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[5007, 820, 5004])).
% 1.00/1.18 tff(5009,plain,
% 1.00/1.18 (node6(s56, s57)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[5008, 5000, 4924, 4996, 4992, 4988, 4971])).
% 1.00/1.18 tff(5010,plain,
% 1.00/1.18 (((~![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(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)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(5011,plain,
% 1.00/1.18 (((~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)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(5012,plain,
% 1.00/1.18 (((~![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))))),
% 1.00/1.18 inference(monotonicity,[status(thm)],[5011])).
% 1.00/1.18 tff(5013,plain,
% 1.00/1.18 (((~![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)))),
% 1.00/1.18 inference(transitivity,[status(thm)],[5012, 5010])).
% 1.00/1.18 tff(5014,plain,
% 1.00/1.18 ((~![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)))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(5015,plain,
% 1.00/1.18 ((~![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(s56, c_n1) | (~m_main_v_state1(s57, c_n1)) | (~node6(s56, s57))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[5014, 5013])).
% 1.00/1.18 tff(5016,plain,
% 1.00/1.18 (~m_main_v_state1(s57, c_n1)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[5015, 835, 4916, 5009])).
% 1.00/1.18 tff(5017,plain,
% 1.00/1.18 (((~![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)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(5018,plain,
% 1.00/1.18 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s57, c_n1) | (~node2(s57)))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(5019,plain,
% 1.00/1.18 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s57, c_n1) | (~node2(s57))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[5018, 5017])).
% 1.00/1.18 tff(5020,plain,
% 1.00/1.18 (~node2(s57)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[5019, 787, 5016])).
% 1.00/1.18 tff(5021,plain,
% 1.00/1.18 (((~![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(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)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(5022,plain,
% 1.00/1.18 (((~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)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(5023,plain,
% 1.00/1.18 (((~![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))))),
% 1.00/1.18 inference(monotonicity,[status(thm)],[5022])).
% 1.00/1.18 tff(5024,plain,
% 1.00/1.18 (((~![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)))),
% 1.00/1.18 inference(transitivity,[status(thm)],[5023, 5021])).
% 1.00/1.18 tff(5025,plain,
% 1.00/1.18 ((~![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))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(5026,plain,
% 1.00/1.18 ((~![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(s56, c_t1)) | m_main_v_state1(s57, c_t1) | (~node6(s56, s57))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[5025, 5024])).
% 1.00/1.18 tff(5027,plain,
% 1.00/1.18 (m_main_v_state1(s57, c_t1)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[5026, 856, 4912, 5009])).
% 1.00/1.18 tff(5028,plain,
% 1.00/1.18 (((~![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)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(5029,plain,
% 1.00/1.18 ((~![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)))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(5030,plain,
% 1.00/1.18 ((~![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))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[5029, 5028])).
% 1.00/1.18 tff(5031,plain,
% 1.00/1.18 (~m_main_v_state2(s57, c_t2)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[5030, 77, 4959])).
% 1.00/1.18 tff(5032,plain,
% 1.00/1.18 (((~![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)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(5033,plain,
% 1.00/1.18 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s57, c_t2) | (~node1(s57)))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(5034,plain,
% 1.00/1.18 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s57, c_t2) | (~node1(s57))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[5033, 5032])).
% 1.00/1.18 tff(5035,plain,
% 1.00/1.18 (~node1(s57)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[5034, 195, 5031])).
% 1.00/1.18 tff(5036,plain,
% 1.00/1.18 (succ(s57, s58) <=> succ(s57, s58)),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(5037,axiom,(succ(s57, s58)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound58')).
% 1.00/1.18 tff(5038,plain,
% 1.00/1.18 (succ(s57, s58)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[5037, 5036])).
% 1.00/1.18 tff(5039,plain,
% 1.00/1.18 (((~![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))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(5040,plain,
% 1.00/1.18 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s57, s58)) | trans(s57, s58))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(5041,plain,
% 1.00/1.18 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s57, s58)) | trans(s57, s58)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[5040, 5039])).
% 1.00/1.18 tff(5042,plain,
% 1.00/1.18 (trans(s57, s58)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[5041, 5038, 32])).
% 1.00/1.18 tff(5043,plain,
% 1.00/1.18 (((~![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))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(5044,plain,
% 1.00/1.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s57, s58)) | node7(s57, s58))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(5045,plain,
% 1.00/1.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s57, s58)) | node7(s57, s58)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[5044, 5043])).
% 1.00/1.18 tff(5046,plain,
% 1.00/1.18 (node7(s57, s58)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[5045, 206, 5042])).
% 1.00/1.18 tff(5047,plain,
% 1.00/1.18 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(5048,plain,
% 1.00/1.18 (((~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)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5049,plain,
% 1.00/1.19 (((~![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(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))))),
% 1.00/1.19 inference(monotonicity,[status(thm)],[5048])).
% 1.00/1.19 tff(5050,plain,
% 1.00/1.19 (((~![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(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)))),
% 1.00/1.19 inference(transitivity,[status(thm)],[5049, 5047])).
% 1.00/1.19 tff(5051,plain,
% 1.00/1.19 ((~![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(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))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(5052,plain,
% 1.00/1.19 ((~![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(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))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[5051, 5050])).
% 1.00/1.19 tff(5053,plain,
% 1.00/1.19 ((~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)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5052, 892, 5046])).
% 1.00/1.19 tff(5054,plain,
% 1.00/1.19 (m_main_v_state1(s58, c_c1)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5053, 5035, 4959, 5027, 5020, 4967])).
% 1.00/1.19 tff(5055,plain,
% 1.00/1.19 (((~![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)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5056,plain,
% 1.00/1.19 ((~![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)))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(5057,plain,
% 1.00/1.19 ((~![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))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[5056, 5055])).
% 1.00/1.19 tff(5058,plain,
% 1.00/1.19 (~m_main_v_state1(s58, c_t1)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5057, 539, 5054])).
% 1.00/1.19 tff(5059,plain,
% 1.00/1.19 (((~![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)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5060,plain,
% 1.00/1.19 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s58, c_t1) | (~node5(s58)))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(5061,plain,
% 1.00/1.19 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s58, c_t1) | (~node5(s58))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[5060, 5059])).
% 1.00/1.19 tff(5062,plain,
% 1.00/1.19 (~node5(s58)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5061, 550, 5058])).
% 1.00/1.19 tff(5063,plain,
% 1.00/1.19 (((~![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))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5064,plain,
% 1.00/1.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s57, s58)) | node14(s57, s58))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(5065,plain,
% 1.00/1.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s57, s58)) | node14(s57, s58)),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[5064, 5063])).
% 1.00/1.19 tff(5066,plain,
% 1.00/1.19 (node14(s57, s58)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5065, 46, 5042])).
% 1.00/1.19 tff(5067,plain,
% 1.00/1.19 (((~![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(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))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5068,plain,
% 1.00/1.19 ((~![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(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | (~node14(s57, s58)) | m_main_v_state2(s58, c_t2))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(5069,plain,
% 1.00/1.19 ((~![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(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | (~node14(s57, s58)) | m_main_v_state2(s58, c_t2)),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[5068, 5067])).
% 1.00/1.19 tff(5070,plain,
% 1.00/1.19 ((~m_main_v_state1(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | m_main_v_state2(s58, c_t2)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5069, 922, 5066])).
% 1.00/1.19 tff(5071,plain,
% 1.00/1.19 (m_main_v_state2(s58, c_t2)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5070, 5027, 4959])).
% 1.00/1.19 tff(5072,plain,
% 1.00/1.19 (((~![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)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5073,plain,
% 1.00/1.19 ((~![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)))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(5074,plain,
% 1.00/1.19 ((~![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))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[5073, 5072])).
% 1.00/1.19 tff(5075,plain,
% 1.00/1.19 (~m_main_v_state2(s58, c_n2)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5074, 77, 5071])).
% 1.00/1.19 tff(5076,plain,
% 1.00/1.19 (((~![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)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5077,plain,
% 1.00/1.19 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s58, c_n2) | (~node4(s58)))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(5078,plain,
% 1.00/1.19 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s58, c_n2) | (~node4(s58))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[5077, 5076])).
% 1.00/1.19 tff(5079,plain,
% 1.00/1.19 (~node4(s58)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5078, 388, 5075])).
% 1.00/1.19 tff(5080,plain,
% 1.00/1.19 (((~![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)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5081,plain,
% 1.00/1.19 ((~![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)))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(5082,plain,
% 1.00/1.19 ((~![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))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[5081, 5080])).
% 1.00/1.19 tff(5083,plain,
% 1.00/1.19 (~m_main_v_state2(s58, c_c2)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5082, 260, 5071])).
% 1.00/1.19 tff(5084,plain,
% 1.00/1.19 (((~![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)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5085,plain,
% 1.00/1.19 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s58, c_c2) | (~node3(s58)))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(5086,plain,
% 1.00/1.19 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s58, c_c2) | (~node3(s58))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[5085, 5084])).
% 1.00/1.19 tff(5087,plain,
% 1.00/1.19 (~node3(s58)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5086, 399, 5083])).
% 1.00/1.19 tff(5088,plain,
% 1.00/1.19 (((~![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)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5089,plain,
% 1.00/1.19 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s58, c_n2) | (~node2(s58)))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(5090,plain,
% 1.00/1.19 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s58, c_n2) | (~node2(s58))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[5089, 5088])).
% 1.00/1.19 tff(5091,plain,
% 1.00/1.19 (~node2(s58)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5090, 410, 5075])).
% 1.00/1.19 tff(5092,plain,
% 1.00/1.19 (((~![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)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5093,plain,
% 1.00/1.19 ((~![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)))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(5094,plain,
% 1.00/1.19 ((~![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))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[5093, 5092])).
% 1.00/1.19 tff(5095,plain,
% 1.00/1.19 (~m_main_v_state1(s58, c_n1)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5094, 454, 5054])).
% 1.00/1.19 tff(5096,plain,
% 1.00/1.19 (((~![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)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5097,plain,
% 1.00/1.19 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s58, c_n1) | (~node1(s58)))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(5098,plain,
% 1.00/1.19 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s58, c_n1) | (~node1(s58))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[5097, 5096])).
% 1.00/1.19 tff(5099,plain,
% 1.00/1.19 (~node1(s58)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5098, 421, 5095])).
% 1.00/1.19 tff(5100,plain,
% 1.00/1.19 (succ(s58, s59) <=> succ(s58, s59)),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5101,axiom,(succ(s58, s59)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound59')).
% 1.00/1.19 tff(5102,plain,
% 1.00/1.19 (succ(s58, s59)),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[5101, 5100])).
% 1.00/1.19 tff(5103,plain,
% 1.00/1.19 (((~![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))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5104,plain,
% 1.00/1.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s58, s59)) | trans(s58, s59))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(5105,plain,
% 1.00/1.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s58, s59)) | trans(s58, s59)),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[5104, 5103])).
% 1.00/1.19 tff(5106,plain,
% 1.00/1.19 (trans(s58, s59)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5105, 5102, 32])).
% 1.00/1.19 tff(5107,plain,
% 1.00/1.19 (((~![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))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5108,plain,
% 1.00/1.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s58, s59)) | node7(s58, s59))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(5109,plain,
% 1.00/1.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s58, s59)) | node7(s58, s59)),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[5108, 5107])).
% 1.00/1.19 tff(5110,plain,
% 1.00/1.19 (node7(s58, s59)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5109, 206, 5106])).
% 1.00/1.19 tff(5111,plain,
% 1.00/1.19 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5112,plain,
% 1.00/1.19 (((~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)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5113,plain,
% 1.00/1.19 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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))))),
% 1.00/1.19 inference(monotonicity,[status(thm)],[5112])).
% 1.00/1.19 tff(5114,plain,
% 1.00/1.19 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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)))),
% 1.00/1.19 inference(transitivity,[status(thm)],[5113, 5111])).
% 1.00/1.19 tff(5115,plain,
% 1.00/1.19 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(5116,plain,
% 1.00/1.19 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[5115, 5114])).
% 1.00/1.19 tff(5117,plain,
% 1.00/1.19 (m_main_v_state1(s59, c_n1) | (~m_main_v_state1(s58, c_c1)) | node1(s58) | node2(s58) | node3(s58) | node4(s58) | node5(s58)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5116, 584, 5110])).
% 1.00/1.19 tff(5118,plain,
% 1.00/1.19 (m_main_v_state1(s59, c_n1)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5117, 5099, 5054, 5091, 5087, 5079, 5062])).
% 1.00/1.19 tff(5119,plain,
% 1.00/1.19 (((~![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)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5120,plain,
% 1.00/1.19 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s57, c_t2) | (~node15(s57)))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(5121,plain,
% 1.00/1.19 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s57, c_t2) | (~node15(s57))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[5120, 5119])).
% 1.00/1.19 tff(5122,plain,
% 1.00/1.19 (~node15(s57)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5121, 103, 5031])).
% 1.00/1.19 tff(5123,plain,
% 1.00/1.19 (((~![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))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5124,plain,
% 1.00/1.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s57, s58)) | node18(s57, s58))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(5125,plain,
% 1.00/1.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s57, s58)) | node18(s57, s58)),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[5124, 5123])).
% 1.00/1.19 tff(5126,plain,
% 1.00/1.19 (node18(s57, s58)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5125, 125, 5042])).
% 1.00/1.19 tff(5127,plain,
% 1.00/1.19 (((~![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(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))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5128,plain,
% 1.00/1.19 (((~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))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5129,plain,
% 1.00/1.19 (((~![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(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)))),
% 1.00/1.19 inference(monotonicity,[status(thm)],[5128])).
% 1.00/1.19 tff(5130,plain,
% 1.00/1.19 (((~![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(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))),
% 1.00/1.19 inference(transitivity,[status(thm)],[5129, 5127])).
% 1.00/1.19 tff(5131,plain,
% 1.00/1.19 ((~![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(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | node15(s57) | (~node18(s57, s58)) | m_main_v_turn(s58, c_1))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(5132,plain,
% 1.00/1.19 ((~![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(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)),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[5131, 5130])).
% 1.00/1.19 tff(5133,plain,
% 1.00/1.19 (node15(s57) | (~m_main_v_state1(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | m_main_v_turn(s58, c_1)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5132, 992, 5126])).
% 1.00/1.19 tff(5134,plain,
% 1.00/1.19 (m_main_v_turn(s58, c_1)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5133, 5122, 4959, 5027])).
% 1.00/1.19 tff(5135,plain,
% 1.00/1.19 (((~![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)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5136,plain,
% 1.00/1.19 ((~![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)))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(5137,plain,
% 1.00/1.19 ((~![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))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[5136, 5135])).
% 1.00/1.19 tff(5138,plain,
% 1.00/1.19 (~m_main_v_turn(s58, c_2)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5137, 156, 5134])).
% 1.00/1.19 tff(5139,plain,
% 1.00/1.19 (((~![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)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5140,plain,
% 1.00/1.19 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s58, c_2) | (~node12(s58)))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(5141,plain,
% 1.00/1.19 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s58, c_2) | (~node12(s58))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[5140, 5139])).
% 1.00/1.19 tff(5142,plain,
% 1.00/1.19 (~node12(s58)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5141, 184, 5138])).
% 1.00/1.19 tff(5143,plain,
% 1.00/1.19 (((~![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)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5144,plain,
% 1.00/1.19 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s58, c_n2) | (~node8(s58)))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(5145,plain,
% 1.00/1.19 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s58, c_n2) | (~node8(s58))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[5144, 5143])).
% 1.00/1.19 tff(5146,plain,
% 1.00/1.19 (~node8(s58)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5145, 271, 5075])).
% 1.00/1.19 tff(5147,plain,
% 1.00/1.19 (((~![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)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5148,plain,
% 1.00/1.19 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s58, c_n2) | (~node9(s58)))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(5149,plain,
% 1.00/1.19 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s58, c_n2) | (~node9(s58))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[5148, 5147])).
% 1.00/1.19 tff(5150,plain,
% 1.00/1.19 (~node9(s58)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5149, 88, 5075])).
% 1.00/1.19 tff(5151,plain,
% 1.00/1.19 (((~![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)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5152,plain,
% 1.00/1.19 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s58, c_n2) | (~node10(s58)))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(5153,plain,
% 1.00/1.19 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s58, c_n2) | (~node10(s58))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[5152, 5151])).
% 1.00/1.19 tff(5154,plain,
% 1.00/1.19 (~node10(s58)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5153, 249, 5075])).
% 1.00/1.19 tff(5155,plain,
% 1.00/1.19 (((~![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)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5156,plain,
% 1.00/1.19 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s58, c_n1) | (~node11(s58)))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(5157,plain,
% 1.00/1.19 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s58, c_n1) | (~node11(s58))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[5156, 5155])).
% 1.00/1.19 tff(5158,plain,
% 1.00/1.19 (~node11(s58)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5157, 238, 5095])).
% 1.00/1.19 tff(5159,plain,
% 1.00/1.19 (((~![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))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5160,plain,
% 1.00/1.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s58, s59)) | node14(s58, s59))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(5161,plain,
% 1.00/1.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s58, s59)) | node14(s58, s59)),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[5160, 5159])).
% 1.00/1.19 tff(5162,plain,
% 1.00/1.19 (node14(s58, s59)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5161, 46, 5106])).
% 1.00/1.19 tff(5163,plain,
% 1.00/1.19 (((~![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(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)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5164,plain,
% 1.00/1.19 ((~![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(s58, c_c2) | node9(s58) | node8(s58) | node10(s58) | node11(s58) | node12(s58) | node13(s58, s59) | (~node14(s58, s59)))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(5165,plain,
% 1.00/1.19 ((~![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(s58, c_c2) | node9(s58) | node8(s58) | node10(s58) | node11(s58) | node12(s58) | node13(s58, s59) | (~node14(s58, s59))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[5164, 5163])).
% 1.00/1.19 tff(5166,plain,
% 1.00/1.19 (m_main_v_state2(s58, c_c2) | node9(s58) | node8(s58) | node10(s58) | node11(s58) | node12(s58) | node13(s58, s59)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5165, 296, 5162])).
% 1.00/1.19 tff(5167,plain,
% 1.00/1.19 (node13(s58, s59)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5166, 5158, 5083, 5154, 5150, 5146, 5142])).
% 1.00/1.19 tff(5168,plain,
% 1.00/1.19 (((~![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(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)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5169,plain,
% 1.00/1.19 (((~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)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5170,plain,
% 1.00/1.19 (((~![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))))),
% 1.00/1.19 inference(monotonicity,[status(thm)],[5169])).
% 1.00/1.19 tff(5171,plain,
% 1.00/1.19 (((~![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)))),
% 1.00/1.19 inference(transitivity,[status(thm)],[5170, 5168])).
% 1.00/1.19 tff(5172,plain,
% 1.00/1.19 ((~![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))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(5173,plain,
% 1.00/1.19 ((~![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(s58, c_t2)) | m_main_v_state2(s59, c_t2) | (~node13(s58, s59))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[5172, 5171])).
% 1.00/1.19 tff(5174,plain,
% 1.00/1.19 (m_main_v_state2(s59, c_t2)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5173, 518, 5071, 5167])).
% 1.00/1.19 tff(5175,plain,
% 1.00/1.19 (succ(s59, s60) <=> succ(s59, s60)),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5176,axiom,(succ(s59, s60)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound60')).
% 1.00/1.19 tff(5177,plain,
% 1.00/1.19 (succ(s59, s60)),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[5176, 5175])).
% 1.00/1.19 tff(5178,plain,
% 1.00/1.19 (((~![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))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5179,plain,
% 1.00/1.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s59, s60)) | trans(s59, s60))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(5180,plain,
% 1.00/1.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s59, s60)) | trans(s59, s60)),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[5179, 5178])).
% 1.00/1.19 tff(5181,plain,
% 1.00/1.19 (trans(s59, s60)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5180, 5177, 32])).
% 1.00/1.19 tff(5182,plain,
% 1.00/1.19 (((~![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))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(5183,plain,
% 1.00/1.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s59, s60)) | node7(s59, s60))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(5184,plain,
% 1.00/1.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s59, s60)) | node7(s59, s60)),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[5183, 5182])).
% 1.00/1.19 tff(5185,plain,
% 1.00/1.19 (node7(s59, s60)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[5184, 206, 5181])).
% 1.00/1.19 tff(5186,plain,
% 1.00/1.19 (((~![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))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5187,plain,
% 1.00/1.20 ((~![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(s59, c_n1)) | (~m_main_v_state2(s59, c_t2)) | (~node7(s59, s60)) | m_main_v_state1(s60, c_t1))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(5188,plain,
% 1.00/1.20 ((~![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(s59, c_n1)) | (~m_main_v_state2(s59, c_t2)) | (~node7(s59, s60)) | m_main_v_state1(s60, c_t1)),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[5187, 5186])).
% 1.00/1.20 tff(5189,plain,
% 1.00/1.20 ((~m_main_v_state1(s59, c_n1)) | (~m_main_v_state2(s59, c_t2)) | m_main_v_state1(s60, c_t1)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5188, 651, 5185])).
% 1.00/1.20 tff(5190,plain,
% 1.00/1.20 (m_main_v_state1(s60, c_t1)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5189, 5174, 5118])).
% 1.00/1.20 tff(5191,plain,
% 1.00/1.20 (((~![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)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5192,plain,
% 1.00/1.20 ((~![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)))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(5193,plain,
% 1.00/1.20 ((~![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))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[5192, 5191])).
% 1.00/1.20 tff(5194,plain,
% 1.00/1.20 (~m_main_v_state1(s60, c_n1)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5193, 10, 5190])).
% 1.00/1.20 tff(5195,plain,
% 1.00/1.20 (((~![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)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5196,plain,
% 1.00/1.20 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s60, c_n1) | (~node1(s60)))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(5197,plain,
% 1.00/1.20 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s60, c_n1) | (~node1(s60))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[5196, 5195])).
% 1.00/1.20 tff(5198,plain,
% 1.00/1.20 (~node1(s60)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5197, 421, 5194])).
% 1.00/1.20 tff(5199,plain,
% 1.00/1.20 (((~![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))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5200,plain,
% 1.00/1.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s59, s60)) | node18(s59, s60))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(5201,plain,
% 1.00/1.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s59, s60)) | node18(s59, s60)),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[5200, 5199])).
% 1.00/1.20 tff(5202,plain,
% 1.00/1.20 (node18(s59, s60)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5201, 125, 5181])).
% 1.00/1.20 tff(5203,plain,
% 1.00/1.20 (((~![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))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5204,plain,
% 1.00/1.20 ((~![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))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(5205,plain,
% 1.00/1.20 ((~![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)),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[5204, 5203])).
% 1.00/1.20 tff(5206,plain,
% 1.00/1.20 ((~m_main_v_state1(s59, c_n1)) | (~m_main_v_state2(s59, c_t2)) | m_main_v_turn(s60, c_2)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5205, 760, 5202])).
% 1.00/1.20 tff(5207,plain,
% 1.00/1.20 (m_main_v_turn(s60, c_2)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5206, 5174, 5118])).
% 1.00/1.20 tff(5208,plain,
% 1.00/1.20 (((~![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)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5209,plain,
% 1.00/1.20 ((~![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)))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(5210,plain,
% 1.00/1.20 ((~![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))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[5209, 5208])).
% 1.00/1.20 tff(5211,plain,
% 1.00/1.20 (~m_main_v_turn(s60, c_1)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5210, 156, 5207])).
% 1.00/1.20 tff(5212,plain,
% 1.00/1.20 (((~![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)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5213,plain,
% 1.00/1.20 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s60, c_1) | (~node5(s60)))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(5214,plain,
% 1.00/1.20 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s60, c_1) | (~node5(s60))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[5213, 5212])).
% 1.00/1.20 tff(5215,plain,
% 1.00/1.20 (~node5(s60)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5214, 776, 5211])).
% 1.00/1.20 tff(5216,plain,
% 1.00/1.20 (((~![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)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5217,plain,
% 1.00/1.20 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s60, c_n1) | (~node2(s60)))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(5218,plain,
% 1.00/1.20 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s60, c_n1) | (~node2(s60))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[5217, 5216])).
% 1.00/1.20 tff(5219,plain,
% 1.00/1.20 (~node2(s60)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5218, 787, 5194])).
% 1.00/1.20 tff(5220,plain,
% 1.00/1.20 (((~![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)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5221,plain,
% 1.00/1.20 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s60, c_n1) | (~node3(s60)))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(5222,plain,
% 1.00/1.20 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s60, c_n1) | (~node3(s60))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[5221, 5220])).
% 1.00/1.20 tff(5223,plain,
% 1.00/1.20 (~node3(s60)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5222, 798, 5194])).
% 1.00/1.20 tff(5224,plain,
% 1.00/1.20 (((~![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)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5225,plain,
% 1.00/1.20 ((~![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)))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(5226,plain,
% 1.00/1.20 ((~![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))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[5225, 5224])).
% 1.00/1.20 tff(5227,plain,
% 1.00/1.20 (~m_main_v_state1(s60, c_c1)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5226, 539, 5190])).
% 1.00/1.20 tff(5228,plain,
% 1.00/1.20 (((~![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(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)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5229,plain,
% 1.00/1.20 (((~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)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5230,plain,
% 1.00/1.20 (((~![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))))),
% 1.00/1.20 inference(monotonicity,[status(thm)],[5229])).
% 1.00/1.20 tff(5231,plain,
% 1.00/1.20 (((~![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)))),
% 1.00/1.20 inference(transitivity,[status(thm)],[5230, 5228])).
% 1.00/1.20 tff(5232,plain,
% 1.00/1.20 ((~![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)))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(5233,plain,
% 1.00/1.20 ((~![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(s58, c_n2) | (~m_main_v_state2(s59, c_n2)) | (~node13(s58, s59))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[5232, 5231])).
% 1.00/1.20 tff(5234,plain,
% 1.00/1.20 (~m_main_v_state2(s59, c_n2)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5233, 311, 5075, 5167])).
% 1.00/1.20 tff(5235,plain,
% 1.00/1.20 (((~![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)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5236,plain,
% 1.00/1.20 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s59, c_n2) | (~node9(s59)))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(5237,plain,
% 1.00/1.20 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s59, c_n2) | (~node9(s59))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[5236, 5235])).
% 1.00/1.20 tff(5238,plain,
% 1.00/1.20 (~node9(s59)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5237, 88, 5234])).
% 1.00/1.20 tff(5239,plain,
% 1.00/1.20 (((~![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)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5240,plain,
% 1.00/1.20 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s59, c_n2) | (~node10(s59)))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(5241,plain,
% 1.00/1.20 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s59, c_n2) | (~node10(s59))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[5240, 5239])).
% 1.00/1.20 tff(5242,plain,
% 1.00/1.20 (~node10(s59)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5241, 249, 5234])).
% 1.00/1.20 tff(5243,plain,
% 1.00/1.20 (((~![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)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5244,plain,
% 1.00/1.20 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s59, c_n2) | (~node8(s59)))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(5245,plain,
% 1.00/1.20 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s59, c_n2) | (~node8(s59))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[5244, 5243])).
% 1.00/1.20 tff(5246,plain,
% 1.00/1.20 (~node8(s59)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5245, 271, 5234])).
% 1.00/1.20 tff(5247,plain,
% 1.00/1.20 (((~![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))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5248,plain,
% 1.00/1.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s59, s60)) | node14(s59, s60))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(5249,plain,
% 1.00/1.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s59, s60)) | node14(s59, s60)),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[5248, 5247])).
% 1.00/1.20 tff(5250,plain,
% 1.00/1.20 (node14(s59, s60)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5249, 46, 5181])).
% 1.00/1.20 tff(5251,plain,
% 1.00/1.20 (((~![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(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))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5252,plain,
% 1.00/1.20 ((~![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(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))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(5253,plain,
% 1.00/1.20 ((~![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(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)),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[5252, 5251])).
% 1.00/1.20 tff(5254,plain,
% 1.00/1.20 ((~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)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5253, 617, 5250])).
% 1.00/1.20 tff(5255,plain,
% 1.00/1.20 (m_main_v_state2(s60, c_c2)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5254, 5246, 5118, 5174, 5242, 5238])).
% 1.00/1.20 tff(5256,plain,
% 1.00/1.20 (((~![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)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5257,plain,
% 1.00/1.20 ((~![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)))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(5258,plain,
% 1.00/1.20 ((~![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))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[5257, 5256])).
% 1.00/1.20 tff(5259,plain,
% 1.00/1.20 (~m_main_v_state2(s60, c_n2)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5258, 697, 5255])).
% 1.00/1.20 tff(5260,plain,
% 1.00/1.20 (((~![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)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5261,plain,
% 1.00/1.20 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s60, c_n2) | (~node4(s60)))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(5262,plain,
% 1.00/1.20 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s60, c_n2) | (~node4(s60))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[5261, 5260])).
% 1.00/1.20 tff(5263,plain,
% 1.00/1.20 (~node4(s60)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5262, 388, 5259])).
% 1.00/1.20 tff(5264,plain,
% 1.00/1.20 (succ(s60, s61) <=> succ(s60, s61)),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5265,axiom,(succ(s60, s61)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound61')).
% 1.00/1.20 tff(5266,plain,
% 1.00/1.20 (succ(s60, s61)),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[5265, 5264])).
% 1.00/1.20 tff(5267,plain,
% 1.00/1.20 (((~![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))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5268,plain,
% 1.00/1.20 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s60, s61)) | trans(s60, s61))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(5269,plain,
% 1.00/1.20 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s60, s61)) | trans(s60, s61)),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[5268, 5267])).
% 1.00/1.20 tff(5270,plain,
% 1.00/1.20 (trans(s60, s61)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5269, 5266, 32])).
% 1.00/1.20 tff(5271,plain,
% 1.00/1.20 (((~![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))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5272,plain,
% 1.00/1.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s60, s61)) | node7(s60, s61))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(5273,plain,
% 1.00/1.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s60, s61)) | node7(s60, s61)),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[5272, 5271])).
% 1.00/1.20 tff(5274,plain,
% 1.00/1.20 (node7(s60, s61)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5273, 206, 5270])).
% 1.00/1.20 tff(5275,plain,
% 1.00/1.20 (((~![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)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5276,plain,
% 1.00/1.20 ((~![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)))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(5277,plain,
% 1.00/1.20 ((~![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))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[5276, 5275])).
% 1.00/1.20 tff(5278,plain,
% 1.00/1.20 (m_main_v_state1(s60, c_c1) | node1(s60) | node2(s60) | node3(s60) | node4(s60) | node5(s60) | node6(s60, s61)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5277, 820, 5274])).
% 1.00/1.20 tff(5279,plain,
% 1.00/1.20 (node6(s60, s61)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5278, 5263, 5227, 5223, 5219, 5215, 5198])).
% 1.00/1.20 tff(5280,plain,
% 1.00/1.20 (((~![V: $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)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5281,plain,
% 1.00/1.20 (((~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)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5282,plain,
% 1.00/1.20 (((~![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))))),
% 1.00/1.20 inference(monotonicity,[status(thm)],[5281])).
% 1.00/1.20 tff(5283,plain,
% 1.00/1.20 (((~![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)))),
% 1.00/1.20 inference(transitivity,[status(thm)],[5282, 5280])).
% 1.00/1.20 tff(5284,plain,
% 1.00/1.20 ((~![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))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(5285,plain,
% 1.00/1.20 ((~![V: $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))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[5284, 5283])).
% 1.00/1.20 tff(5286,plain,
% 1.00/1.20 (m_main_v_state1(s61, c_t1)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5285, 856, 5190, 5279])).
% 1.00/1.20 tff(5287,plain,
% 1.00/1.20 (((~![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)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5288,plain,
% 1.00/1.20 ((~![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)))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(5289,plain,
% 1.00/1.20 ((~![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))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[5288, 5287])).
% 1.00/1.20 tff(5290,plain,
% 1.00/1.20 (~m_main_v_state2(s60, c_t2)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5289, 260, 5255])).
% 1.00/1.20 tff(5291,plain,
% 1.00/1.20 (((~![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)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5292,plain,
% 1.00/1.20 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s60, c_t2) | (~node12(s60)))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(5293,plain,
% 1.00/1.20 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s60, c_t2) | (~node12(s60))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[5292, 5291])).
% 1.00/1.20 tff(5294,plain,
% 1.00/1.20 (~node12(s60)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5293, 633, 5290])).
% 1.00/1.20 tff(5295,plain,
% 1.00/1.20 (((~![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)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5296,plain,
% 1.00/1.20 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s60, c_n1) | (~node11(s60)))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(5297,plain,
% 1.00/1.20 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s60, c_n1) | (~node11(s60))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[5296, 5295])).
% 1.00/1.20 tff(5298,plain,
% 1.00/1.20 (~node11(s60)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5297, 238, 5194])).
% 1.00/1.20 tff(5299,plain,
% 1.00/1.20 (((~![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)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5300,plain,
% 1.00/1.20 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s60, c_c1) | (~node10(s60)))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(5301,plain,
% 1.00/1.20 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s60, c_c1) | (~node10(s60))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[5300, 5299])).
% 1.00/1.20 tff(5302,plain,
% 1.00/1.20 (~node10(s60)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5301, 675, 5227])).
% 1.00/1.20 tff(5303,plain,
% 1.00/1.20 (((~![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)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5304,plain,
% 1.00/1.20 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s60, c_n1) | (~node9(s60)))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(5305,plain,
% 1.00/1.20 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s60, c_n1) | (~node9(s60))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[5304, 5303])).
% 1.00/1.20 tff(5306,plain,
% 1.00/1.20 (~node9(s60)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5305, 686, 5194])).
% 1.00/1.20 tff(5307,plain,
% 1.00/1.20 (((~![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)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5308,plain,
% 1.00/1.20 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s60, c_n2) | (~node8(s60)))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(5309,plain,
% 1.00/1.20 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s60, c_n2) | (~node8(s60))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[5308, 5307])).
% 1.00/1.20 tff(5310,plain,
% 1.00/1.20 (~node8(s60)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5309, 271, 5259])).
% 1.00/1.20 tff(5311,plain,
% 1.00/1.20 (((~![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))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(5312,plain,
% 1.00/1.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s60, s61)) | node14(s60, s61))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(5313,plain,
% 1.00/1.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s60, s61)) | node14(s60, s61)),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[5312, 5311])).
% 1.00/1.20 tff(5314,plain,
% 1.00/1.20 (node14(s60, s61)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[5313, 46, 5270])).
% 1.00/1.20 tff(5315,plain,
% 1.00/1.20 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(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)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5316,plain,
% 1.00/1.21 (((~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)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5317,plain,
% 1.00/1.21 (((~![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(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))))),
% 1.00/1.21 inference(monotonicity,[status(thm)],[5316])).
% 1.00/1.21 tff(5318,plain,
% 1.00/1.21 (((~![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(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)))),
% 1.00/1.21 inference(transitivity,[status(thm)],[5317, 5315])).
% 1.00/1.21 tff(5319,plain,
% 1.00/1.21 ((~![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(s60, c_c2)) | node9(s60) | node8(s60) | node10(s60) | node11(s60) | node12(s60) | (~node14(s60, s61)) | m_main_v_state2(s61, c_n2))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(5320,plain,
% 1.00/1.21 ((~![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(s61, c_n2) | node9(s60) | node8(s60) | node10(s60) | node11(s60) | node12(s60) | (~node14(s60, s61)) | (~m_main_v_state2(s60, c_c2))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[5319, 5318])).
% 1.00/1.21 tff(5321,plain,
% 1.00/1.21 (m_main_v_state2(s61, c_n2) | node9(s60) | node8(s60) | node10(s60) | node11(s60) | node12(s60) | (~m_main_v_state2(s60, c_c2))),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5320, 726, 5314])).
% 1.00/1.21 tff(5322,plain,
% 1.00/1.21 (m_main_v_state2(s61, c_n2)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5321, 5310, 5255, 5306, 5302, 5298, 5294])).
% 1.00/1.21 tff(5323,plain,
% 1.00/1.21 (((~![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)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5324,plain,
% 1.00/1.21 ((~![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)))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(5325,plain,
% 1.00/1.21 ((~![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))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[5324, 5323])).
% 1.00/1.21 tff(5326,plain,
% 1.00/1.21 (~m_main_v_state2(s61, c_t2)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5325, 77, 5322])).
% 1.00/1.21 tff(5327,plain,
% 1.00/1.21 (((~![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)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5328,plain,
% 1.00/1.21 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s61, c_t2) | (~node15(s61)))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(5329,plain,
% 1.00/1.21 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s61, c_t2) | (~node15(s61))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[5328, 5327])).
% 1.00/1.21 tff(5330,plain,
% 1.00/1.21 (~node15(s61)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5329, 103, 5326])).
% 1.00/1.21 tff(5331,plain,
% 1.00/1.21 (succ(s61, s62) <=> succ(s61, s62)),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5332,axiom,(succ(s61, s62)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound62')).
% 1.00/1.21 tff(5333,plain,
% 1.00/1.21 (succ(s61, s62)),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[5332, 5331])).
% 1.00/1.21 tff(5334,plain,
% 1.00/1.21 (((~![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))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5335,plain,
% 1.00/1.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s61, s62)) | trans(s61, s62))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(5336,plain,
% 1.00/1.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s61, s62)) | trans(s61, s62)),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[5335, 5334])).
% 1.00/1.21 tff(5337,plain,
% 1.00/1.21 (trans(s61, s62)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5336, 5333, 32])).
% 1.00/1.21 tff(5338,plain,
% 1.00/1.21 (((~![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))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5339,plain,
% 1.00/1.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s61, s62)) | node18(s61, s62))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(5340,plain,
% 1.00/1.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s61, s62)) | node18(s61, s62)),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[5339, 5338])).
% 1.00/1.21 tff(5341,plain,
% 1.00/1.21 (node18(s61, s62)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5340, 125, 5337])).
% 1.00/1.21 tff(5342,plain,
% 1.00/1.21 (((~![Y: $i, X: $i] : ((~m_main_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))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5343,plain,
% 1.00/1.21 (((~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))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5344,plain,
% 1.00/1.21 (((~![Y: $i, X: $i] : ((~m_main_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)))),
% 1.00/1.21 inference(monotonicity,[status(thm)],[5343])).
% 1.00/1.21 tff(5345,plain,
% 1.00/1.21 (((~![Y: $i, X: $i] : ((~m_main_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))),
% 1.00/1.21 inference(transitivity,[status(thm)],[5344, 5342])).
% 1.00/1.21 tff(5346,plain,
% 1.00/1.21 ((~![Y: $i, X: $i] : ((~m_main_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))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(5347,plain,
% 1.00/1.21 ((~![Y: $i, X: $i] : ((~m_main_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)),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[5346, 5345])).
% 1.00/1.21 tff(5348,plain,
% 1.00/1.21 (node15(s61) | (~m_main_v_state1(s61, c_t1)) | (~m_main_v_state2(s61, c_n2)) | m_main_v_turn(s62, c_1)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5347, 992, 5341])).
% 1.00/1.21 tff(5349,plain,
% 1.00/1.21 (m_main_v_turn(s62, c_1)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5348, 5330, 5322, 5286])).
% 1.00/1.21 tff(5350,plain,
% 1.00/1.21 (((~![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)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5351,plain,
% 1.00/1.21 ((~![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)))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(5352,plain,
% 1.00/1.21 ((~![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))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[5351, 5350])).
% 1.00/1.21 tff(5353,plain,
% 1.00/1.21 (~m_main_v_turn(s62, c_2)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5352, 156, 5349])).
% 1.00/1.21 tff(5354,plain,
% 1.00/1.21 (((~![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)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5355,plain,
% 1.00/1.21 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s62, c_2) | (~node12(s62)))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(5356,plain,
% 1.00/1.21 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s62, c_2) | (~node12(s62))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[5355, 5354])).
% 1.00/1.21 tff(5357,plain,
% 1.00/1.21 (~node12(s62)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5356, 184, 5353])).
% 1.00/1.21 tff(5358,plain,
% 1.00/1.21 (((~![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))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5359,plain,
% 1.00/1.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s61, s62)) | node14(s61, s62))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(5360,plain,
% 1.00/1.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s61, s62)) | node14(s61, s62)),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[5359, 5358])).
% 1.00/1.21 tff(5361,plain,
% 1.00/1.21 (node14(s61, s62)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5360, 46, 5337])).
% 1.00/1.21 tff(5362,plain,
% 1.00/1.21 (((~![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(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))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5363,plain,
% 1.00/1.21 ((~![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(s61, c_t1)) | (~m_main_v_state2(s61, c_n2)) | (~node14(s61, s62)) | m_main_v_state2(s62, c_t2))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(5364,plain,
% 1.00/1.21 ((~![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(s61, c_t1)) | (~m_main_v_state2(s61, c_n2)) | (~node14(s61, s62)) | m_main_v_state2(s62, c_t2)),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[5363, 5362])).
% 1.00/1.21 tff(5365,plain,
% 1.00/1.21 ((~m_main_v_state1(s61, c_t1)) | (~m_main_v_state2(s61, c_n2)) | m_main_v_state2(s62, c_t2)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5364, 922, 5361])).
% 1.00/1.21 tff(5366,plain,
% 1.00/1.21 (m_main_v_state2(s62, c_t2)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5365, 5286, 5322])).
% 1.00/1.21 tff(5367,plain,
% 1.00/1.21 (((~![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)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5368,plain,
% 1.00/1.21 ((~![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)))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(5369,plain,
% 1.00/1.21 ((~![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))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[5368, 5367])).
% 1.00/1.21 tff(5370,plain,
% 1.00/1.21 (~m_main_v_state2(s62, c_n2)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5369, 77, 5366])).
% 1.00/1.21 tff(5371,plain,
% 1.00/1.21 (((~![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)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5372,plain,
% 1.00/1.21 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s62, c_n2) | (~node8(s62)))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(5373,plain,
% 1.00/1.21 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s62, c_n2) | (~node8(s62))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[5372, 5371])).
% 1.00/1.21 tff(5374,plain,
% 1.00/1.21 (~node8(s62)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5373, 271, 5370])).
% 1.00/1.21 tff(5375,plain,
% 1.00/1.21 (((~![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)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5376,plain,
% 1.00/1.21 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s62, c_n2) | (~node9(s62)))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(5377,plain,
% 1.00/1.21 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s62, c_n2) | (~node9(s62))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[5376, 5375])).
% 1.00/1.21 tff(5378,plain,
% 1.00/1.21 (~node9(s62)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5377, 88, 5370])).
% 1.00/1.21 tff(5379,plain,
% 1.00/1.21 (((~![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)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5380,plain,
% 1.00/1.21 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s62, c_n2) | (~node10(s62)))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(5381,plain,
% 1.00/1.21 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s62, c_n2) | (~node10(s62))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[5380, 5379])).
% 1.00/1.21 tff(5382,plain,
% 1.00/1.21 (~node10(s62)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5381, 249, 5370])).
% 1.00/1.21 tff(5383,plain,
% 1.00/1.21 (((~![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)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5384,plain,
% 1.00/1.21 ((~![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)))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(5385,plain,
% 1.00/1.21 ((~![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))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[5384, 5383])).
% 1.00/1.21 tff(5386,plain,
% 1.00/1.21 (~m_main_v_state2(s62, c_c2)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5385, 260, 5366])).
% 1.00/1.21 tff(5387,plain,
% 1.00/1.21 (((~![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)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5388,plain,
% 1.00/1.21 ((~![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)))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(5389,plain,
% 1.00/1.21 ((~![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))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[5388, 5387])).
% 1.00/1.21 tff(5390,plain,
% 1.00/1.21 (~m_main_v_state2(s61, c_c2)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5389, 697, 5322])).
% 1.00/1.21 tff(5391,plain,
% 1.00/1.21 (((~![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)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5392,plain,
% 1.00/1.21 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s61, c_c2) | (~node3(s61)))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(5393,plain,
% 1.00/1.21 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s61, c_c2) | (~node3(s61))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[5392, 5391])).
% 1.00/1.21 tff(5394,plain,
% 1.00/1.21 (~node3(s61)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5393, 399, 5390])).
% 1.00/1.21 tff(5395,plain,
% 1.00/1.21 (((~![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(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)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5396,plain,
% 1.00/1.21 (((~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)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5397,plain,
% 1.00/1.21 (((~![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))))),
% 1.00/1.21 inference(monotonicity,[status(thm)],[5396])).
% 1.00/1.21 tff(5398,plain,
% 1.00/1.21 (((~![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)))),
% 1.00/1.21 inference(transitivity,[status(thm)],[5397, 5395])).
% 1.00/1.21 tff(5399,plain,
% 1.00/1.21 ((~![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)))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(5400,plain,
% 1.00/1.21 ((~![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(s60, c_n1) | (~m_main_v_state1(s61, c_n1)) | (~node6(s60, s61))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[5399, 5398])).
% 1.00/1.21 tff(5401,plain,
% 1.00/1.21 (~m_main_v_state1(s61, c_n1)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5400, 835, 5194, 5279])).
% 1.00/1.21 tff(5402,plain,
% 1.00/1.21 (((~![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)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5403,plain,
% 1.00/1.21 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s61, c_n1) | (~node2(s61)))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(5404,plain,
% 1.00/1.21 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s61, c_n1) | (~node2(s61))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[5403, 5402])).
% 1.00/1.21 tff(5405,plain,
% 1.00/1.21 (~node2(s61)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5404, 787, 5401])).
% 1.00/1.21 tff(5406,plain,
% 1.00/1.21 (((~![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)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5407,plain,
% 1.00/1.21 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s61, c_t2) | (~node1(s61)))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(5408,plain,
% 1.00/1.21 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s61, c_t2) | (~node1(s61))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[5407, 5406])).
% 1.00/1.21 tff(5409,plain,
% 1.00/1.21 (~node1(s61)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5408, 195, 5326])).
% 1.00/1.21 tff(5410,plain,
% 1.00/1.21 (((~![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))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5411,plain,
% 1.00/1.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s61, s62)) | node7(s61, s62))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(5412,plain,
% 1.00/1.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s61, s62)) | node7(s61, s62)),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[5411, 5410])).
% 1.00/1.21 tff(5413,plain,
% 1.00/1.21 (node7(s61, s62)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5412, 206, 5337])).
% 1.00/1.21 tff(5414,plain,
% 1.00/1.21 (((~![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(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)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5415,plain,
% 1.00/1.21 (((~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)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5416,plain,
% 1.00/1.21 (((~![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(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))))),
% 1.00/1.21 inference(monotonicity,[status(thm)],[5415])).
% 1.00/1.21 tff(5417,plain,
% 1.00/1.21 (((~![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(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)))),
% 1.00/1.21 inference(transitivity,[status(thm)],[5416, 5414])).
% 1.00/1.21 tff(5418,plain,
% 1.00/1.21 ((~![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(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))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(5419,plain,
% 1.00/1.21 ((~![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(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))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[5418, 5417])).
% 1.00/1.21 tff(5420,plain,
% 1.00/1.21 ((~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)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5419, 892, 5413])).
% 1.00/1.21 tff(5421,plain,
% 1.00/1.21 (m_main_v_state1(s62, c_c1)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5420, 5409, 5322, 5286, 5405, 5394])).
% 1.00/1.21 tff(5422,plain,
% 1.00/1.21 (((~![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)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5423,plain,
% 1.00/1.21 ((~![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)))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(5424,plain,
% 1.00/1.21 ((~![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))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[5423, 5422])).
% 1.00/1.21 tff(5425,plain,
% 1.00/1.21 (~m_main_v_state1(s62, c_n1)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5424, 454, 5421])).
% 1.00/1.21 tff(5426,plain,
% 1.00/1.21 (((~![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)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5427,plain,
% 1.00/1.21 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s62, c_n1) | (~node11(s62)))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(5428,plain,
% 1.00/1.21 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s62, c_n1) | (~node11(s62))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[5427, 5426])).
% 1.00/1.21 tff(5429,plain,
% 1.00/1.21 (~node11(s62)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5428, 238, 5425])).
% 1.00/1.21 tff(5430,plain,
% 1.00/1.21 (succ(s62, s63) <=> succ(s62, s63)),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5431,axiom,(succ(s62, s63)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound63')).
% 1.00/1.21 tff(5432,plain,
% 1.00/1.21 (succ(s62, s63)),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[5431, 5430])).
% 1.00/1.21 tff(5433,plain,
% 1.00/1.21 (((~![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))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5434,plain,
% 1.00/1.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s62, s63)) | trans(s62, s63))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(5435,plain,
% 1.00/1.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s62, s63)) | trans(s62, s63)),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[5434, 5433])).
% 1.00/1.21 tff(5436,plain,
% 1.00/1.21 (trans(s62, s63)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5435, 5432, 32])).
% 1.00/1.21 tff(5437,plain,
% 1.00/1.21 (((~![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))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5438,plain,
% 1.00/1.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s62, s63)) | node14(s62, s63))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(5439,plain,
% 1.00/1.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s62, s63)) | node14(s62, s63)),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[5438, 5437])).
% 1.00/1.21 tff(5440,plain,
% 1.00/1.21 (node14(s62, s63)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5439, 46, 5436])).
% 1.00/1.21 tff(5441,plain,
% 1.00/1.21 (((~![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)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5442,plain,
% 1.00/1.21 ((~![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)))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(5443,plain,
% 1.00/1.21 ((~![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))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[5442, 5441])).
% 1.00/1.21 tff(5444,plain,
% 1.00/1.21 (m_main_v_state2(s62, c_c2) | node9(s62) | node8(s62) | node10(s62) | node11(s62) | node12(s62) | node13(s62, s63)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5443, 296, 5440])).
% 1.00/1.21 tff(5445,plain,
% 1.00/1.21 (node13(s62, s63)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[5444, 5429, 5386, 5382, 5378, 5374, 5357])).
% 1.00/1.21 tff(5446,plain,
% 1.00/1.21 (((~![V: $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)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5447,plain,
% 1.00/1.21 (((~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)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(5448,plain,
% 1.00/1.21 (((~![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))))),
% 1.00/1.22 inference(monotonicity,[status(thm)],[5447])).
% 1.00/1.22 tff(5449,plain,
% 1.00/1.22 (((~![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)))),
% 1.00/1.22 inference(transitivity,[status(thm)],[5448, 5446])).
% 1.00/1.22 tff(5450,plain,
% 1.00/1.22 ((~![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)))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(5451,plain,
% 1.00/1.22 ((~![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(s62, c_n2) | (~m_main_v_state2(s63, c_n2)) | (~node13(s62, s63))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[5450, 5449])).
% 1.00/1.22 tff(5452,plain,
% 1.00/1.22 (~m_main_v_state2(s63, c_n2)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[5451, 311, 5370, 5445])).
% 1.00/1.22 tff(5453,plain,
% 1.00/1.22 (((~![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)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5454,plain,
% 1.00/1.22 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s63, c_n2) | (~node9(s63)))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(5455,plain,
% 1.00/1.22 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s63, c_n2) | (~node9(s63))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[5454, 5453])).
% 1.00/1.22 tff(5456,plain,
% 1.00/1.22 (~node9(s63)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[5455, 88, 5452])).
% 1.00/1.22 tff(5457,plain,
% 1.00/1.22 (((~![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)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5458,plain,
% 1.00/1.22 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s63, c_n2) | (~node10(s63)))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(5459,plain,
% 1.00/1.22 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s63, c_n2) | (~node10(s63))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[5458, 5457])).
% 1.00/1.22 tff(5460,plain,
% 1.00/1.22 (~node10(s63)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[5459, 249, 5452])).
% 1.00/1.22 tff(5461,plain,
% 1.00/1.22 (((~![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(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)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5462,plain,
% 1.00/1.22 (((~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)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5463,plain,
% 1.00/1.22 (((~![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))))),
% 1.00/1.22 inference(monotonicity,[status(thm)],[5462])).
% 1.00/1.22 tff(5464,plain,
% 1.00/1.22 (((~![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)))),
% 1.00/1.22 inference(transitivity,[status(thm)],[5463, 5461])).
% 1.00/1.22 tff(5465,plain,
% 1.00/1.22 ((~![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))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(5466,plain,
% 1.00/1.22 ((~![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(s62, c_t2)) | m_main_v_state2(s63, c_t2) | (~node13(s62, s63))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[5465, 5464])).
% 1.00/1.22 tff(5467,plain,
% 1.00/1.22 (m_main_v_state2(s63, c_t2)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[5466, 518, 5366, 5445])).
% 1.00/1.22 tff(5468,plain,
% 1.00/1.22 (((~![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)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5469,plain,
% 1.00/1.22 ((~![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)))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(5470,plain,
% 1.00/1.22 ((~![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))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[5469, 5468])).
% 1.00/1.22 tff(5471,plain,
% 1.00/1.22 (~m_main_v_state1(s62, c_t1)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[5470, 539, 5421])).
% 1.00/1.22 tff(5472,plain,
% 1.00/1.22 (((~![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)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5473,plain,
% 1.00/1.22 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s62, c_t1) | (~node5(s62)))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(5474,plain,
% 1.00/1.22 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s62, c_t1) | (~node5(s62))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[5473, 5472])).
% 1.00/1.22 tff(5475,plain,
% 1.00/1.22 (~node5(s62)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[5474, 550, 5471])).
% 1.00/1.22 tff(5476,plain,
% 1.00/1.22 (((~![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)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5477,plain,
% 1.00/1.22 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s62, c_n2) | (~node4(s62)))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(5478,plain,
% 1.00/1.22 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s62, c_n2) | (~node4(s62))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[5477, 5476])).
% 1.00/1.22 tff(5479,plain,
% 1.00/1.22 (~node4(s62)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[5478, 388, 5370])).
% 1.00/1.22 tff(5480,plain,
% 1.00/1.22 (((~![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)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5481,plain,
% 1.00/1.22 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s62, c_c2) | (~node3(s62)))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(5482,plain,
% 1.00/1.22 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s62, c_c2) | (~node3(s62))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[5481, 5480])).
% 1.00/1.22 tff(5483,plain,
% 1.00/1.22 (~node3(s62)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[5482, 399, 5386])).
% 1.00/1.22 tff(5484,plain,
% 1.00/1.22 (((~![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)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5485,plain,
% 1.00/1.22 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s62, c_n2) | (~node2(s62)))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(5486,plain,
% 1.00/1.22 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s62, c_n2) | (~node2(s62))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[5485, 5484])).
% 1.00/1.22 tff(5487,plain,
% 1.00/1.22 (~node2(s62)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[5486, 410, 5370])).
% 1.00/1.22 tff(5488,plain,
% 1.00/1.22 (((~![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)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5489,plain,
% 1.00/1.22 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s62, c_n1) | (~node1(s62)))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(5490,plain,
% 1.00/1.22 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s62, c_n1) | (~node1(s62))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[5489, 5488])).
% 1.00/1.22 tff(5491,plain,
% 1.00/1.22 (~node1(s62)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[5490, 421, 5425])).
% 1.00/1.22 tff(5492,plain,
% 1.00/1.22 (((~![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))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5493,plain,
% 1.00/1.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s62, s63)) | node7(s62, s63))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(5494,plain,
% 1.00/1.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s62, s63)) | node7(s62, s63)),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[5493, 5492])).
% 1.00/1.22 tff(5495,plain,
% 1.00/1.22 (node7(s62, s63)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[5494, 206, 5436])).
% 1.00/1.22 tff(5496,plain,
% 1.00/1.22 (((~![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(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)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5497,plain,
% 1.00/1.22 (((~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)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5498,plain,
% 1.00/1.22 (((~![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(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))))),
% 1.00/1.22 inference(monotonicity,[status(thm)],[5497])).
% 1.00/1.22 tff(5499,plain,
% 1.00/1.22 (((~![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(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)))),
% 1.00/1.22 inference(transitivity,[status(thm)],[5498, 5496])).
% 1.00/1.22 tff(5500,plain,
% 1.00/1.22 ((~![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(s62, c_c1)) | node1(s62) | node2(s62) | node3(s62) | node4(s62) | node5(s62) | (~node7(s62, s63)) | m_main_v_state1(s63, c_n1))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(5501,plain,
% 1.00/1.22 ((~![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(s63, c_n1) | (~m_main_v_state1(s62, c_c1)) | node1(s62) | node2(s62) | node3(s62) | node4(s62) | node5(s62) | (~node7(s62, s63))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[5500, 5499])).
% 1.00/1.22 tff(5502,plain,
% 1.00/1.22 (m_main_v_state1(s63, c_n1) | (~m_main_v_state1(s62, c_c1)) | node1(s62) | node2(s62) | node3(s62) | node4(s62) | node5(s62)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[5501, 584, 5495])).
% 1.00/1.22 tff(5503,plain,
% 1.00/1.22 (m_main_v_state1(s63, c_n1)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[5502, 5491, 5421, 5487, 5483, 5479, 5475])).
% 1.00/1.22 tff(5504,plain,
% 1.00/1.22 (((~![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)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5505,plain,
% 1.00/1.22 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s63, c_n2) | (~node8(s63)))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(5506,plain,
% 1.00/1.22 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s63, c_n2) | (~node8(s63))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[5505, 5504])).
% 1.00/1.22 tff(5507,plain,
% 1.00/1.22 (~node8(s63)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[5506, 271, 5452])).
% 1.00/1.22 tff(5508,plain,
% 1.00/1.22 (succ(s63, s64) <=> succ(s63, s64)),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5509,axiom,(succ(s63, s64)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound64')).
% 1.00/1.22 tff(5510,plain,
% 1.00/1.22 (succ(s63, s64)),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[5509, 5508])).
% 1.00/1.22 tff(5511,plain,
% 1.00/1.22 (((~![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))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5512,plain,
% 1.00/1.22 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s63, s64)) | trans(s63, s64))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(5513,plain,
% 1.00/1.22 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s63, s64)) | trans(s63, s64)),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[5512, 5511])).
% 1.00/1.22 tff(5514,plain,
% 1.00/1.22 (trans(s63, s64)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[5513, 5510, 32])).
% 1.00/1.22 tff(5515,plain,
% 1.00/1.22 (((~![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))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5516,plain,
% 1.00/1.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s63, s64)) | node14(s63, s64))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(5517,plain,
% 1.00/1.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s63, s64)) | node14(s63, s64)),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[5516, 5515])).
% 1.00/1.22 tff(5518,plain,
% 1.00/1.22 (node14(s63, s64)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[5517, 46, 5514])).
% 1.00/1.22 tff(5519,plain,
% 1.00/1.22 (((~![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))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5520,plain,
% 1.00/1.22 ((~![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))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(5521,plain,
% 1.00/1.22 ((~![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)),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[5520, 5519])).
% 1.00/1.22 tff(5522,plain,
% 1.00/1.22 ((~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)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[5521, 617, 5518])).
% 1.00/1.22 tff(5523,plain,
% 1.00/1.22 (m_main_v_state2(s64, c_c2)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[5522, 5507, 5503, 5467, 5460, 5456])).
% 1.00/1.22 tff(5524,plain,
% 1.00/1.22 (((~![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)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5525,plain,
% 1.00/1.22 ((~![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)))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(5526,plain,
% 1.00/1.22 ((~![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))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[5525, 5524])).
% 1.00/1.22 tff(5527,plain,
% 1.00/1.22 (~m_main_v_state2(s64, c_t2)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[5526, 260, 5523])).
% 1.00/1.22 tff(5528,plain,
% 1.00/1.22 (((~![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)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5529,plain,
% 1.00/1.22 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s64, c_t2) | (~node12(s64)))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(5530,plain,
% 1.00/1.22 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s64, c_t2) | (~node12(s64))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[5529, 5528])).
% 1.00/1.22 tff(5531,plain,
% 1.00/1.22 (~node12(s64)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[5530, 633, 5527])).
% 1.00/1.22 tff(5532,plain,
% 1.00/1.22 (((~![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))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5533,plain,
% 1.00/1.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s63, s64)) | node7(s63, s64))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(5534,plain,
% 1.00/1.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s63, s64)) | node7(s63, s64)),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[5533, 5532])).
% 1.00/1.22 tff(5535,plain,
% 1.00/1.22 (node7(s63, s64)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[5534, 206, 5514])).
% 1.00/1.22 tff(5536,plain,
% 1.00/1.22 (((~![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(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))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5537,plain,
% 1.00/1.22 ((~![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(s63, c_n1)) | (~m_main_v_state2(s63, c_t2)) | (~node7(s63, s64)) | m_main_v_state1(s64, c_t1))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(5538,plain,
% 1.00/1.22 ((~![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(s63, c_n1)) | (~m_main_v_state2(s63, c_t2)) | (~node7(s63, s64)) | m_main_v_state1(s64, c_t1)),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[5537, 5536])).
% 1.00/1.22 tff(5539,plain,
% 1.00/1.22 ((~m_main_v_state1(s63, c_n1)) | (~m_main_v_state2(s63, c_t2)) | m_main_v_state1(s64, c_t1)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[5538, 651, 5535])).
% 1.00/1.22 tff(5540,plain,
% 1.00/1.22 (m_main_v_state1(s64, c_t1)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[5539, 5467, 5503])).
% 1.00/1.22 tff(5541,plain,
% 1.00/1.22 (((~![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)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5542,plain,
% 1.00/1.22 ((~![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)))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(5543,plain,
% 1.00/1.22 ((~![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))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[5542, 5541])).
% 1.00/1.22 tff(5544,plain,
% 1.00/1.22 (~m_main_v_state1(s64, c_n1)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[5543, 10, 5540])).
% 1.00/1.22 tff(5545,plain,
% 1.00/1.22 (((~![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)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5546,plain,
% 1.00/1.22 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s64, c_n1) | (~node11(s64)))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(5547,plain,
% 1.00/1.22 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s64, c_n1) | (~node11(s64))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[5546, 5545])).
% 1.00/1.22 tff(5548,plain,
% 1.00/1.22 (~node11(s64)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[5547, 238, 5544])).
% 1.00/1.22 tff(5549,plain,
% 1.00/1.22 (((~![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)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5550,plain,
% 1.00/1.22 ((~![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)))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(5551,plain,
% 1.00/1.22 ((~![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))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[5550, 5549])).
% 1.00/1.22 tff(5552,plain,
% 1.00/1.22 (~m_main_v_state1(s64, c_c1)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[5551, 539, 5540])).
% 1.00/1.22 tff(5553,plain,
% 1.00/1.22 (((~![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)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5554,plain,
% 1.00/1.22 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s64, c_c1) | (~node10(s64)))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(5555,plain,
% 1.00/1.22 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s64, c_c1) | (~node10(s64))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[5554, 5553])).
% 1.00/1.22 tff(5556,plain,
% 1.00/1.22 (~node10(s64)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[5555, 675, 5552])).
% 1.00/1.22 tff(5557,plain,
% 1.00/1.22 (((~![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)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5558,plain,
% 1.00/1.22 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s64, c_n1) | (~node9(s64)))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(5559,plain,
% 1.00/1.22 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s64, c_n1) | (~node9(s64))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[5558, 5557])).
% 1.00/1.22 tff(5560,plain,
% 1.00/1.22 (~node9(s64)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[5559, 686, 5544])).
% 1.00/1.22 tff(5561,plain,
% 1.00/1.22 (((~![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)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5562,plain,
% 1.00/1.22 ((~![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)))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(5563,plain,
% 1.00/1.22 ((~![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))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[5562, 5561])).
% 1.00/1.22 tff(5564,plain,
% 1.00/1.22 (~m_main_v_state2(s64, c_n2)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[5563, 697, 5523])).
% 1.00/1.22 tff(5565,plain,
% 1.00/1.22 (((~![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)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5566,plain,
% 1.00/1.22 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s64, c_n2) | (~node8(s64)))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(5567,plain,
% 1.00/1.22 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s64, c_n2) | (~node8(s64))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[5566, 5565])).
% 1.00/1.22 tff(5568,plain,
% 1.00/1.22 (~node8(s64)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[5567, 271, 5564])).
% 1.00/1.22 tff(5569,plain,
% 1.00/1.22 (succ(s64, s65) <=> succ(s64, s65)),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5570,axiom,(succ(s64, s65)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound65')).
% 1.00/1.22 tff(5571,plain,
% 1.00/1.22 (succ(s64, s65)),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[5570, 5569])).
% 1.00/1.22 tff(5572,plain,
% 1.00/1.22 (((~![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))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5573,plain,
% 1.00/1.22 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s64, s65)) | trans(s64, s65))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(5574,plain,
% 1.00/1.22 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s64, s65)) | trans(s64, s65)),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[5573, 5572])).
% 1.00/1.22 tff(5575,plain,
% 1.00/1.22 (trans(s64, s65)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[5574, 5571, 32])).
% 1.00/1.22 tff(5576,plain,
% 1.00/1.22 (((~![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))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(5577,plain,
% 1.00/1.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s64, s65)) | node14(s64, s65))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.23 tff(5578,plain,
% 1.00/1.23 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s64, s65)) | node14(s64, s65)),
% 1.00/1.23 inference(modus_ponens,[status(thm)],[5577, 5576])).
% 1.00/1.23 tff(5579,plain,
% 1.00/1.23 (node14(s64, s65)),
% 1.00/1.23 inference(unit_resolution,[status(thm)],[5578, 46, 5575])).
% 1.00/1.23 tff(5580,plain,
% 1.00/1.23 (((~![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(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)))),
% 1.00/1.23 inference(rewrite,[status(thm)],[])).
% 1.00/1.23 tff(5581,plain,
% 1.00/1.23 (((~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)))),
% 1.00/1.23 inference(rewrite,[status(thm)],[])).
% 1.00/1.23 tff(5582,plain,
% 1.00/1.23 (((~![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(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))))),
% 1.00/1.23 inference(monotonicity,[status(thm)],[5581])).
% 1.00/1.23 tff(5583,plain,
% 1.00/1.23 (((~![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(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)))),
% 1.00/1.23 inference(transitivity,[status(thm)],[5582, 5580])).
% 1.00/1.23 tff(5584,plain,
% 1.00/1.23 ((~![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(s64, c_c2)) | node9(s64) | node8(s64) | node10(s64) | node11(s64) | node12(s64) | (~node14(s64, s65)) | m_main_v_state2(s65, c_n2))),
% 1.00/1.23 inference(quant_inst,[status(thm)],[])).
% 1.00/1.23 tff(5585,plain,
% 1.00/1.23 ((~![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(s65, c_n2) | node9(s64) | node8(s64) | node10(s64) | node11(s64) | node12(s64) | (~node14(s64, s65)) | (~m_main_v_state2(s64, c_c2))),
% 1.00/1.23 inference(modus_ponens,[status(thm)],[5584, 5583])).
% 1.00/1.23 tff(5586,plain,
% 1.00/1.23 (m_main_v_state2(s65, c_n2) | node9(s64) | node8(s64) | node10(s64) | node11(s64) | node12(s64) | (~m_main_v_state2(s64, c_c2))),
% 1.00/1.23 inference(unit_resolution,[status(thm)],[5585, 726, 5579])).
% 1.00/1.23 tff(5587,plain,
% 1.00/1.23 (m_main_v_state2(s65, c_n2)),
% 1.00/1.23 inference(unit_resolution,[status(thm)],[5586, 5568, 5523, 5560, 5556, 5548, 5531])).
% 1.00/1.23 tff(5588,plain,
% 1.00/1.23 (((~![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)))),
% 1.00/1.23 inference(rewrite,[status(thm)],[])).
% 1.00/1.23 tff(5589,plain,
% 1.00/1.23 ((~![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)))),
% 1.00/1.23 inference(quant_inst,[status(thm)],[])).
% 1.00/1.23 tff(5590,plain,
% 1.00/1.23 ((~![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))),
% 1.00/1.23 inference(modus_ponens,[status(thm)],[5589, 5588])).
% 1.00/1.23 tff(5591,plain,
% 1.00/1.23 (~m_main_v_state2(s65, c_c2)),
% 1.00/1.23 inference(unit_resolution,[status(thm)],[5590, 697, 5587])).
% 1.00/1.23 tff(5592,plain,
% 1.00/1.23 (((~![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)))),
% 1.00/1.23 inference(rewrite,[status(thm)],[])).
% 1.00/1.23 tff(5593,plain,
% 1.00/1.23 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s65, c_c2) | (~node3(s65)))),
% 1.00/1.23 inference(quant_inst,[status(thm)],[])).
% 1.00/1.23 tff(5594,plain,
% 1.00/1.23 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s65, c_c2) | (~node3(s65))),
% 1.00/1.23 inference(modus_ponens,[status(thm)],[5593, 5592])).
% 1.00/1.23 tff(5595,plain,
% 1.00/1.23 (~node3(s65)),
% 1.00/1.23 inference(unit_resolution,[status(thm)],[5594, 399, 5591])).
% 1.00/1.23 tff(5596,plain,
% 1.00/1.23 (((~![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)))),
% 1.00/1.23 inference(rewrite,[status(thm)],[])).
% 1.00/1.23 tff(5597,plain,
% 1.00/1.23 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s64, c_n1) | (~node1(s64)))),
% 1.00/1.23 inference(quant_inst,[status(thm)],[])).
% 1.00/1.23 tff(5598,plain,
% 1.00/1.23 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s64, c_n1) | (~node1(s64))),
% 1.00/1.23 inference(modus_ponens,[status(thm)],[5597, 5596])).
% 1.00/1.23 tff(5599,plain,
% 1.00/1.23 (~node1(s64)),
% 1.00/1.23 inference(unit_resolution,[status(thm)],[5598, 421, 5544])).
% 1.00/1.23 tff(5600,plain,
% 1.00/1.23 (((~![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))),
% 1.00/1.23 inference(rewrite,[status(thm)],[])).
% 1.00/1.23 tff(5601,plain,
% 1.00/1.23 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s63, s64)) | node18(s63, s64))),
% 1.00/1.23 inference(quant_inst,[status(thm)],[])).
% 1.00/1.23 tff(5602,plain,
% 1.00/1.23 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s63, s64)) | node18(s63, s64)),
% 1.00/1.23 inference(modus_ponens,[status(thm)],[5601, 5600])).
% 1.00/1.23 tff(5603,plain,
% 1.00/1.23 (node18(s63, s64)),
% 1.00/1.23 inference(unit_resolution,[status(thm)],[5602, 125, 5514])).
% 1.00/1.23 tff(5604,plain,
% 1.00/1.23 (((~![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(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))),
% 1.00/1.23 inference(rewrite,[status(thm)],[])).
% 1.00/1.23 tff(5605,plain,
% 1.00/1.23 ((~![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(s63, c_n1)) | (~m_main_v_state2(s63, c_t2)) | (~node18(s63, s64)) | m_main_v_turn(s64, c_2))),
% 1.00/1.23 inference(quant_inst,[status(thm)],[])).
% 1.00/1.23 tff(5606,plain,
% 1.00/1.23 ((~![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(s63, c_n1)) | (~m_main_v_state2(s63, c_t2)) | (~node18(s63, s64)) | m_main_v_turn(s64, c_2)),
% 1.00/1.23 inference(modus_ponens,[status(thm)],[5605, 5604])).
% 1.00/1.23 tff(5607,plain,
% 1.00/1.23 ((~m_main_v_state1(s63, c_n1)) | (~m_main_v_state2(s63, c_t2)) | m_main_v_turn(s64, c_2)),
% 1.00/1.23 inference(unit_resolution,[status(thm)],[5606, 760, 5603])).
% 1.00/1.23 tff(5608,plain,
% 1.00/1.23 (m_main_v_turn(s64, c_2)),
% 1.00/1.23 inference(unit_resolution,[status(thm)],[5607, 5467, 5503])).
% 1.00/1.23 tff(5609,plain,
% 1.00/1.23 (((~![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)))),
% 1.00/1.23 inference(rewrite,[status(thm)],[])).
% 1.00/1.23 tff(5610,plain,
% 1.00/1.23 ((~![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)))),
% 1.00/1.23 inference(quant_inst,[status(thm)],[])).
% 1.00/1.23 tff(5611,plain,
% 1.00/1.23 ((~![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))),
% 1.00/1.23 inference(modus_ponens,[status(thm)],[5610, 5609])).
% 1.00/1.23 tff(5612,plain,
% 1.00/1.23 (~m_main_v_turn(s64, c_1)),
% 1.00/1.23 inference(unit_resolution,[status(thm)],[5611, 156, 5608])).
% 1.00/1.23 tff(5613,plain,
% 1.00/1.23 (((~![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)))),
% 1.00/1.23 inference(rewrite,[status(thm)],[])).
% 1.00/1.23 tff(5614,plain,
% 1.00/1.23 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s64, c_1) | (~node5(s64)))),
% 1.00/1.23 inference(quant_inst,[status(thm)],[])).
% 1.00/1.23 tff(5615,plain,
% 1.00/1.23 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s64, c_1) | (~node5(s64))),
% 1.00/1.23 inference(modus_ponens,[status(thm)],[5614, 5613])).
% 1.00/1.23 tff(5616,plain,
% 1.00/1.23 (~node5(s64)),
% 1.00/1.23 inference(unit_resolution,[status(thm)],[5615, 776, 5612])).
% 1.00/1.23 tff(5617,plain,
% 1.00/1.23 (((~![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)))),
% 1.00/1.23 inference(rewrite,[status(thm)],[])).
% 1.00/1.23 tff(5618,plain,
% 1.00/1.23 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s64, c_n1) | (~node2(s64)))),
% 1.00/1.23 inference(quant_inst,[status(thm)],[])).
% 1.00/1.23 tff(5619,plain,
% 1.00/1.23 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s64, c_n1) | (~node2(s64))),
% 1.00/1.23 inference(modus_ponens,[status(thm)],[5618, 5617])).
% 1.00/1.23 tff(5620,plain,
% 1.00/1.23 (~node2(s64)),
% 1.00/1.23 inference(unit_resolution,[status(thm)],[5619, 787, 5544])).
% 1.00/1.23 tff(5621,plain,
% 1.00/1.23 (((~![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)))),
% 1.00/1.23 inference(rewrite,[status(thm)],[])).
% 1.00/1.23 tff(5622,plain,
% 1.00/1.23 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s64, c_n1) | (~node3(s64)))),
% 1.00/1.23 inference(quant_inst,[status(thm)],[])).
% 1.00/1.23 tff(5623,plain,
% 1.00/1.23 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s64, c_n1) | (~node3(s64))),
% 1.00/1.23 inference(modus_ponens,[status(thm)],[5622, 5621])).
% 1.00/1.23 tff(5624,plain,
% 1.00/1.23 (~node3(s64)),
% 1.00/1.23 inference(unit_resolution,[status(thm)],[5623, 798, 5544])).
% 1.00/1.23 tff(5625,plain,
% 1.00/1.23 (((~![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)))),
% 1.00/1.23 inference(rewrite,[status(thm)],[])).
% 1.00/1.23 tff(5626,plain,
% 1.00/1.23 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s64, c_n2) | (~node4(s64)))),
% 1.00/1.23 inference(quant_inst,[status(thm)],[])).
% 1.00/1.23 tff(5627,plain,
% 1.00/1.23 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s64, c_n2) | (~node4(s64))),
% 1.00/1.23 inference(modus_ponens,[status(thm)],[5626, 5625])).
% 1.00/1.23 tff(5628,plain,
% 1.00/1.23 (~node4(s64)),
% 1.00/1.23 inference(unit_resolution,[status(thm)],[5627, 388, 5564])).
% 1.00/1.23 tff(5629,plain,
% 1.00/1.23 (((~![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))),
% 1.00/1.23 inference(rewrite,[status(thm)],[])).
% 1.00/1.23 tff(5630,plain,
% 1.00/1.23 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s64, s65)) | node7(s64, s65))),
% 1.00/1.23 inference(quant_inst,[status(thm)],[])).
% 1.00/1.23 tff(5631,plain,
% 1.00/1.23 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s64, s65)) | node7(s64, s65)),
% 1.00/1.23 inference(modus_ponens,[status(thm)],[5630, 5629])).
% 1.00/1.23 tff(5632,plain,
% 1.00/1.23 (node7(s64, s65)),
% 1.00/1.23 inference(unit_resolution,[status(thm)],[5631, 206, 5575])).
% 1.00/1.23 tff(5633,plain,
% 1.00/1.23 (((~![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(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)))),
% 1.00/1.23 inference(rewrite,[status(thm)],[])).
% 1.00/1.23 tff(5634,plain,
% 1.00/1.23 ((~![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(s64, c_c1) | node1(s64) | node2(s64) | node3(s64) | node4(s64) | node5(s64) | node6(s64, s65) | (~node7(s64, s65)))),
% 1.00/1.23 inference(quant_inst,[status(thm)],[])).
% 1.00/1.23 tff(5635,plain,
% 1.00/1.23 ((~![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(s64, c_c1) | node1(s64) | node2(s64) | node3(s64) | node4(s64) | node5(s64) | node6(s64, s65) | (~node7(s64, s65))),
% 1.00/1.23 inference(modus_ponens,[status(thm)],[5634, 5633])).
% 1.00/1.23 tff(5636,plain,
% 1.00/1.23 (m_main_v_state1(s64, c_c1) | node1(s64) | node2(s64) | node3(s64) | node4(s64) | node5(s64) | node6(s64, s65)),
% 1.00/1.23 inference(unit_resolution,[status(thm)],[5635, 820, 5632])).
% 1.00/1.23 tff(5637,plain,
% 1.00/1.23 (node6(s64, s65)),
% 1.00/1.23 inference(unit_resolution,[status(thm)],[5636, 5628, 5552, 5624, 5620, 5616, 5599])).
% 1.00/1.23 tff(5638,plain,
% 1.00/1.23 (((~![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(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)))),
% 1.00/1.23 inference(rewrite,[status(thm)],[])).
% 1.00/1.23 tff(5639,plain,
% 1.00/1.23 (((~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)))),
% 1.00/1.23 inference(rewrite,[status(thm)],[])).
% 1.00/1.23 tff(5640,plain,
% 1.00/1.23 (((~![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))))),
% 1.00/1.23 inference(monotonicity,[status(thm)],[5639])).
% 1.00/1.23 tff(5641,plain,
% 1.00/1.23 (((~![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)))),
% 1.00/1.23 inference(transitivity,[status(thm)],[5640, 5638])).
% 1.00/1.23 tff(5642,plain,
% 1.00/1.23 ((~![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)))),
% 1.00/1.23 inference(quant_inst,[status(thm)],[])).
% 1.00/1.23 tff(5643,plain,
% 1.00/1.23 ((~![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(s64, c_n1) | (~m_main_v_state1(s65, c_n1)) | (~node6(s64, s65))),
% 1.00/1.23 inference(modus_ponens,[status(thm)],[5642, 5641])).
% 1.00/1.23 tff(5644,plain,
% 1.00/1.23 (~m_main_v_state1(s65, c_n1)),
% 1.00/1.23 inference(unit_resolution,[status(thm)],[5643, 835, 5544, 5637])).
% 1.00/1.23 tff(5645,plain,
% 1.00/1.23 (((~![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)))),
% 1.00/1.23 inference(rewrite,[status(thm)],[])).
% 1.00/1.23 tff(5646,plain,
% 1.00/1.23 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s65, c_n1) | (~node2(s65)))),
% 1.00/1.23 inference(quant_inst,[status(thm)],[])).
% 1.00/1.23 tff(5647,plain,
% 1.00/1.23 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s65, c_n1) | (~node2(s65))),
% 1.00/1.23 inference(modus_ponens,[status(thm)],[5646, 5645])).
% 1.00/1.23 tff(5648,plain,
% 1.00/1.23 (~node2(s65)),
% 1.00/1.23 inference(unit_resolution,[status(thm)],[5647, 787, 5644])).
% 1.00/1.23 tff(5649,plain,
% 1.00/1.23 (((~![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(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)))),
% 1.00/1.23 inference(rewrite,[status(thm)],[])).
% 1.00/1.23 tff(5650,plain,
% 1.00/1.23 (((~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)))),
% 1.00/1.23 inference(rewrite,[status(thm)],[])).
% 1.00/1.23 tff(5651,plain,
% 1.00/1.23 (((~![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))))),
% 1.00/1.23 inference(monotonicity,[status(thm)],[5650])).
% 1.00/1.23 tff(5652,plain,
% 1.00/1.23 (((~![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)))),
% 1.00/1.23 inference(transitivity,[status(thm)],[5651, 5649])).
% 1.00/1.23 tff(5653,plain,
% 1.00/1.23 ((~![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))),
% 1.00/1.23 inference(quant_inst,[status(thm)],[])).
% 1.00/1.23 tff(5654,plain,
% 1.00/1.23 ((~![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(s64, c_t1)) | m_main_v_state1(s65, c_t1) | (~node6(s64, s65))),
% 1.00/1.23 inference(modus_ponens,[status(thm)],[5653, 5652])).
% 1.00/1.23 tff(5655,plain,
% 1.00/1.23 (m_main_v_state1(s65, c_t1)),
% 1.00/1.23 inference(unit_resolution,[status(thm)],[5654, 856, 5540, 5637])).
% 1.00/1.23 tff(5656,plain,
% 1.00/1.23 (((~![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)))),
% 1.00/1.23 inference(rewrite,[status(thm)],[])).
% 1.00/1.23 tff(5657,plain,
% 1.00/1.23 ((~![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)))),
% 1.00/1.23 inference(quant_inst,[status(thm)],[])).
% 1.00/1.23 tff(5658,plain,
% 1.00/1.23 ((~![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))),
% 1.00/1.23 inference(modus_ponens,[status(thm)],[5657, 5656])).
% 1.00/1.23 tff(5659,plain,
% 1.00/1.23 (~m_main_v_state2(s65, c_t2)),
% 1.00/1.23 inference(unit_resolution,[status(thm)],[5658, 77, 5587])).
% 1.00/1.23 tff(5660,plain,
% 1.00/1.23 (((~![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)))),
% 1.00/1.23 inference(rewrite,[status(thm)],[])).
% 1.00/1.23 tff(5661,plain,
% 1.00/1.23 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s65, c_t2) | (~node1(s65)))),
% 1.00/1.23 inference(quant_inst,[status(thm)],[])).
% 1.00/1.23 tff(5662,plain,
% 1.00/1.23 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s65, c_t2) | (~node1(s65))),
% 1.00/1.23 inference(modus_ponens,[status(thm)],[5661, 5660])).
% 1.00/1.23 tff(5663,plain,
% 1.00/1.23 (~node1(s65)),
% 1.00/1.23 inference(unit_resolution,[status(thm)],[5662, 195, 5659])).
% 1.00/1.23 tff(5664,plain,
% 1.00/1.23 (succ(s65, s66) <=> succ(s65, s66)),
% 1.00/1.23 inference(rewrite,[status(thm)],[])).
% 1.00/1.23 tff(5665,axiom,(succ(s65, s66)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound66')).
% 1.00/1.23 tff(5666,plain,
% 1.00/1.23 (succ(s65, s66)),
% 1.00/1.23 inference(modus_ponens,[status(thm)],[5665, 5664])).
% 1.00/1.23 tff(5667,plain,
% 1.00/1.23 (((~![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))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(5668,plain,
% 1.07/1.23 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s65, s66)) | trans(s65, s66))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(5669,plain,
% 1.07/1.23 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s65, s66)) | trans(s65, s66)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[5668, 5667])).
% 1.07/1.23 tff(5670,plain,
% 1.07/1.23 (trans(s65, s66)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[5669, 5666, 32])).
% 1.07/1.23 tff(5671,plain,
% 1.07/1.23 (((~![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))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(5672,plain,
% 1.07/1.23 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s65, s66)) | node7(s65, s66))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(5673,plain,
% 1.07/1.23 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s65, s66)) | node7(s65, s66)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[5672, 5671])).
% 1.07/1.23 tff(5674,plain,
% 1.07/1.23 (node7(s65, s66)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[5673, 206, 5670])).
% 1.07/1.23 tff(5675,plain,
% 1.07/1.23 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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)))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(5676,plain,
% 1.07/1.23 (((~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)))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(5677,plain,
% 1.07/1.23 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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))))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[5676])).
% 1.07/1.23 tff(5678,plain,
% 1.07/1.23 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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)))),
% 1.07/1.23 inference(transitivity,[status(thm)],[5677, 5675])).
% 1.07/1.23 tff(5679,plain,
% 1.07/1.23 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(5680,plain,
% 1.07/1.23 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[5679, 5678])).
% 1.07/1.23 tff(5681,plain,
% 1.07/1.23 ((~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)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[5680, 892, 5674])).
% 1.07/1.23 tff(5682,plain,
% 1.07/1.23 (m_main_v_state1(s66, c_c1)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[5681, 5663, 5587, 5655, 5648, 5595])).
% 1.07/1.23 tff(5683,plain,
% 1.07/1.23 (((~![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)))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(5684,plain,
% 1.07/1.23 ((~![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)))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(5685,plain,
% 1.07/1.23 ((~![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))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[5684, 5683])).
% 1.07/1.23 tff(5686,plain,
% 1.07/1.23 (~m_main_v_state1(s66, c_t1)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[5685, 539, 5682])).
% 1.07/1.23 tff(5687,plain,
% 1.07/1.23 (((~![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)))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(5688,plain,
% 1.07/1.23 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s66, c_t1) | (~node5(s66)))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(5689,plain,
% 1.07/1.23 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s66, c_t1) | (~node5(s66))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[5688, 5687])).
% 1.07/1.23 tff(5690,plain,
% 1.07/1.23 (~node5(s66)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[5689, 550, 5686])).
% 1.07/1.23 tff(5691,plain,
% 1.07/1.23 (((~![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))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(5692,plain,
% 1.07/1.23 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s65, s66)) | node14(s65, s66))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(5693,plain,
% 1.07/1.23 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s65, s66)) | node14(s65, s66)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[5692, 5691])).
% 1.07/1.23 tff(5694,plain,
% 1.07/1.23 (node14(s65, s66)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[5693, 46, 5670])).
% 1.07/1.23 tff(5695,plain,
% 1.07/1.23 (((~![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))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(5696,plain,
% 1.07/1.23 ((~![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))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(5697,plain,
% 1.07/1.23 ((~![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)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[5696, 5695])).
% 1.07/1.23 tff(5698,plain,
% 1.07/1.23 ((~m_main_v_state1(s65, c_t1)) | (~m_main_v_state2(s65, c_n2)) | m_main_v_state2(s66, c_t2)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[5697, 922, 5694])).
% 1.07/1.23 tff(5699,plain,
% 1.07/1.23 (m_main_v_state2(s66, c_t2)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[5698, 5655, 5587])).
% 1.07/1.23 tff(5700,plain,
% 1.07/1.23 (((~![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)))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(5701,plain,
% 1.07/1.23 ((~![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)))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(5702,plain,
% 1.07/1.23 ((~![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))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[5701, 5700])).
% 1.07/1.23 tff(5703,plain,
% 1.07/1.23 (~m_main_v_state2(s66, c_n2)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[5702, 77, 5699])).
% 1.07/1.23 tff(5704,plain,
% 1.07/1.23 (((~![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)))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(5705,plain,
% 1.07/1.23 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s66, c_n2) | (~node4(s66)))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(5706,plain,
% 1.07/1.23 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s66, c_n2) | (~node4(s66))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[5705, 5704])).
% 1.07/1.23 tff(5707,plain,
% 1.07/1.23 (~node4(s66)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[5706, 388, 5703])).
% 1.07/1.24 tff(5708,plain,
% 1.07/1.24 (((~![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)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5709,plain,
% 1.07/1.24 ((~![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)))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(5710,plain,
% 1.07/1.24 ((~![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))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[5709, 5708])).
% 1.07/1.24 tff(5711,plain,
% 1.07/1.24 (~m_main_v_state2(s66, c_c2)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5710, 260, 5699])).
% 1.07/1.24 tff(5712,plain,
% 1.07/1.24 (((~![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)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5713,plain,
% 1.07/1.24 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s66, c_c2) | (~node3(s66)))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(5714,plain,
% 1.07/1.24 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s66, c_c2) | (~node3(s66))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[5713, 5712])).
% 1.07/1.24 tff(5715,plain,
% 1.07/1.24 (~node3(s66)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5714, 399, 5711])).
% 1.07/1.24 tff(5716,plain,
% 1.07/1.24 (((~![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)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5717,plain,
% 1.07/1.24 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s66, c_n2) | (~node2(s66)))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(5718,plain,
% 1.07/1.24 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s66, c_n2) | (~node2(s66))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[5717, 5716])).
% 1.07/1.24 tff(5719,plain,
% 1.07/1.24 (~node2(s66)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5718, 410, 5703])).
% 1.07/1.24 tff(5720,plain,
% 1.07/1.24 (((~![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)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5721,plain,
% 1.07/1.24 ((~![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)))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(5722,plain,
% 1.07/1.24 ((~![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))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[5721, 5720])).
% 1.07/1.24 tff(5723,plain,
% 1.07/1.24 (~m_main_v_state1(s66, c_n1)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5722, 454, 5682])).
% 1.07/1.24 tff(5724,plain,
% 1.07/1.24 (((~![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)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5725,plain,
% 1.07/1.24 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s66, c_n1) | (~node1(s66)))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(5726,plain,
% 1.07/1.24 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s66, c_n1) | (~node1(s66))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[5725, 5724])).
% 1.07/1.24 tff(5727,plain,
% 1.07/1.24 (~node1(s66)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5726, 421, 5723])).
% 1.07/1.24 tff(5728,plain,
% 1.07/1.24 (succ(s66, s67) <=> succ(s66, s67)),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5729,axiom,(succ(s66, s67)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound67')).
% 1.07/1.24 tff(5730,plain,
% 1.07/1.24 (succ(s66, s67)),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[5729, 5728])).
% 1.07/1.24 tff(5731,plain,
% 1.07/1.24 (((~![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))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5732,plain,
% 1.07/1.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s66, s67)) | trans(s66, s67))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(5733,plain,
% 1.07/1.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s66, s67)) | trans(s66, s67)),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[5732, 5731])).
% 1.07/1.24 tff(5734,plain,
% 1.07/1.24 (trans(s66, s67)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5733, 5730, 32])).
% 1.07/1.24 tff(5735,plain,
% 1.07/1.24 (((~![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))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5736,plain,
% 1.07/1.24 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s66, s67)) | node7(s66, s67))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(5737,plain,
% 1.07/1.24 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s66, s67)) | node7(s66, s67)),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[5736, 5735])).
% 1.07/1.24 tff(5738,plain,
% 1.07/1.24 (node7(s66, s67)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5737, 206, 5734])).
% 1.07/1.24 tff(5739,plain,
% 1.07/1.24 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5740,plain,
% 1.07/1.24 (((~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)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5741,plain,
% 1.07/1.24 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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))))),
% 1.07/1.24 inference(monotonicity,[status(thm)],[5740])).
% 1.07/1.24 tff(5742,plain,
% 1.07/1.24 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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)))),
% 1.07/1.24 inference(transitivity,[status(thm)],[5741, 5739])).
% 1.07/1.24 tff(5743,plain,
% 1.07/1.24 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(5744,plain,
% 1.07/1.24 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[5743, 5742])).
% 1.07/1.24 tff(5745,plain,
% 1.07/1.24 (m_main_v_state1(s67, c_n1) | (~m_main_v_state1(s66, c_c1)) | node1(s66) | node2(s66) | node3(s66) | node4(s66) | node5(s66)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5744, 584, 5738])).
% 1.07/1.24 tff(5746,plain,
% 1.07/1.24 (m_main_v_state1(s67, c_n1)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5745, 5727, 5682, 5719, 5715, 5707, 5690])).
% 1.07/1.24 tff(5747,plain,
% 1.07/1.24 (((~![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)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5748,plain,
% 1.07/1.24 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s65, c_t2) | (~node15(s65)))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(5749,plain,
% 1.07/1.24 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s65, c_t2) | (~node15(s65))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[5748, 5747])).
% 1.07/1.24 tff(5750,plain,
% 1.07/1.24 (~node15(s65)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5749, 103, 5659])).
% 1.07/1.24 tff(5751,plain,
% 1.07/1.24 (((~![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))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5752,plain,
% 1.07/1.24 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s65, s66)) | node18(s65, s66))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(5753,plain,
% 1.07/1.24 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s65, s66)) | node18(s65, s66)),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[5752, 5751])).
% 1.07/1.24 tff(5754,plain,
% 1.07/1.24 (node18(s65, s66)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5753, 125, 5670])).
% 1.07/1.24 tff(5755,plain,
% 1.07/1.24 (((~![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(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))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5756,plain,
% 1.07/1.24 (((~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))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5757,plain,
% 1.07/1.24 (((~![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(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)))),
% 1.07/1.24 inference(monotonicity,[status(thm)],[5756])).
% 1.07/1.24 tff(5758,plain,
% 1.07/1.24 (((~![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(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))),
% 1.07/1.24 inference(transitivity,[status(thm)],[5757, 5755])).
% 1.07/1.24 tff(5759,plain,
% 1.07/1.24 ((~![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(s65, c_t1)) | (~m_main_v_state2(s65, c_n2)) | node15(s65) | (~node18(s65, s66)) | m_main_v_turn(s66, c_1))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(5760,plain,
% 1.07/1.24 ((~![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(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)),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[5759, 5758])).
% 1.07/1.24 tff(5761,plain,
% 1.07/1.24 (node15(s65) | (~m_main_v_state1(s65, c_t1)) | (~m_main_v_state2(s65, c_n2)) | m_main_v_turn(s66, c_1)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5760, 992, 5754])).
% 1.07/1.24 tff(5762,plain,
% 1.07/1.24 (m_main_v_turn(s66, c_1)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5761, 5750, 5587, 5655])).
% 1.07/1.24 tff(5763,plain,
% 1.07/1.24 (((~![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)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5764,plain,
% 1.07/1.24 ((~![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)))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(5765,plain,
% 1.07/1.24 ((~![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))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[5764, 5763])).
% 1.07/1.24 tff(5766,plain,
% 1.07/1.24 (~m_main_v_turn(s66, c_2)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5765, 156, 5762])).
% 1.07/1.24 tff(5767,plain,
% 1.07/1.24 (((~![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)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5768,plain,
% 1.07/1.24 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s66, c_2) | (~node12(s66)))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(5769,plain,
% 1.07/1.24 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s66, c_2) | (~node12(s66))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[5768, 5767])).
% 1.07/1.24 tff(5770,plain,
% 1.07/1.24 (~node12(s66)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5769, 184, 5766])).
% 1.07/1.24 tff(5771,plain,
% 1.07/1.24 (((~![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)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5772,plain,
% 1.07/1.24 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s66, c_n2) | (~node8(s66)))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(5773,plain,
% 1.07/1.24 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s66, c_n2) | (~node8(s66))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[5772, 5771])).
% 1.07/1.24 tff(5774,plain,
% 1.07/1.24 (~node8(s66)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5773, 271, 5703])).
% 1.07/1.24 tff(5775,plain,
% 1.07/1.24 (((~![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)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5776,plain,
% 1.07/1.24 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s66, c_n2) | (~node9(s66)))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(5777,plain,
% 1.07/1.24 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s66, c_n2) | (~node9(s66))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[5776, 5775])).
% 1.07/1.24 tff(5778,plain,
% 1.07/1.24 (~node9(s66)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5777, 88, 5703])).
% 1.07/1.24 tff(5779,plain,
% 1.07/1.24 (((~![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)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5780,plain,
% 1.07/1.24 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s66, c_n2) | (~node10(s66)))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(5781,plain,
% 1.07/1.24 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s66, c_n2) | (~node10(s66))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[5780, 5779])).
% 1.07/1.24 tff(5782,plain,
% 1.07/1.24 (~node10(s66)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5781, 249, 5703])).
% 1.07/1.24 tff(5783,plain,
% 1.07/1.24 (((~![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)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5784,plain,
% 1.07/1.24 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s66, c_n1) | (~node11(s66)))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(5785,plain,
% 1.07/1.24 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s66, c_n1) | (~node11(s66))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[5784, 5783])).
% 1.07/1.24 tff(5786,plain,
% 1.07/1.24 (~node11(s66)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5785, 238, 5723])).
% 1.07/1.24 tff(5787,plain,
% 1.07/1.24 (((~![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))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5788,plain,
% 1.07/1.24 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s66, s67)) | node14(s66, s67))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(5789,plain,
% 1.07/1.24 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s66, s67)) | node14(s66, s67)),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[5788, 5787])).
% 1.07/1.24 tff(5790,plain,
% 1.07/1.24 (node14(s66, s67)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5789, 46, 5734])).
% 1.07/1.24 tff(5791,plain,
% 1.07/1.24 (((~![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)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5792,plain,
% 1.07/1.24 ((~![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)))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(5793,plain,
% 1.07/1.24 ((~![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))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[5792, 5791])).
% 1.07/1.24 tff(5794,plain,
% 1.07/1.24 (m_main_v_state2(s66, c_c2) | node9(s66) | node8(s66) | node10(s66) | node11(s66) | node12(s66) | node13(s66, s67)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5793, 296, 5790])).
% 1.07/1.24 tff(5795,plain,
% 1.07/1.24 (node13(s66, s67)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5794, 5786, 5711, 5782, 5778, 5774, 5770])).
% 1.07/1.24 tff(5796,plain,
% 1.07/1.24 (((~![V: $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)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5797,plain,
% 1.07/1.24 (((~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)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5798,plain,
% 1.07/1.24 (((~![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))))),
% 1.07/1.24 inference(monotonicity,[status(thm)],[5797])).
% 1.07/1.24 tff(5799,plain,
% 1.07/1.24 (((~![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)))),
% 1.07/1.24 inference(transitivity,[status(thm)],[5798, 5796])).
% 1.07/1.24 tff(5800,plain,
% 1.07/1.24 ((~![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))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(5801,plain,
% 1.07/1.24 ((~![V: $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))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[5800, 5799])).
% 1.07/1.24 tff(5802,plain,
% 1.07/1.24 (m_main_v_state2(s67, c_t2)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5801, 518, 5699, 5795])).
% 1.07/1.24 tff(5803,plain,
% 1.07/1.24 (succ(s67, s68) <=> succ(s67, s68)),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5804,axiom,(succ(s67, s68)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound68')).
% 1.07/1.24 tff(5805,plain,
% 1.07/1.24 (succ(s67, s68)),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[5804, 5803])).
% 1.07/1.24 tff(5806,plain,
% 1.07/1.24 (((~![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))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5807,plain,
% 1.07/1.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s67, s68)) | trans(s67, s68))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(5808,plain,
% 1.07/1.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s67, s68)) | trans(s67, s68)),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[5807, 5806])).
% 1.07/1.24 tff(5809,plain,
% 1.07/1.24 (trans(s67, s68)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5808, 5805, 32])).
% 1.07/1.24 tff(5810,plain,
% 1.07/1.24 (((~![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))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5811,plain,
% 1.07/1.24 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s67, s68)) | node7(s67, s68))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(5812,plain,
% 1.07/1.24 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s67, s68)) | node7(s67, s68)),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[5811, 5810])).
% 1.07/1.24 tff(5813,plain,
% 1.07/1.24 (node7(s67, s68)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5812, 206, 5809])).
% 1.07/1.24 tff(5814,plain,
% 1.07/1.24 (((~![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))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5815,plain,
% 1.07/1.24 ((~![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))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(5816,plain,
% 1.07/1.24 ((~![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)),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[5815, 5814])).
% 1.07/1.24 tff(5817,plain,
% 1.07/1.24 ((~m_main_v_state1(s67, c_n1)) | (~m_main_v_state2(s67, c_t2)) | m_main_v_state1(s68, c_t1)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5816, 651, 5813])).
% 1.07/1.24 tff(5818,plain,
% 1.07/1.24 (m_main_v_state1(s68, c_t1)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5817, 5802, 5746])).
% 1.07/1.24 tff(5819,plain,
% 1.07/1.24 (((~![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)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5820,plain,
% 1.07/1.24 ((~![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)))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(5821,plain,
% 1.07/1.24 ((~![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))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[5820, 5819])).
% 1.07/1.24 tff(5822,plain,
% 1.07/1.24 (~m_main_v_state1(s68, c_n1)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5821, 10, 5818])).
% 1.07/1.24 tff(5823,plain,
% 1.07/1.24 (((~![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)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5824,plain,
% 1.07/1.24 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s68, c_n1) | (~node1(s68)))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(5825,plain,
% 1.07/1.24 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s68, c_n1) | (~node1(s68))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[5824, 5823])).
% 1.07/1.24 tff(5826,plain,
% 1.07/1.24 (~node1(s68)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5825, 421, 5822])).
% 1.07/1.24 tff(5827,plain,
% 1.07/1.24 (((~![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))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5828,plain,
% 1.07/1.24 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s67, s68)) | node18(s67, s68))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(5829,plain,
% 1.07/1.24 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s67, s68)) | node18(s67, s68)),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[5828, 5827])).
% 1.07/1.24 tff(5830,plain,
% 1.07/1.24 (node18(s67, s68)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5829, 125, 5809])).
% 1.07/1.24 tff(5831,plain,
% 1.07/1.24 (((~![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))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5832,plain,
% 1.07/1.24 ((~![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))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(5833,plain,
% 1.07/1.24 ((~![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)),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[5832, 5831])).
% 1.07/1.24 tff(5834,plain,
% 1.07/1.24 ((~m_main_v_state1(s67, c_n1)) | (~m_main_v_state2(s67, c_t2)) | m_main_v_turn(s68, c_2)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5833, 760, 5830])).
% 1.07/1.24 tff(5835,plain,
% 1.07/1.24 (m_main_v_turn(s68, c_2)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[5834, 5802, 5746])).
% 1.07/1.24 tff(5836,plain,
% 1.07/1.25 (((~![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)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5837,plain,
% 1.07/1.25 ((~![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)))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(5838,plain,
% 1.07/1.25 ((~![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))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[5837, 5836])).
% 1.07/1.25 tff(5839,plain,
% 1.07/1.25 (~m_main_v_turn(s68, c_1)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[5838, 156, 5835])).
% 1.07/1.25 tff(5840,plain,
% 1.07/1.25 (((~![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)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5841,plain,
% 1.07/1.25 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s68, c_1) | (~node5(s68)))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(5842,plain,
% 1.07/1.25 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s68, c_1) | (~node5(s68))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[5841, 5840])).
% 1.07/1.25 tff(5843,plain,
% 1.07/1.25 (~node5(s68)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[5842, 776, 5839])).
% 1.07/1.25 tff(5844,plain,
% 1.07/1.25 (((~![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)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5845,plain,
% 1.07/1.25 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s68, c_n1) | (~node2(s68)))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(5846,plain,
% 1.07/1.25 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s68, c_n1) | (~node2(s68))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[5845, 5844])).
% 1.07/1.25 tff(5847,plain,
% 1.07/1.25 (~node2(s68)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[5846, 787, 5822])).
% 1.07/1.25 tff(5848,plain,
% 1.07/1.25 (((~![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)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5849,plain,
% 1.07/1.25 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s68, c_n1) | (~node3(s68)))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(5850,plain,
% 1.07/1.25 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s68, c_n1) | (~node3(s68))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[5849, 5848])).
% 1.07/1.25 tff(5851,plain,
% 1.07/1.25 (~node3(s68)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[5850, 798, 5822])).
% 1.07/1.25 tff(5852,plain,
% 1.07/1.25 (((~![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)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5853,plain,
% 1.07/1.25 ((~![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)))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(5854,plain,
% 1.07/1.25 ((~![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))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[5853, 5852])).
% 1.07/1.25 tff(5855,plain,
% 1.07/1.25 (~m_main_v_state1(s68, c_c1)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[5854, 539, 5818])).
% 1.07/1.25 tff(5856,plain,
% 1.07/1.25 (((~![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(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)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5857,plain,
% 1.07/1.25 (((~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)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5858,plain,
% 1.07/1.25 (((~![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))))),
% 1.07/1.25 inference(monotonicity,[status(thm)],[5857])).
% 1.07/1.25 tff(5859,plain,
% 1.07/1.25 (((~![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)))),
% 1.07/1.25 inference(transitivity,[status(thm)],[5858, 5856])).
% 1.07/1.25 tff(5860,plain,
% 1.07/1.25 ((~![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)))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(5861,plain,
% 1.07/1.25 ((~![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(s66, c_n2) | (~m_main_v_state2(s67, c_n2)) | (~node13(s66, s67))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[5860, 5859])).
% 1.07/1.25 tff(5862,plain,
% 1.07/1.25 (~m_main_v_state2(s67, c_n2)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[5861, 311, 5703, 5795])).
% 1.07/1.25 tff(5863,plain,
% 1.07/1.25 (((~![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)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5864,plain,
% 1.07/1.25 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s67, c_n2) | (~node9(s67)))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(5865,plain,
% 1.07/1.25 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s67, c_n2) | (~node9(s67))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[5864, 5863])).
% 1.07/1.25 tff(5866,plain,
% 1.07/1.25 (~node9(s67)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[5865, 88, 5862])).
% 1.07/1.25 tff(5867,plain,
% 1.07/1.25 (((~![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)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5868,plain,
% 1.07/1.25 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s67, c_n2) | (~node10(s67)))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(5869,plain,
% 1.07/1.25 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s67, c_n2) | (~node10(s67))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[5868, 5867])).
% 1.07/1.25 tff(5870,plain,
% 1.07/1.25 (~node10(s67)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[5869, 249, 5862])).
% 1.07/1.25 tff(5871,plain,
% 1.07/1.25 (((~![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)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5872,plain,
% 1.07/1.25 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s67, c_n2) | (~node8(s67)))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(5873,plain,
% 1.07/1.25 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s67, c_n2) | (~node8(s67))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[5872, 5871])).
% 1.07/1.25 tff(5874,plain,
% 1.07/1.25 (~node8(s67)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[5873, 271, 5862])).
% 1.07/1.25 tff(5875,plain,
% 1.07/1.25 (((~![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))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5876,plain,
% 1.07/1.25 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s67, s68)) | node14(s67, s68))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(5877,plain,
% 1.07/1.25 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s67, s68)) | node14(s67, s68)),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[5876, 5875])).
% 1.07/1.25 tff(5878,plain,
% 1.07/1.25 (node14(s67, s68)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[5877, 46, 5809])).
% 1.07/1.25 tff(5879,plain,
% 1.07/1.25 (((~![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(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))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5880,plain,
% 1.07/1.25 ((~![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(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))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(5881,plain,
% 1.07/1.25 ((~![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(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)),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[5880, 5879])).
% 1.07/1.25 tff(5882,plain,
% 1.07/1.25 ((~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)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[5881, 617, 5878])).
% 1.07/1.25 tff(5883,plain,
% 1.07/1.25 (m_main_v_state2(s68, c_c2)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[5882, 5874, 5746, 5802, 5870, 5866])).
% 1.07/1.25 tff(5884,plain,
% 1.07/1.25 (((~![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)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5885,plain,
% 1.07/1.25 ((~![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)))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(5886,plain,
% 1.07/1.25 ((~![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))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[5885, 5884])).
% 1.07/1.25 tff(5887,plain,
% 1.07/1.25 (~m_main_v_state2(s68, c_n2)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[5886, 697, 5883])).
% 1.07/1.25 tff(5888,plain,
% 1.07/1.25 (((~![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)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5889,plain,
% 1.07/1.25 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s68, c_n2) | (~node4(s68)))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(5890,plain,
% 1.07/1.25 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s68, c_n2) | (~node4(s68))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[5889, 5888])).
% 1.07/1.25 tff(5891,plain,
% 1.07/1.25 (~node4(s68)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[5890, 388, 5887])).
% 1.07/1.25 tff(5892,plain,
% 1.07/1.25 (succ(s68, s69) <=> succ(s68, s69)),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5893,axiom,(succ(s68, s69)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound69')).
% 1.07/1.25 tff(5894,plain,
% 1.07/1.25 (succ(s68, s69)),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[5893, 5892])).
% 1.07/1.25 tff(5895,plain,
% 1.07/1.25 (((~![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))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5896,plain,
% 1.07/1.25 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s68, s69)) | trans(s68, s69))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(5897,plain,
% 1.07/1.25 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s68, s69)) | trans(s68, s69)),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[5896, 5895])).
% 1.07/1.25 tff(5898,plain,
% 1.07/1.25 (trans(s68, s69)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[5897, 5894, 32])).
% 1.07/1.25 tff(5899,plain,
% 1.07/1.25 (((~![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))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5900,plain,
% 1.07/1.25 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s68, s69)) | node7(s68, s69))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(5901,plain,
% 1.07/1.25 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s68, s69)) | node7(s68, s69)),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[5900, 5899])).
% 1.07/1.25 tff(5902,plain,
% 1.07/1.25 (node7(s68, s69)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[5901, 206, 5898])).
% 1.07/1.25 tff(5903,plain,
% 1.07/1.25 (((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(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)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5904,plain,
% 1.07/1.25 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s68, c_c1) | node1(s68) | node2(s68) | node3(s68) | node4(s68) | node5(s68) | node6(s68, s69) | (~node7(s68, s69)))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(5905,plain,
% 1.07/1.25 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s68, c_c1) | node1(s68) | node2(s68) | node3(s68) | node4(s68) | node5(s68) | node6(s68, s69) | (~node7(s68, s69))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[5904, 5903])).
% 1.07/1.25 tff(5906,plain,
% 1.07/1.25 (m_main_v_state1(s68, c_c1) | node1(s68) | node2(s68) | node3(s68) | node4(s68) | node5(s68) | node6(s68, s69)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[5905, 820, 5902])).
% 1.07/1.25 tff(5907,plain,
% 1.07/1.25 (node6(s68, s69)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[5906, 5891, 5855, 5851, 5847, 5843, 5826])).
% 1.07/1.25 tff(5908,plain,
% 1.07/1.25 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~m_main_v_state1(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)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5909,plain,
% 1.07/1.25 (((~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)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5910,plain,
% 1.07/1.25 (((~![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))))),
% 1.07/1.25 inference(monotonicity,[status(thm)],[5909])).
% 1.07/1.25 tff(5911,plain,
% 1.07/1.25 (((~![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)))),
% 1.07/1.25 inference(transitivity,[status(thm)],[5910, 5908])).
% 1.07/1.25 tff(5912,plain,
% 1.07/1.25 ((~![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))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(5913,plain,
% 1.07/1.25 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | (~m_main_v_state1(s68, c_t1)) | m_main_v_state1(s69, c_t1) | (~node6(s68, s69))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[5912, 5911])).
% 1.07/1.25 tff(5914,plain,
% 1.07/1.25 (m_main_v_state1(s69, c_t1)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[5913, 856, 5818, 5907])).
% 1.07/1.25 tff(5915,plain,
% 1.07/1.25 (((~![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)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5916,plain,
% 1.07/1.25 ((~![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)))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(5917,plain,
% 1.07/1.25 ((~![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))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[5916, 5915])).
% 1.07/1.25 tff(5918,plain,
% 1.07/1.25 (~m_main_v_state2(s68, c_t2)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[5917, 260, 5883])).
% 1.07/1.25 tff(5919,plain,
% 1.07/1.25 (((~![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)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5920,plain,
% 1.07/1.25 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s68, c_t2) | (~node12(s68)))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(5921,plain,
% 1.07/1.25 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s68, c_t2) | (~node12(s68))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[5920, 5919])).
% 1.07/1.25 tff(5922,plain,
% 1.07/1.25 (~node12(s68)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[5921, 633, 5918])).
% 1.07/1.25 tff(5923,plain,
% 1.07/1.25 (((~![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)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5924,plain,
% 1.07/1.25 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s68, c_n1) | (~node11(s68)))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(5925,plain,
% 1.07/1.25 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s68, c_n1) | (~node11(s68))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[5924, 5923])).
% 1.07/1.25 tff(5926,plain,
% 1.07/1.25 (~node11(s68)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[5925, 238, 5822])).
% 1.07/1.25 tff(5927,plain,
% 1.07/1.25 (((~![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)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5928,plain,
% 1.07/1.25 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s68, c_c1) | (~node10(s68)))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(5929,plain,
% 1.07/1.25 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s68, c_c1) | (~node10(s68))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[5928, 5927])).
% 1.07/1.25 tff(5930,plain,
% 1.07/1.25 (~node10(s68)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[5929, 675, 5855])).
% 1.07/1.25 tff(5931,plain,
% 1.07/1.25 (((~![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)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5932,plain,
% 1.07/1.25 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s68, c_n1) | (~node9(s68)))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(5933,plain,
% 1.07/1.25 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s68, c_n1) | (~node9(s68))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[5932, 5931])).
% 1.07/1.25 tff(5934,plain,
% 1.07/1.25 (~node9(s68)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[5933, 686, 5822])).
% 1.07/1.25 tff(5935,plain,
% 1.07/1.25 (((~![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)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5936,plain,
% 1.07/1.25 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s68, c_n2) | (~node8(s68)))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(5937,plain,
% 1.07/1.25 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s68, c_n2) | (~node8(s68))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[5936, 5935])).
% 1.07/1.25 tff(5938,plain,
% 1.07/1.25 (~node8(s68)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[5937, 271, 5887])).
% 1.07/1.25 tff(5939,plain,
% 1.07/1.25 (((~![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))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5940,plain,
% 1.07/1.25 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s68, s69)) | node14(s68, s69))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(5941,plain,
% 1.07/1.25 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s68, s69)) | node14(s68, s69)),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[5940, 5939])).
% 1.07/1.25 tff(5942,plain,
% 1.07/1.25 (node14(s68, s69)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[5941, 46, 5898])).
% 1.07/1.25 tff(5943,plain,
% 1.07/1.25 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | 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)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5944,plain,
% 1.07/1.25 (((~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)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5945,plain,
% 1.07/1.25 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | 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))))),
% 1.07/1.25 inference(monotonicity,[status(thm)],[5944])).
% 1.07/1.25 tff(5946,plain,
% 1.07/1.25 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | 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)))),
% 1.07/1.25 inference(transitivity,[status(thm)],[5945, 5943])).
% 1.07/1.25 tff(5947,plain,
% 1.07/1.25 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | 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))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(5948,plain,
% 1.07/1.25 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | 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))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[5947, 5946])).
% 1.07/1.25 tff(5949,plain,
% 1.07/1.25 (m_main_v_state2(s69, c_n2) | node9(s68) | node8(s68) | node10(s68) | node11(s68) | node12(s68) | (~m_main_v_state2(s68, c_c2))),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[5948, 726, 5942])).
% 1.07/1.25 tff(5950,plain,
% 1.07/1.25 (m_main_v_state2(s69, c_n2)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[5949, 5938, 5883, 5934, 5930, 5926, 5922])).
% 1.07/1.25 tff(5951,plain,
% 1.07/1.25 (((~![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)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5952,plain,
% 1.07/1.25 ((~![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)))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(5953,plain,
% 1.07/1.25 ((~![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))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[5952, 5951])).
% 1.07/1.25 tff(5954,plain,
% 1.07/1.25 (~m_main_v_state2(s69, c_t2)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[5953, 77, 5950])).
% 1.07/1.25 tff(5955,plain,
% 1.07/1.25 (((~![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)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5956,plain,
% 1.07/1.25 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s69, c_t2) | (~node15(s69)))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(5957,plain,
% 1.07/1.25 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s69, c_t2) | (~node15(s69))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[5956, 5955])).
% 1.07/1.25 tff(5958,plain,
% 1.07/1.25 (~node15(s69)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[5957, 103, 5954])).
% 1.07/1.25 tff(5959,plain,
% 1.07/1.25 (succ(s69, s70) <=> succ(s69, s70)),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(5960,axiom,(succ(s69, s70)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound70')).
% 1.07/1.25 tff(5961,plain,
% 1.07/1.25 (succ(s69, s70)),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[5960, 5959])).
% 1.07/1.25 tff(5962,plain,
% 1.07/1.25 (((~![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))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(5963,plain,
% 1.07/1.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s69, s70)) | trans(s69, s70))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(5964,plain,
% 1.07/1.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s69, s70)) | trans(s69, s70)),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[5963, 5962])).
% 1.07/1.26 tff(5965,plain,
% 1.07/1.26 (trans(s69, s70)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[5964, 5961, 32])).
% 1.07/1.26 tff(5966,plain,
% 1.07/1.26 (((~![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))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(5967,plain,
% 1.07/1.26 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s69, s70)) | node18(s69, s70))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(5968,plain,
% 1.07/1.26 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s69, s70)) | node18(s69, s70)),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[5967, 5966])).
% 1.07/1.26 tff(5969,plain,
% 1.07/1.26 (node18(s69, s70)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[5968, 125, 5965])).
% 1.07/1.26 tff(5970,plain,
% 1.07/1.26 (((~![Y: $i, X: $i] : ((~m_main_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))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(5971,plain,
% 1.07/1.26 (((~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))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(5972,plain,
% 1.07/1.26 (((~![Y: $i, X: $i] : ((~m_main_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)))),
% 1.07/1.26 inference(monotonicity,[status(thm)],[5971])).
% 1.07/1.26 tff(5973,plain,
% 1.07/1.26 (((~![Y: $i, X: $i] : ((~m_main_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))),
% 1.07/1.26 inference(transitivity,[status(thm)],[5972, 5970])).
% 1.07/1.26 tff(5974,plain,
% 1.07/1.26 ((~![Y: $i, X: $i] : ((~m_main_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))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(5975,plain,
% 1.07/1.26 ((~![Y: $i, X: $i] : ((~m_main_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)),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[5974, 5973])).
% 1.07/1.26 tff(5976,plain,
% 1.07/1.26 (node15(s69) | (~m_main_v_state1(s69, c_t1)) | (~m_main_v_state2(s69, c_n2)) | m_main_v_turn(s70, c_1)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[5975, 992, 5969])).
% 1.07/1.26 tff(5977,plain,
% 1.07/1.26 (m_main_v_turn(s70, c_1)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[5976, 5958, 5950, 5914])).
% 1.07/1.26 tff(5978,plain,
% 1.07/1.26 (((~![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)))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(5979,plain,
% 1.07/1.26 ((~![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)))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(5980,plain,
% 1.07/1.26 ((~![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))),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[5979, 5978])).
% 1.07/1.26 tff(5981,plain,
% 1.07/1.26 (~m_main_v_turn(s70, c_2)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[5980, 156, 5977])).
% 1.07/1.26 tff(5982,plain,
% 1.07/1.26 (((~![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)))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(5983,plain,
% 1.07/1.26 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s70, c_2) | (~node12(s70)))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(5984,plain,
% 1.07/1.26 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s70, c_2) | (~node12(s70))),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[5983, 5982])).
% 1.07/1.26 tff(5985,plain,
% 1.07/1.26 (~node12(s70)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[5984, 184, 5981])).
% 1.07/1.26 tff(5986,plain,
% 1.07/1.26 (((~![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))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(5987,plain,
% 1.07/1.26 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s69, s70)) | node14(s69, s70))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(5988,plain,
% 1.07/1.26 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s69, s70)) | node14(s69, s70)),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[5987, 5986])).
% 1.07/1.26 tff(5989,plain,
% 1.07/1.26 (node14(s69, s70)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[5988, 46, 5965])).
% 1.07/1.26 tff(5990,plain,
% 1.07/1.26 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(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))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(5991,plain,
% 1.07/1.26 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s69, c_t1)) | (~m_main_v_state2(s69, c_n2)) | (~node14(s69, s70)) | m_main_v_state2(s70, c_t2))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(5992,plain,
% 1.07/1.26 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s69, c_t1)) | (~m_main_v_state2(s69, c_n2)) | (~node14(s69, s70)) | m_main_v_state2(s70, c_t2)),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[5991, 5990])).
% 1.07/1.26 tff(5993,plain,
% 1.07/1.26 ((~m_main_v_state1(s69, c_t1)) | (~m_main_v_state2(s69, c_n2)) | m_main_v_state2(s70, c_t2)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[5992, 922, 5989])).
% 1.07/1.26 tff(5994,plain,
% 1.07/1.26 (m_main_v_state2(s70, c_t2)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[5993, 5914, 5950])).
% 1.07/1.26 tff(5995,plain,
% 1.07/1.26 (((~![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)))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(5996,plain,
% 1.07/1.26 ((~![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)))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(5997,plain,
% 1.07/1.26 ((~![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))),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[5996, 5995])).
% 1.07/1.26 tff(5998,plain,
% 1.07/1.26 (~m_main_v_state2(s70, c_n2)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[5997, 77, 5994])).
% 1.07/1.26 tff(5999,plain,
% 1.07/1.26 (((~![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)))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(6000,plain,
% 1.07/1.26 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s70, c_n2) | (~node8(s70)))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(6001,plain,
% 1.07/1.26 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s70, c_n2) | (~node8(s70))),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[6000, 5999])).
% 1.07/1.26 tff(6002,plain,
% 1.07/1.26 (~node8(s70)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[6001, 271, 5998])).
% 1.07/1.26 tff(6003,plain,
% 1.07/1.26 (((~![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)))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(6004,plain,
% 1.07/1.26 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s70, c_n2) | (~node9(s70)))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(6005,plain,
% 1.07/1.26 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s70, c_n2) | (~node9(s70))),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[6004, 6003])).
% 1.07/1.26 tff(6006,plain,
% 1.07/1.26 (~node9(s70)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[6005, 88, 5998])).
% 1.07/1.26 tff(6007,plain,
% 1.07/1.26 (((~![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)))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(6008,plain,
% 1.07/1.26 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s70, c_n2) | (~node10(s70)))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(6009,plain,
% 1.07/1.26 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s70, c_n2) | (~node10(s70))),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[6008, 6007])).
% 1.07/1.26 tff(6010,plain,
% 1.07/1.26 (~node10(s70)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[6009, 249, 5998])).
% 1.07/1.26 tff(6011,plain,
% 1.07/1.26 (((~![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)))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(6012,plain,
% 1.07/1.26 ((~![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)))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(6013,plain,
% 1.07/1.26 ((~![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))),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[6012, 6011])).
% 1.07/1.26 tff(6014,plain,
% 1.07/1.26 (~m_main_v_state2(s70, c_c2)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[6013, 260, 5994])).
% 1.07/1.26 tff(6015,plain,
% 1.07/1.26 (((~![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)))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(6016,plain,
% 1.07/1.26 ((~![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)))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(6017,plain,
% 1.07/1.26 ((~![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))),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[6016, 6015])).
% 1.07/1.26 tff(6018,plain,
% 1.07/1.26 (~m_main_v_state2(s69, c_c2)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[6017, 697, 5950])).
% 1.07/1.26 tff(6019,plain,
% 1.07/1.26 (((~![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)))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(6020,plain,
% 1.07/1.26 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s69, c_c2) | (~node3(s69)))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(6021,plain,
% 1.07/1.26 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s69, c_c2) | (~node3(s69))),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[6020, 6019])).
% 1.07/1.26 tff(6022,plain,
% 1.07/1.26 (~node3(s69)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[6021, 399, 6018])).
% 1.07/1.26 tff(6023,plain,
% 1.07/1.26 (((~![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(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)))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(6024,plain,
% 1.07/1.26 (((~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)))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(6025,plain,
% 1.07/1.26 (((~![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))))),
% 1.07/1.26 inference(monotonicity,[status(thm)],[6024])).
% 1.07/1.26 tff(6026,plain,
% 1.07/1.26 (((~![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)))),
% 1.07/1.26 inference(transitivity,[status(thm)],[6025, 6023])).
% 1.07/1.26 tff(6027,plain,
% 1.07/1.26 ((~![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)))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(6028,plain,
% 1.07/1.26 ((~![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(s68, c_n1) | (~m_main_v_state1(s69, c_n1)) | (~node6(s68, s69))),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[6027, 6026])).
% 1.07/1.26 tff(6029,plain,
% 1.07/1.26 (~m_main_v_state1(s69, c_n1)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[6028, 835, 5822, 5907])).
% 1.07/1.26 tff(6030,plain,
% 1.07/1.26 (((~![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)))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(6031,plain,
% 1.07/1.26 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s69, c_n1) | (~node2(s69)))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(6032,plain,
% 1.07/1.26 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s69, c_n1) | (~node2(s69))),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[6031, 6030])).
% 1.07/1.26 tff(6033,plain,
% 1.07/1.26 (~node2(s69)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[6032, 787, 6029])).
% 1.07/1.26 tff(6034,plain,
% 1.07/1.26 (((~![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)))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(6035,plain,
% 1.07/1.26 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s69, c_t2) | (~node1(s69)))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(6036,plain,
% 1.07/1.26 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s69, c_t2) | (~node1(s69))),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[6035, 6034])).
% 1.07/1.26 tff(6037,plain,
% 1.07/1.26 (~node1(s69)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[6036, 195, 5954])).
% 1.07/1.26 tff(6038,plain,
% 1.07/1.26 (((~![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))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(6039,plain,
% 1.07/1.26 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s69, s70)) | node7(s69, s70))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(6040,plain,
% 1.07/1.26 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s69, s70)) | node7(s69, s70)),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[6039, 6038])).
% 1.07/1.26 tff(6041,plain,
% 1.07/1.26 (node7(s69, s70)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[6040, 206, 5965])).
% 1.07/1.26 tff(6042,plain,
% 1.07/1.26 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(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)))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(6043,plain,
% 1.07/1.26 (((~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)))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(6044,plain,
% 1.07/1.26 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(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))))),
% 1.07/1.26 inference(monotonicity,[status(thm)],[6043])).
% 1.07/1.26 tff(6045,plain,
% 1.07/1.26 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(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)))),
% 1.07/1.26 inference(transitivity,[status(thm)],[6044, 6042])).
% 1.07/1.26 tff(6046,plain,
% 1.07/1.26 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(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))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(6047,plain,
% 1.07/1.26 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(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))),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[6046, 6045])).
% 1.07/1.26 tff(6048,plain,
% 1.07/1.26 ((~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)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[6047, 892, 6041])).
% 1.07/1.26 tff(6049,plain,
% 1.07/1.26 (m_main_v_state1(s70, c_c1)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[6048, 6037, 5950, 5914, 6033, 6022])).
% 1.07/1.26 tff(6050,plain,
% 1.07/1.26 (((~![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)))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(6051,plain,
% 1.07/1.26 ((~![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)))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(6052,plain,
% 1.07/1.26 ((~![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))),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[6051, 6050])).
% 1.07/1.26 tff(6053,plain,
% 1.07/1.26 (~m_main_v_state1(s70, c_n1)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[6052, 454, 6049])).
% 1.07/1.26 tff(6054,plain,
% 1.07/1.26 (((~![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)))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(6055,plain,
% 1.07/1.26 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s70, c_n1) | (~node11(s70)))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(6056,plain,
% 1.07/1.26 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s70, c_n1) | (~node11(s70))),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[6055, 6054])).
% 1.07/1.26 tff(6057,plain,
% 1.07/1.26 (~node11(s70)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[6056, 238, 6053])).
% 1.07/1.26 tff(6058,plain,
% 1.07/1.26 (succ(s70, s71) <=> succ(s70, s71)),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(6059,axiom,(succ(s70, s71)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound71')).
% 1.07/1.26 tff(6060,plain,
% 1.07/1.26 (succ(s70, s71)),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[6059, 6058])).
% 1.07/1.26 tff(6061,plain,
% 1.07/1.26 (((~![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))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(6062,plain,
% 1.07/1.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s70, s71)) | trans(s70, s71))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(6063,plain,
% 1.07/1.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s70, s71)) | trans(s70, s71)),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[6062, 6061])).
% 1.07/1.26 tff(6064,plain,
% 1.07/1.26 (trans(s70, s71)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[6063, 6060, 32])).
% 1.07/1.26 tff(6065,plain,
% 1.07/1.26 (((~![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))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(6066,plain,
% 1.07/1.26 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s70, s71)) | node14(s70, s71))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(6067,plain,
% 1.07/1.26 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s70, s71)) | node14(s70, s71)),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[6066, 6065])).
% 1.07/1.26 tff(6068,plain,
% 1.07/1.26 (node14(s70, s71)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[6067, 46, 6064])).
% 1.07/1.26 tff(6069,plain,
% 1.07/1.26 (((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(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)))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(6070,plain,
% 1.07/1.26 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s70, c_c2) | node9(s70) | node8(s70) | node10(s70) | node11(s70) | node12(s70) | node13(s70, s71) | (~node14(s70, s71)))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(6071,plain,
% 1.07/1.26 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s70, c_c2) | node9(s70) | node8(s70) | node10(s70) | node11(s70) | node12(s70) | node13(s70, s71) | (~node14(s70, s71))),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[6070, 6069])).
% 1.07/1.26 tff(6072,plain,
% 1.07/1.26 (m_main_v_state2(s70, c_c2) | node9(s70) | node8(s70) | node10(s70) | node11(s70) | node12(s70) | node13(s70, s71)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[6071, 296, 6068])).
% 1.07/1.26 tff(6073,plain,
% 1.07/1.26 (node13(s70, s71)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[6072, 6057, 6014, 6010, 6006, 6002, 5985])).
% 1.07/1.26 tff(6074,plain,
% 1.07/1.26 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | (m_main_v_state2(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)))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(6075,plain,
% 1.07/1.26 (((~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)))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(6076,plain,
% 1.07/1.26 (((~![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))))),
% 1.07/1.26 inference(monotonicity,[status(thm)],[6075])).
% 1.07/1.26 tff(6077,plain,
% 1.07/1.26 (((~![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)))),
% 1.07/1.26 inference(transitivity,[status(thm)],[6076, 6074])).
% 1.07/1.26 tff(6078,plain,
% 1.07/1.26 ((~![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)))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(6079,plain,
% 1.07/1.26 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s70, c_n2) | (~m_main_v_state2(s71, c_n2)) | (~node13(s70, s71))),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[6078, 6077])).
% 1.07/1.26 tff(6080,plain,
% 1.07/1.26 (~m_main_v_state2(s71, c_n2)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[6079, 311, 5998, 6073])).
% 1.07/1.26 tff(6081,plain,
% 1.07/1.26 (((~![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)))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(6082,plain,
% 1.07/1.26 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s71, c_n2) | (~node9(s71)))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(6083,plain,
% 1.07/1.26 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s71, c_n2) | (~node9(s71))),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[6082, 6081])).
% 1.07/1.26 tff(6084,plain,
% 1.07/1.26 (~node9(s71)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[6083, 88, 6080])).
% 1.07/1.26 tff(6085,plain,
% 1.07/1.26 (((~![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)))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(6086,plain,
% 1.07/1.26 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s71, c_n2) | (~node10(s71)))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(6087,plain,
% 1.07/1.26 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s71, c_n2) | (~node10(s71))),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[6086, 6085])).
% 1.07/1.26 tff(6088,plain,
% 1.07/1.26 (~node10(s71)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[6087, 249, 6080])).
% 1.07/1.26 tff(6089,plain,
% 1.07/1.26 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(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)))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(6090,plain,
% 1.07/1.26 (((~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)))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(6091,plain,
% 1.07/1.26 (((~![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))))),
% 1.07/1.26 inference(monotonicity,[status(thm)],[6090])).
% 1.07/1.26 tff(6092,plain,
% 1.07/1.26 (((~![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)))),
% 1.07/1.27 inference(transitivity,[status(thm)],[6091, 6089])).
% 1.07/1.27 tff(6093,plain,
% 1.07/1.27 ((~![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))),
% 1.07/1.27 inference(quant_inst,[status(thm)],[])).
% 1.07/1.27 tff(6094,plain,
% 1.07/1.27 ((~![V: $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))),
% 1.07/1.27 inference(modus_ponens,[status(thm)],[6093, 6092])).
% 1.07/1.27 tff(6095,plain,
% 1.07/1.27 (m_main_v_state2(s71, c_t2)),
% 1.07/1.27 inference(unit_resolution,[status(thm)],[6094, 518, 5994, 6073])).
% 1.07/1.27 tff(6096,plain,
% 1.07/1.27 (((~![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)))),
% 1.07/1.27 inference(rewrite,[status(thm)],[])).
% 1.07/1.27 tff(6097,plain,
% 1.07/1.27 ((~![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)))),
% 1.07/1.27 inference(quant_inst,[status(thm)],[])).
% 1.07/1.27 tff(6098,plain,
% 1.07/1.27 ((~![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))),
% 1.07/1.27 inference(modus_ponens,[status(thm)],[6097, 6096])).
% 1.07/1.27 tff(6099,plain,
% 1.07/1.27 (~m_main_v_state1(s70, c_t1)),
% 1.07/1.27 inference(unit_resolution,[status(thm)],[6098, 539, 6049])).
% 1.07/1.27 tff(6100,plain,
% 1.07/1.27 (((~![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)))),
% 1.07/1.27 inference(rewrite,[status(thm)],[])).
% 1.07/1.27 tff(6101,plain,
% 1.07/1.27 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s70, c_t1) | (~node5(s70)))),
% 1.07/1.27 inference(quant_inst,[status(thm)],[])).
% 1.07/1.27 tff(6102,plain,
% 1.07/1.27 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s70, c_t1) | (~node5(s70))),
% 1.07/1.27 inference(modus_ponens,[status(thm)],[6101, 6100])).
% 1.07/1.27 tff(6103,plain,
% 1.07/1.27 (~node5(s70)),
% 1.07/1.27 inference(unit_resolution,[status(thm)],[6102, 550, 6099])).
% 1.07/1.27 tff(6104,plain,
% 1.07/1.27 (((~![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)))),
% 1.07/1.27 inference(rewrite,[status(thm)],[])).
% 1.07/1.27 tff(6105,plain,
% 1.07/1.27 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s70, c_n2) | (~node4(s70)))),
% 1.07/1.27 inference(quant_inst,[status(thm)],[])).
% 1.07/1.27 tff(6106,plain,
% 1.07/1.27 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s70, c_n2) | (~node4(s70))),
% 1.07/1.27 inference(modus_ponens,[status(thm)],[6105, 6104])).
% 1.07/1.27 tff(6107,plain,
% 1.07/1.27 (~node4(s70)),
% 1.07/1.27 inference(unit_resolution,[status(thm)],[6106, 388, 5998])).
% 1.07/1.27 tff(6108,plain,
% 1.07/1.27 (((~![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)))),
% 1.07/1.27 inference(rewrite,[status(thm)],[])).
% 1.07/1.27 tff(6109,plain,
% 1.07/1.27 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s70, c_c2) | (~node3(s70)))),
% 1.07/1.27 inference(quant_inst,[status(thm)],[])).
% 1.07/1.27 tff(6110,plain,
% 1.07/1.27 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s70, c_c2) | (~node3(s70))),
% 1.07/1.27 inference(modus_ponens,[status(thm)],[6109, 6108])).
% 1.07/1.27 tff(6111,plain,
% 1.07/1.27 (~node3(s70)),
% 1.07/1.27 inference(unit_resolution,[status(thm)],[6110, 399, 6014])).
% 1.07/1.27 tff(6112,plain,
% 1.07/1.27 (((~![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)))),
% 1.07/1.27 inference(rewrite,[status(thm)],[])).
% 1.07/1.27 tff(6113,plain,
% 1.07/1.27 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s70, c_n2) | (~node2(s70)))),
% 1.07/1.27 inference(quant_inst,[status(thm)],[])).
% 1.07/1.27 tff(6114,plain,
% 1.07/1.27 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s70, c_n2) | (~node2(s70))),
% 1.07/1.27 inference(modus_ponens,[status(thm)],[6113, 6112])).
% 1.07/1.27 tff(6115,plain,
% 1.07/1.27 (~node2(s70)),
% 1.07/1.27 inference(unit_resolution,[status(thm)],[6114, 410, 5998])).
% 1.07/1.27 tff(6116,plain,
% 1.07/1.27 (((~![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)))),
% 1.07/1.27 inference(rewrite,[status(thm)],[])).
% 1.07/1.27 tff(6117,plain,
% 1.07/1.27 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s70, c_n1) | (~node1(s70)))),
% 1.07/1.27 inference(quant_inst,[status(thm)],[])).
% 1.07/1.27 tff(6118,plain,
% 1.07/1.27 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s70, c_n1) | (~node1(s70))),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[6117, 6116])).
% 1.11/1.27 tff(6119,plain,
% 1.11/1.27 (~node1(s70)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[6118, 421, 6053])).
% 1.11/1.27 tff(6120,plain,
% 1.11/1.27 (((~![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))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(6121,plain,
% 1.11/1.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s70, s71)) | node7(s70, s71))),
% 1.11/1.27 inference(quant_inst,[status(thm)],[])).
% 1.11/1.27 tff(6122,plain,
% 1.11/1.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s70, s71)) | node7(s70, s71)),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[6121, 6120])).
% 1.11/1.27 tff(6123,plain,
% 1.11/1.27 (node7(s70, s71)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[6122, 206, 6064])).
% 1.11/1.27 tff(6124,plain,
% 1.11/1.27 (((~![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(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)))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(6125,plain,
% 1.11/1.27 (((~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)))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(6126,plain,
% 1.11/1.27 (((~![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(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))))),
% 1.11/1.27 inference(monotonicity,[status(thm)],[6125])).
% 1.11/1.27 tff(6127,plain,
% 1.11/1.27 (((~![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(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)))),
% 1.11/1.27 inference(transitivity,[status(thm)],[6126, 6124])).
% 1.11/1.27 tff(6128,plain,
% 1.11/1.27 ((~![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(s70, c_c1)) | node1(s70) | node2(s70) | node3(s70) | node4(s70) | node5(s70) | (~node7(s70, s71)) | m_main_v_state1(s71, c_n1))),
% 1.11/1.27 inference(quant_inst,[status(thm)],[])).
% 1.11/1.27 tff(6129,plain,
% 1.11/1.27 ((~![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(s71, c_n1) | (~m_main_v_state1(s70, c_c1)) | node1(s70) | node2(s70) | node3(s70) | node4(s70) | node5(s70) | (~node7(s70, s71))),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[6128, 6127])).
% 1.11/1.27 tff(6130,plain,
% 1.11/1.27 (m_main_v_state1(s71, c_n1) | (~m_main_v_state1(s70, c_c1)) | node1(s70) | node2(s70) | node3(s70) | node4(s70) | node5(s70)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[6129, 584, 6123])).
% 1.11/1.27 tff(6131,plain,
% 1.11/1.27 (m_main_v_state1(s71, c_n1)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[6130, 6119, 6049, 6115, 6111, 6107, 6103])).
% 1.11/1.27 tff(6132,plain,
% 1.11/1.27 (((~![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)))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(6133,plain,
% 1.11/1.27 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s71, c_n2) | (~node8(s71)))),
% 1.11/1.27 inference(quant_inst,[status(thm)],[])).
% 1.11/1.27 tff(6134,plain,
% 1.11/1.27 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s71, c_n2) | (~node8(s71))),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[6133, 6132])).
% 1.11/1.27 tff(6135,plain,
% 1.11/1.27 (~node8(s71)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[6134, 271, 6080])).
% 1.11/1.27 tff(6136,plain,
% 1.11/1.27 (succ(s71, s72) <=> succ(s71, s72)),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(6137,axiom,(succ(s71, s72)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound72')).
% 1.11/1.27 tff(6138,plain,
% 1.11/1.27 (succ(s71, s72)),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[6137, 6136])).
% 1.11/1.27 tff(6139,plain,
% 1.11/1.27 (((~![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))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(6140,plain,
% 1.11/1.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s71, s72)) | trans(s71, s72))),
% 1.11/1.27 inference(quant_inst,[status(thm)],[])).
% 1.11/1.27 tff(6141,plain,
% 1.11/1.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s71, s72)) | trans(s71, s72)),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[6140, 6139])).
% 1.11/1.27 tff(6142,plain,
% 1.11/1.27 (trans(s71, s72)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[6141, 6138, 32])).
% 1.11/1.27 tff(6143,plain,
% 1.11/1.27 (((~![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))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(6144,plain,
% 1.11/1.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s71, s72)) | node14(s71, s72))),
% 1.11/1.27 inference(quant_inst,[status(thm)],[])).
% 1.11/1.27 tff(6145,plain,
% 1.11/1.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s71, s72)) | node14(s71, s72)),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[6144, 6143])).
% 1.11/1.27 tff(6146,plain,
% 1.11/1.27 (node14(s71, s72)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[6145, 46, 6142])).
% 1.11/1.27 tff(6147,plain,
% 1.11/1.27 (((~![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))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(6148,plain,
% 1.11/1.27 ((~![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))),
% 1.11/1.27 inference(quant_inst,[status(thm)],[])).
% 1.11/1.27 tff(6149,plain,
% 1.11/1.27 ((~![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)),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[6148, 6147])).
% 1.11/1.27 tff(6150,plain,
% 1.11/1.27 ((~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)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[6149, 617, 6146])).
% 1.11/1.27 tff(6151,plain,
% 1.11/1.27 (m_main_v_state2(s72, c_c2)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[6150, 6135, 6131, 6095, 6088, 6084])).
% 1.11/1.27 tff(6152,plain,
% 1.11/1.27 (((~![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)))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(6153,plain,
% 1.11/1.27 ((~![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)))),
% 1.11/1.27 inference(quant_inst,[status(thm)],[])).
% 1.11/1.27 tff(6154,plain,
% 1.11/1.27 ((~![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))),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[6153, 6152])).
% 1.11/1.27 tff(6155,plain,
% 1.11/1.27 (~m_main_v_state2(s72, c_t2)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[6154, 260, 6151])).
% 1.11/1.27 tff(6156,plain,
% 1.11/1.27 (((~![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)))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(6157,plain,
% 1.11/1.27 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s72, c_t2) | (~node12(s72)))),
% 1.11/1.27 inference(quant_inst,[status(thm)],[])).
% 1.11/1.27 tff(6158,plain,
% 1.11/1.27 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s72, c_t2) | (~node12(s72))),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[6157, 6156])).
% 1.11/1.27 tff(6159,plain,
% 1.11/1.27 (~node12(s72)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[6158, 633, 6155])).
% 1.11/1.27 tff(6160,plain,
% 1.11/1.27 (((~![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))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(6161,plain,
% 1.11/1.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s71, s72)) | node7(s71, s72))),
% 1.11/1.27 inference(quant_inst,[status(thm)],[])).
% 1.11/1.27 tff(6162,plain,
% 1.11/1.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s71, s72)) | node7(s71, s72)),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[6161, 6160])).
% 1.11/1.27 tff(6163,plain,
% 1.11/1.27 (node7(s71, s72)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[6162, 206, 6142])).
% 1.11/1.27 tff(6164,plain,
% 1.11/1.27 (((~![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))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(6165,plain,
% 1.11/1.27 ((~![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))),
% 1.11/1.27 inference(quant_inst,[status(thm)],[])).
% 1.11/1.27 tff(6166,plain,
% 1.11/1.27 ((~![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)),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[6165, 6164])).
% 1.11/1.27 tff(6167,plain,
% 1.11/1.27 ((~m_main_v_state1(s71, c_n1)) | (~m_main_v_state2(s71, c_t2)) | m_main_v_state1(s72, c_t1)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[6166, 651, 6163])).
% 1.11/1.27 tff(6168,plain,
% 1.11/1.27 (m_main_v_state1(s72, c_t1)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[6167, 6095, 6131])).
% 1.11/1.27 tff(6169,plain,
% 1.11/1.27 (((~![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)))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(6170,plain,
% 1.11/1.27 ((~![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)))),
% 1.11/1.27 inference(quant_inst,[status(thm)],[])).
% 1.11/1.27 tff(6171,plain,
% 1.11/1.27 ((~![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))),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[6170, 6169])).
% 1.11/1.27 tff(6172,plain,
% 1.11/1.27 (~m_main_v_state1(s72, c_n1)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[6171, 10, 6168])).
% 1.11/1.27 tff(6173,plain,
% 1.11/1.27 (((~![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)))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(6174,plain,
% 1.11/1.27 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s72, c_n1) | (~node11(s72)))),
% 1.11/1.27 inference(quant_inst,[status(thm)],[])).
% 1.11/1.27 tff(6175,plain,
% 1.11/1.27 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s72, c_n1) | (~node11(s72))),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[6174, 6173])).
% 1.11/1.27 tff(6176,plain,
% 1.11/1.27 (~node11(s72)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[6175, 238, 6172])).
% 1.11/1.27 tff(6177,plain,
% 1.11/1.27 (((~![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)))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(6178,plain,
% 1.11/1.27 ((~![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)))),
% 1.11/1.27 inference(quant_inst,[status(thm)],[])).
% 1.11/1.27 tff(6179,plain,
% 1.11/1.27 ((~![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))),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[6178, 6177])).
% 1.11/1.27 tff(6180,plain,
% 1.11/1.27 (~m_main_v_state1(s72, c_c1)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[6179, 539, 6168])).
% 1.11/1.27 tff(6181,plain,
% 1.11/1.27 (((~![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)))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(6182,plain,
% 1.11/1.27 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s72, c_c1) | (~node10(s72)))),
% 1.11/1.27 inference(quant_inst,[status(thm)],[])).
% 1.11/1.27 tff(6183,plain,
% 1.11/1.27 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s72, c_c1) | (~node10(s72))),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[6182, 6181])).
% 1.11/1.27 tff(6184,plain,
% 1.11/1.27 (~node10(s72)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[6183, 675, 6180])).
% 1.11/1.27 tff(6185,plain,
% 1.11/1.27 (((~![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)))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(6186,plain,
% 1.11/1.27 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s72, c_n1) | (~node9(s72)))),
% 1.11/1.27 inference(quant_inst,[status(thm)],[])).
% 1.11/1.27 tff(6187,plain,
% 1.11/1.27 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s72, c_n1) | (~node9(s72))),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[6186, 6185])).
% 1.11/1.27 tff(6188,plain,
% 1.11/1.27 (~node9(s72)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[6187, 686, 6172])).
% 1.11/1.27 tff(6189,plain,
% 1.11/1.27 (((~![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)))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(6190,plain,
% 1.11/1.27 ((~![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)))),
% 1.11/1.27 inference(quant_inst,[status(thm)],[])).
% 1.11/1.27 tff(6191,plain,
% 1.11/1.27 ((~![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))),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[6190, 6189])).
% 1.11/1.27 tff(6192,plain,
% 1.11/1.27 (~m_main_v_state2(s72, c_n2)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[6191, 697, 6151])).
% 1.11/1.27 tff(6193,plain,
% 1.11/1.27 (((~![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)))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(6194,plain,
% 1.11/1.27 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s72, c_n2) | (~node8(s72)))),
% 1.11/1.27 inference(quant_inst,[status(thm)],[])).
% 1.11/1.27 tff(6195,plain,
% 1.11/1.27 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s72, c_n2) | (~node8(s72))),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[6194, 6193])).
% 1.11/1.27 tff(6196,plain,
% 1.11/1.27 (~node8(s72)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[6195, 271, 6192])).
% 1.11/1.27 tff(6197,plain,
% 1.11/1.27 (succ(s72, s73) <=> succ(s72, s73)),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(6198,axiom,(succ(s72, s73)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound73')).
% 1.11/1.27 tff(6199,plain,
% 1.11/1.27 (succ(s72, s73)),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[6198, 6197])).
% 1.11/1.27 tff(6200,plain,
% 1.11/1.27 (((~![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))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(6201,plain,
% 1.11/1.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s72, s73)) | trans(s72, s73))),
% 1.11/1.27 inference(quant_inst,[status(thm)],[])).
% 1.11/1.27 tff(6202,plain,
% 1.11/1.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s72, s73)) | trans(s72, s73)),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[6201, 6200])).
% 1.11/1.27 tff(6203,plain,
% 1.11/1.27 (trans(s72, s73)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[6202, 6199, 32])).
% 1.11/1.27 tff(6204,plain,
% 1.11/1.27 (((~![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))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(6205,plain,
% 1.11/1.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s72, s73)) | node14(s72, s73))),
% 1.11/1.27 inference(quant_inst,[status(thm)],[])).
% 1.11/1.27 tff(6206,plain,
% 1.11/1.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s72, s73)) | node14(s72, s73)),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[6205, 6204])).
% 1.11/1.27 tff(6207,plain,
% 1.11/1.27 (node14(s72, s73)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[6206, 46, 6203])).
% 1.11/1.27 tff(6208,plain,
% 1.11/1.27 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | 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)))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(6209,plain,
% 1.11/1.27 (((~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)))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(6210,plain,
% 1.11/1.27 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | 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))))),
% 1.11/1.27 inference(monotonicity,[status(thm)],[6209])).
% 1.11/1.27 tff(6211,plain,
% 1.11/1.27 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | 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)))),
% 1.11/1.27 inference(transitivity,[status(thm)],[6210, 6208])).
% 1.11/1.27 tff(6212,plain,
% 1.11/1.27 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | 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))),
% 1.11/1.27 inference(quant_inst,[status(thm)],[])).
% 1.11/1.27 tff(6213,plain,
% 1.11/1.27 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | 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))),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[6212, 6211])).
% 1.11/1.27 tff(6214,plain,
% 1.11/1.27 (m_main_v_state2(s73, c_n2) | node9(s72) | node8(s72) | node10(s72) | node11(s72) | node12(s72) | (~m_main_v_state2(s72, c_c2))),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[6213, 726, 6207])).
% 1.11/1.27 tff(6215,plain,
% 1.11/1.27 (m_main_v_state2(s73, c_n2)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[6214, 6196, 6151, 6188, 6184, 6176, 6159])).
% 1.11/1.27 tff(6216,plain,
% 1.11/1.27 (((~![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)))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(6217,plain,
% 1.11/1.27 ((~![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)))),
% 1.11/1.27 inference(quant_inst,[status(thm)],[])).
% 1.11/1.27 tff(6218,plain,
% 1.11/1.27 ((~![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))),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[6217, 6216])).
% 1.11/1.27 tff(6219,plain,
% 1.11/1.27 (~m_main_v_state2(s73, c_c2)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[6218, 697, 6215])).
% 1.11/1.27 tff(6220,plain,
% 1.11/1.27 (((~![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)))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(6221,plain,
% 1.11/1.27 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s73, c_c2) | (~node3(s73)))),
% 1.11/1.27 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(6222,plain,
% 1.11/1.28 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s73, c_c2) | (~node3(s73))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[6221, 6220])).
% 1.11/1.28 tff(6223,plain,
% 1.11/1.28 (~node3(s73)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[6222, 399, 6219])).
% 1.11/1.28 tff(6224,plain,
% 1.11/1.28 (((~![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)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(6225,plain,
% 1.11/1.28 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s72, c_n1) | (~node1(s72)))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(6226,plain,
% 1.11/1.28 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s72, c_n1) | (~node1(s72))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[6225, 6224])).
% 1.11/1.28 tff(6227,plain,
% 1.11/1.28 (~node1(s72)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[6226, 421, 6172])).
% 1.11/1.28 tff(6228,plain,
% 1.11/1.28 (((~![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))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(6229,plain,
% 1.11/1.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s71, s72)) | node18(s71, s72))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(6230,plain,
% 1.11/1.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s71, s72)) | node18(s71, s72)),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[6229, 6228])).
% 1.11/1.28 tff(6231,plain,
% 1.11/1.28 (node18(s71, s72)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[6230, 125, 6142])).
% 1.11/1.28 tff(6232,plain,
% 1.11/1.28 (((~![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(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))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(6233,plain,
% 1.11/1.28 ((~![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(s71, c_n1)) | (~m_main_v_state2(s71, c_t2)) | (~node18(s71, s72)) | m_main_v_turn(s72, c_2))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(6234,plain,
% 1.11/1.28 ((~![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(s71, c_n1)) | (~m_main_v_state2(s71, c_t2)) | (~node18(s71, s72)) | m_main_v_turn(s72, c_2)),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[6233, 6232])).
% 1.11/1.28 tff(6235,plain,
% 1.11/1.28 ((~m_main_v_state1(s71, c_n1)) | (~m_main_v_state2(s71, c_t2)) | m_main_v_turn(s72, c_2)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[6234, 760, 6231])).
% 1.11/1.28 tff(6236,plain,
% 1.11/1.28 (m_main_v_turn(s72, c_2)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[6235, 6095, 6131])).
% 1.11/1.28 tff(6237,plain,
% 1.11/1.28 (((~![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)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(6238,plain,
% 1.11/1.28 ((~![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)))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(6239,plain,
% 1.11/1.28 ((~![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))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[6238, 6237])).
% 1.11/1.28 tff(6240,plain,
% 1.11/1.28 (~m_main_v_turn(s72, c_1)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[6239, 156, 6236])).
% 1.11/1.28 tff(6241,plain,
% 1.11/1.28 (((~![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)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(6242,plain,
% 1.11/1.28 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s72, c_1) | (~node5(s72)))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(6243,plain,
% 1.11/1.28 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s72, c_1) | (~node5(s72))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[6242, 6241])).
% 1.11/1.28 tff(6244,plain,
% 1.11/1.28 (~node5(s72)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[6243, 776, 6240])).
% 1.11/1.28 tff(6245,plain,
% 1.11/1.28 (((~![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)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(6246,plain,
% 1.11/1.28 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s72, c_n1) | (~node2(s72)))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(6247,plain,
% 1.11/1.28 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s72, c_n1) | (~node2(s72))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[6246, 6245])).
% 1.11/1.28 tff(6248,plain,
% 1.11/1.28 (~node2(s72)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[6247, 787, 6172])).
% 1.11/1.28 tff(6249,plain,
% 1.11/1.28 (((~![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)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(6250,plain,
% 1.11/1.28 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s72, c_n1) | (~node3(s72)))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(6251,plain,
% 1.11/1.28 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s72, c_n1) | (~node3(s72))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[6250, 6249])).
% 1.11/1.28 tff(6252,plain,
% 1.11/1.28 (~node3(s72)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[6251, 798, 6172])).
% 1.11/1.28 tff(6253,plain,
% 1.11/1.28 (((~![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)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(6254,plain,
% 1.11/1.28 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s72, c_n2) | (~node4(s72)))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(6255,plain,
% 1.11/1.28 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s72, c_n2) | (~node4(s72))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[6254, 6253])).
% 1.11/1.28 tff(6256,plain,
% 1.11/1.28 (~node4(s72)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[6255, 388, 6192])).
% 1.11/1.28 tff(6257,plain,
% 1.11/1.28 (((~![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))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(6258,plain,
% 1.11/1.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s72, s73)) | node7(s72, s73))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(6259,plain,
% 1.11/1.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s72, s73)) | node7(s72, s73)),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[6258, 6257])).
% 1.11/1.28 tff(6260,plain,
% 1.11/1.28 (node7(s72, s73)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[6259, 206, 6203])).
% 1.11/1.28 tff(6261,plain,
% 1.11/1.28 (((~![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)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(6262,plain,
% 1.11/1.28 ((~![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)))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(6263,plain,
% 1.11/1.28 ((~![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))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[6262, 6261])).
% 1.11/1.28 tff(6264,plain,
% 1.11/1.28 (m_main_v_state1(s72, c_c1) | node1(s72) | node2(s72) | node3(s72) | node4(s72) | node5(s72) | node6(s72, s73)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[6263, 820, 6260])).
% 1.11/1.28 tff(6265,plain,
% 1.11/1.28 (node6(s72, s73)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[6264, 6256, 6180, 6252, 6248, 6244, 6227])).
% 1.11/1.28 tff(6266,plain,
% 1.11/1.28 (((~![V: $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)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(6267,plain,
% 1.11/1.28 (((~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)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(6268,plain,
% 1.11/1.28 (((~![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))))),
% 1.11/1.28 inference(monotonicity,[status(thm)],[6267])).
% 1.11/1.28 tff(6269,plain,
% 1.11/1.28 (((~![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)))),
% 1.11/1.28 inference(transitivity,[status(thm)],[6268, 6266])).
% 1.11/1.28 tff(6270,plain,
% 1.11/1.28 ((~![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)))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(6271,plain,
% 1.11/1.28 ((~![V: $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))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[6270, 6269])).
% 1.11/1.28 tff(6272,plain,
% 1.11/1.28 (~m_main_v_state1(s73, c_n1)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[6271, 835, 6172, 6265])).
% 1.11/1.28 tff(6273,plain,
% 1.11/1.28 (((~![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)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(6274,plain,
% 1.11/1.28 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s73, c_n1) | (~node2(s73)))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(6275,plain,
% 1.11/1.28 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s73, c_n1) | (~node2(s73))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[6274, 6273])).
% 1.11/1.28 tff(6276,plain,
% 1.11/1.28 (~node2(s73)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[6275, 787, 6272])).
% 1.11/1.28 tff(6277,plain,
% 1.11/1.28 (((~![V: $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)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(6278,plain,
% 1.11/1.28 (((~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)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(6279,plain,
% 1.11/1.28 (((~![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))))),
% 1.11/1.28 inference(monotonicity,[status(thm)],[6278])).
% 1.11/1.28 tff(6280,plain,
% 1.11/1.28 (((~![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)))),
% 1.11/1.28 inference(transitivity,[status(thm)],[6279, 6277])).
% 1.11/1.28 tff(6281,plain,
% 1.11/1.28 ((~![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))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(6282,plain,
% 1.11/1.28 ((~![V: $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))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[6281, 6280])).
% 1.11/1.28 tff(6283,plain,
% 1.11/1.28 (m_main_v_state1(s73, c_t1)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[6282, 856, 6168, 6265])).
% 1.11/1.28 tff(6284,plain,
% 1.11/1.28 (((~![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)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(6285,plain,
% 1.11/1.28 ((~![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)))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(6286,plain,
% 1.11/1.28 ((~![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))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[6285, 6284])).
% 1.11/1.28 tff(6287,plain,
% 1.11/1.28 (~m_main_v_state2(s73, c_t2)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[6286, 77, 6215])).
% 1.11/1.28 tff(6288,plain,
% 1.11/1.28 (((~![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)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(6289,plain,
% 1.11/1.28 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s73, c_t2) | (~node1(s73)))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(6290,plain,
% 1.11/1.28 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s73, c_t2) | (~node1(s73))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[6289, 6288])).
% 1.11/1.28 tff(6291,plain,
% 1.11/1.28 (~node1(s73)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[6290, 195, 6287])).
% 1.11/1.28 tff(6292,plain,
% 1.11/1.28 (succ(s73, s74) <=> succ(s73, s74)),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(6293,axiom,(succ(s73, s74)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound74')).
% 1.11/1.28 tff(6294,plain,
% 1.11/1.28 (succ(s73, s74)),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[6293, 6292])).
% 1.11/1.28 tff(6295,plain,
% 1.11/1.28 (((~![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))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(6296,plain,
% 1.11/1.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s73, s74)) | trans(s73, s74))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(6297,plain,
% 1.11/1.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s73, s74)) | trans(s73, s74)),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[6296, 6295])).
% 1.11/1.28 tff(6298,plain,
% 1.11/1.28 (trans(s73, s74)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[6297, 6294, 32])).
% 1.11/1.28 tff(6299,plain,
% 1.11/1.28 (((~![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))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(6300,plain,
% 1.11/1.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s73, s74)) | node7(s73, s74))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(6301,plain,
% 1.11/1.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s73, s74)) | node7(s73, s74)),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[6300, 6299])).
% 1.11/1.28 tff(6302,plain,
% 1.11/1.28 (node7(s73, s74)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[6301, 206, 6298])).
% 1.11/1.28 tff(6303,plain,
% 1.11/1.28 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(6304,plain,
% 1.11/1.28 (((~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)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(6305,plain,
% 1.11/1.28 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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))))),
% 1.11/1.28 inference(monotonicity,[status(thm)],[6304])).
% 1.11/1.28 tff(6306,plain,
% 1.11/1.28 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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)))),
% 1.11/1.28 inference(transitivity,[status(thm)],[6305, 6303])).
% 1.11/1.28 tff(6307,plain,
% 1.11/1.28 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(6308,plain,
% 1.11/1.28 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[6307, 6306])).
% 1.11/1.28 tff(6309,plain,
% 1.11/1.28 ((~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)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[6308, 892, 6302])).
% 1.11/1.28 tff(6310,plain,
% 1.11/1.28 (m_main_v_state1(s74, c_c1)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[6309, 6291, 6215, 6283, 6276, 6223])).
% 1.11/1.28 tff(6311,plain,
% 1.11/1.28 (((~![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)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(6312,plain,
% 1.11/1.28 ((~![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)))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(6313,plain,
% 1.11/1.28 ((~![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))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[6312, 6311])).
% 1.11/1.28 tff(6314,plain,
% 1.11/1.28 (~m_main_v_state1(s74, c_t1)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[6313, 539, 6310])).
% 1.11/1.28 tff(6315,plain,
% 1.11/1.28 (((~![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)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(6316,plain,
% 1.11/1.28 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s74, c_t1) | (~node5(s74)))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(6317,plain,
% 1.11/1.28 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s74, c_t1) | (~node5(s74))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[6316, 6315])).
% 1.11/1.28 tff(6318,plain,
% 1.11/1.28 (~node5(s74)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[6317, 550, 6314])).
% 1.11/1.28 tff(6319,plain,
% 1.11/1.28 (((~![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))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(6320,plain,
% 1.11/1.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s73, s74)) | node14(s73, s74))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(6321,plain,
% 1.11/1.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s73, s74)) | node14(s73, s74)),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[6320, 6319])).
% 1.11/1.28 tff(6322,plain,
% 1.11/1.28 (node14(s73, s74)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[6321, 46, 6298])).
% 1.11/1.28 tff(6323,plain,
% 1.11/1.28 (((~![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))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(6324,plain,
% 1.11/1.28 ((~![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))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(6325,plain,
% 1.11/1.28 ((~![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)),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[6324, 6323])).
% 1.11/1.28 tff(6326,plain,
% 1.11/1.28 ((~m_main_v_state1(s73, c_t1)) | (~m_main_v_state2(s73, c_n2)) | m_main_v_state2(s74, c_t2)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[6325, 922, 6322])).
% 1.11/1.28 tff(6327,plain,
% 1.11/1.28 (m_main_v_state2(s74, c_t2)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[6326, 6283, 6215])).
% 1.11/1.28 tff(6328,plain,
% 1.11/1.28 (((~![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)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(6329,plain,
% 1.11/1.28 ((~![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)))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(6330,plain,
% 1.11/1.28 ((~![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))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[6329, 6328])).
% 1.11/1.28 tff(6331,plain,
% 1.11/1.28 (~m_main_v_state2(s74, c_n2)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[6330, 77, 6327])).
% 1.11/1.28 tff(6332,plain,
% 1.11/1.28 (((~![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)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(6333,plain,
% 1.11/1.28 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s74, c_n2) | (~node4(s74)))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(6334,plain,
% 1.11/1.28 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s74, c_n2) | (~node4(s74))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[6333, 6332])).
% 1.11/1.28 tff(6335,plain,
% 1.11/1.28 (~node4(s74)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[6334, 388, 6331])).
% 1.11/1.28 tff(6336,plain,
% 1.11/1.28 (((~![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)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(6337,plain,
% 1.11/1.28 ((~![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)))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(6338,plain,
% 1.11/1.28 ((~![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))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[6337, 6336])).
% 1.11/1.28 tff(6339,plain,
% 1.11/1.28 (~m_main_v_state2(s74, c_c2)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[6338, 260, 6327])).
% 1.11/1.28 tff(6340,plain,
% 1.11/1.28 (((~![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)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(6341,plain,
% 1.11/1.28 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s74, c_c2) | (~node3(s74)))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(6342,plain,
% 1.11/1.28 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s74, c_c2) | (~node3(s74))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[6341, 6340])).
% 1.11/1.28 tff(6343,plain,
% 1.11/1.28 (~node3(s74)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[6342, 399, 6339])).
% 1.11/1.28 tff(6344,plain,
% 1.11/1.28 (((~![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)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(6345,plain,
% 1.11/1.28 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s74, c_n2) | (~node2(s74)))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(6346,plain,
% 1.11/1.29 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s74, c_n2) | (~node2(s74))),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[6345, 6344])).
% 1.11/1.29 tff(6347,plain,
% 1.11/1.29 (~node2(s74)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[6346, 410, 6331])).
% 1.11/1.29 tff(6348,plain,
% 1.11/1.29 (((~![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)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(6349,plain,
% 1.11/1.29 ((~![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)))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(6350,plain,
% 1.11/1.29 ((~![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))),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[6349, 6348])).
% 1.11/1.29 tff(6351,plain,
% 1.11/1.29 (~m_main_v_state1(s74, c_n1)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[6350, 454, 6310])).
% 1.11/1.29 tff(6352,plain,
% 1.11/1.29 (((~![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)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(6353,plain,
% 1.11/1.29 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s74, c_n1) | (~node1(s74)))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(6354,plain,
% 1.11/1.29 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s74, c_n1) | (~node1(s74))),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[6353, 6352])).
% 1.11/1.29 tff(6355,plain,
% 1.11/1.29 (~node1(s74)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[6354, 421, 6351])).
% 1.11/1.29 tff(6356,plain,
% 1.11/1.29 (succ(s74, s75) <=> succ(s74, s75)),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(6357,axiom,(succ(s74, s75)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound75')).
% 1.11/1.29 tff(6358,plain,
% 1.11/1.29 (succ(s74, s75)),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[6357, 6356])).
% 1.11/1.29 tff(6359,plain,
% 1.11/1.29 (((~![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))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(6360,plain,
% 1.11/1.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s74, s75)) | trans(s74, s75))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(6361,plain,
% 1.11/1.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s74, s75)) | trans(s74, s75)),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[6360, 6359])).
% 1.11/1.29 tff(6362,plain,
% 1.11/1.29 (trans(s74, s75)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[6361, 6358, 32])).
% 1.11/1.29 tff(6363,plain,
% 1.11/1.29 (((~![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))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(6364,plain,
% 1.11/1.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s74, s75)) | node7(s74, s75))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(6365,plain,
% 1.11/1.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s74, s75)) | node7(s74, s75)),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[6364, 6363])).
% 1.11/1.29 tff(6366,plain,
% 1.11/1.29 (node7(s74, s75)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[6365, 206, 6362])).
% 1.11/1.29 tff(6367,plain,
% 1.11/1.29 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(6368,plain,
% 1.11/1.29 (((~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)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(6369,plain,
% 1.11/1.29 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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))))),
% 1.11/1.29 inference(monotonicity,[status(thm)],[6368])).
% 1.11/1.29 tff(6370,plain,
% 1.11/1.29 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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)))),
% 1.11/1.29 inference(transitivity,[status(thm)],[6369, 6367])).
% 1.11/1.29 tff(6371,plain,
% 1.11/1.29 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(6372,plain,
% 1.11/1.29 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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))),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[6371, 6370])).
% 1.11/1.29 tff(6373,plain,
% 1.11/1.29 (m_main_v_state1(s75, c_n1) | (~m_main_v_state1(s74, c_c1)) | node1(s74) | node2(s74) | node3(s74) | node4(s74) | node5(s74)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[6372, 584, 6366])).
% 1.11/1.29 tff(6374,plain,
% 1.11/1.29 (m_main_v_state1(s75, c_n1)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[6373, 6355, 6310, 6347, 6343, 6335, 6318])).
% 1.11/1.29 tff(6375,plain,
% 1.11/1.29 (((~![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)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(6376,plain,
% 1.11/1.29 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s73, c_t2) | (~node15(s73)))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(6377,plain,
% 1.11/1.29 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s73, c_t2) | (~node15(s73))),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[6376, 6375])).
% 1.11/1.29 tff(6378,plain,
% 1.11/1.29 (~node15(s73)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[6377, 103, 6287])).
% 1.11/1.29 tff(6379,plain,
% 1.11/1.29 (((~![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))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(6380,plain,
% 1.11/1.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s73, s74)) | node18(s73, s74))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(6381,plain,
% 1.11/1.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s73, s74)) | node18(s73, s74)),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[6380, 6379])).
% 1.11/1.29 tff(6382,plain,
% 1.11/1.29 (node18(s73, s74)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[6381, 125, 6298])).
% 1.11/1.29 tff(6383,plain,
% 1.11/1.29 (((~![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(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))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(6384,plain,
% 1.11/1.29 (((~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))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(6385,plain,
% 1.11/1.29 (((~![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(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)))),
% 1.11/1.29 inference(monotonicity,[status(thm)],[6384])).
% 1.11/1.29 tff(6386,plain,
% 1.11/1.29 (((~![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(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))),
% 1.11/1.29 inference(transitivity,[status(thm)],[6385, 6383])).
% 1.11/1.29 tff(6387,plain,
% 1.11/1.29 ((~![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(s73, c_t1)) | (~m_main_v_state2(s73, c_n2)) | node15(s73) | (~node18(s73, s74)) | m_main_v_turn(s74, c_1))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(6388,plain,
% 1.11/1.29 ((~![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(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)),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[6387, 6386])).
% 1.11/1.29 tff(6389,plain,
% 1.11/1.29 (node15(s73) | (~m_main_v_state1(s73, c_t1)) | (~m_main_v_state2(s73, c_n2)) | m_main_v_turn(s74, c_1)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[6388, 992, 6382])).
% 1.11/1.29 tff(6390,plain,
% 1.11/1.29 (m_main_v_turn(s74, c_1)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[6389, 6378, 6215, 6283])).
% 1.11/1.29 tff(6391,plain,
% 1.11/1.29 (((~![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)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(6392,plain,
% 1.11/1.29 ((~![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)))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(6393,plain,
% 1.11/1.29 ((~![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))),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[6392, 6391])).
% 1.11/1.29 tff(6394,plain,
% 1.11/1.29 (~m_main_v_turn(s74, c_2)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[6393, 156, 6390])).
% 1.11/1.29 tff(6395,plain,
% 1.11/1.29 (((~![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)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(6396,plain,
% 1.11/1.29 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s74, c_2) | (~node12(s74)))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(6397,plain,
% 1.11/1.29 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s74, c_2) | (~node12(s74))),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[6396, 6395])).
% 1.11/1.29 tff(6398,plain,
% 1.11/1.29 (~node12(s74)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[6397, 184, 6394])).
% 1.11/1.29 tff(6399,plain,
% 1.11/1.29 (((~![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)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(6400,plain,
% 1.11/1.29 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s74, c_n2) | (~node8(s74)))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(6401,plain,
% 1.11/1.29 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s74, c_n2) | (~node8(s74))),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[6400, 6399])).
% 1.11/1.29 tff(6402,plain,
% 1.11/1.29 (~node8(s74)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[6401, 271, 6331])).
% 1.11/1.29 tff(6403,plain,
% 1.11/1.29 (((~![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)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(6404,plain,
% 1.11/1.29 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s74, c_n2) | (~node9(s74)))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(6405,plain,
% 1.11/1.29 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s74, c_n2) | (~node9(s74))),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[6404, 6403])).
% 1.11/1.29 tff(6406,plain,
% 1.11/1.29 (~node9(s74)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[6405, 88, 6331])).
% 1.11/1.29 tff(6407,plain,
% 1.11/1.29 (((~![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)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(6408,plain,
% 1.11/1.29 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s74, c_n2) | (~node10(s74)))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(6409,plain,
% 1.11/1.29 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s74, c_n2) | (~node10(s74))),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[6408, 6407])).
% 1.11/1.29 tff(6410,plain,
% 1.11/1.29 (~node10(s74)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[6409, 249, 6331])).
% 1.11/1.29 tff(6411,plain,
% 1.11/1.29 (((~![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)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(6412,plain,
% 1.11/1.29 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s74, c_n1) | (~node11(s74)))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(6413,plain,
% 1.11/1.29 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s74, c_n1) | (~node11(s74))),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[6412, 6411])).
% 1.11/1.29 tff(6414,plain,
% 1.11/1.29 (~node11(s74)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[6413, 238, 6351])).
% 1.11/1.29 tff(6415,plain,
% 1.11/1.29 (((~![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))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(6416,plain,
% 1.11/1.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s74, s75)) | node14(s74, s75))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(6417,plain,
% 1.11/1.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s74, s75)) | node14(s74, s75)),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[6416, 6415])).
% 1.11/1.29 tff(6418,plain,
% 1.11/1.29 (node14(s74, s75)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[6417, 46, 6362])).
% 1.11/1.29 tff(6419,plain,
% 1.11/1.29 (((~![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)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(6420,plain,
% 1.11/1.29 ((~![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)))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(6421,plain,
% 1.11/1.29 ((~![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))),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[6420, 6419])).
% 1.11/1.29 tff(6422,plain,
% 1.11/1.29 (m_main_v_state2(s74, c_c2) | node9(s74) | node8(s74) | node10(s74) | node11(s74) | node12(s74) | node13(s74, s75)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[6421, 296, 6418])).
% 1.11/1.29 tff(6423,plain,
% 1.11/1.29 (node13(s74, s75)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[6422, 6414, 6339, 6410, 6406, 6402, 6398])).
% 1.11/1.29 tff(6424,plain,
% 1.11/1.29 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~m_main_v_state2(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)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(6425,plain,
% 1.11/1.29 (((~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)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(6426,plain,
% 1.11/1.29 (((~![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))))),
% 1.11/1.29 inference(monotonicity,[status(thm)],[6425])).
% 1.11/1.29 tff(6427,plain,
% 1.11/1.29 (((~![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)))),
% 1.11/1.29 inference(transitivity,[status(thm)],[6426, 6424])).
% 1.11/1.29 tff(6428,plain,
% 1.11/1.29 ((~![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))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(6429,plain,
% 1.11/1.29 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | (~m_main_v_state2(s74, c_t2)) | m_main_v_state2(s75, c_t2) | (~node13(s74, s75))),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[6428, 6427])).
% 1.11/1.29 tff(6430,plain,
% 1.11/1.29 (m_main_v_state2(s75, c_t2)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[6429, 518, 6327, 6423])).
% 1.11/1.29 tff(6431,plain,
% 1.11/1.29 (succ(s75, s76) <=> succ(s75, s76)),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(6432,axiom,(succ(s75, s76)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound76')).
% 1.11/1.29 tff(6433,plain,
% 1.11/1.29 (succ(s75, s76)),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[6432, 6431])).
% 1.11/1.29 tff(6434,plain,
% 1.11/1.29 (((~![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))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(6435,plain,
% 1.11/1.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s75, s76)) | trans(s75, s76))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(6436,plain,
% 1.11/1.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s75, s76)) | trans(s75, s76)),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[6435, 6434])).
% 1.11/1.29 tff(6437,plain,
% 1.11/1.29 (trans(s75, s76)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[6436, 6433, 32])).
% 1.11/1.29 tff(6438,plain,
% 1.11/1.29 (((~![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))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(6439,plain,
% 1.11/1.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s75, s76)) | node7(s75, s76))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(6440,plain,
% 1.11/1.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s75, s76)) | node7(s75, s76)),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[6439, 6438])).
% 1.11/1.29 tff(6441,plain,
% 1.11/1.29 (node7(s75, s76)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[6440, 206, 6437])).
% 1.11/1.29 tff(6442,plain,
% 1.11/1.29 (((~![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))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(6443,plain,
% 1.11/1.29 ((~![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))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(6444,plain,
% 1.11/1.29 ((~![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)),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[6443, 6442])).
% 1.11/1.29 tff(6445,plain,
% 1.11/1.29 ((~m_main_v_state1(s75, c_n1)) | (~m_main_v_state2(s75, c_t2)) | m_main_v_state1(s76, c_t1)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[6444, 651, 6441])).
% 1.11/1.29 tff(6446,plain,
% 1.11/1.29 (m_main_v_state1(s76, c_t1)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[6445, 6430, 6374])).
% 1.11/1.29 tff(6447,plain,
% 1.11/1.29 (((~![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)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(6448,plain,
% 1.11/1.29 ((~![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)))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(6449,plain,
% 1.11/1.29 ((~![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))),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[6448, 6447])).
% 1.11/1.29 tff(6450,plain,
% 1.11/1.29 (~m_main_v_state1(s76, c_n1)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[6449, 10, 6446])).
% 1.11/1.29 tff(6451,plain,
% 1.11/1.29 (((~![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)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(6452,plain,
% 1.11/1.29 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s76, c_n1) | (~node1(s76)))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(6453,plain,
% 1.11/1.29 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s76, c_n1) | (~node1(s76))),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[6452, 6451])).
% 1.11/1.29 tff(6454,plain,
% 1.11/1.29 (~node1(s76)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[6453, 421, 6450])).
% 1.11/1.29 tff(6455,plain,
% 1.11/1.29 (((~![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))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(6456,plain,
% 1.11/1.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s75, s76)) | node18(s75, s76))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(6457,plain,
% 1.11/1.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s75, s76)) | node18(s75, s76)),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[6456, 6455])).
% 1.11/1.29 tff(6458,plain,
% 1.11/1.29 (node18(s75, s76)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[6457, 125, 6437])).
% 1.11/1.29 tff(6459,plain,
% 1.11/1.29 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(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))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(6460,plain,
% 1.11/1.29 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s75, c_n1)) | (~m_main_v_state2(s75, c_t2)) | (~node18(s75, s76)) | m_main_v_turn(s76, c_2))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(6461,plain,
% 1.11/1.29 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s75, c_n1)) | (~m_main_v_state2(s75, c_t2)) | (~node18(s75, s76)) | m_main_v_turn(s76, c_2)),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[6460, 6459])).
% 1.11/1.29 tff(6462,plain,
% 1.11/1.29 ((~m_main_v_state1(s75, c_n1)) | (~m_main_v_state2(s75, c_t2)) | m_main_v_turn(s76, c_2)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[6461, 760, 6458])).
% 1.11/1.29 tff(6463,plain,
% 1.11/1.29 (m_main_v_turn(s76, c_2)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[6462, 6430, 6374])).
% 1.11/1.29 tff(6464,plain,
% 1.11/1.29 (((~![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)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(6465,plain,
% 1.11/1.29 ((~![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)))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(6466,plain,
% 1.11/1.29 ((~![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))),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[6465, 6464])).
% 1.11/1.29 tff(6467,plain,
% 1.11/1.29 (~m_main_v_turn(s76, c_1)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[6466, 156, 6463])).
% 1.11/1.29 tff(6468,plain,
% 1.11/1.29 (((~![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)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6469,plain,
% 1.11/1.30 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s76, c_1) | (~node5(s76)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(6470,plain,
% 1.11/1.30 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s76, c_1) | (~node5(s76))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[6469, 6468])).
% 1.11/1.30 tff(6471,plain,
% 1.11/1.30 (~node5(s76)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[6470, 776, 6467])).
% 1.11/1.30 tff(6472,plain,
% 1.11/1.30 (((~![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)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6473,plain,
% 1.11/1.30 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s76, c_n1) | (~node2(s76)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(6474,plain,
% 1.11/1.30 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s76, c_n1) | (~node2(s76))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[6473, 6472])).
% 1.11/1.30 tff(6475,plain,
% 1.11/1.30 (~node2(s76)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[6474, 787, 6450])).
% 1.11/1.30 tff(6476,plain,
% 1.11/1.30 (((~![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)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6477,plain,
% 1.11/1.30 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s76, c_n1) | (~node3(s76)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(6478,plain,
% 1.11/1.30 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s76, c_n1) | (~node3(s76))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[6477, 6476])).
% 1.11/1.30 tff(6479,plain,
% 1.11/1.30 (~node3(s76)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[6478, 798, 6450])).
% 1.11/1.30 tff(6480,plain,
% 1.11/1.30 (((~![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)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6481,plain,
% 1.11/1.30 ((~![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)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(6482,plain,
% 1.11/1.30 ((~![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))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[6481, 6480])).
% 1.11/1.30 tff(6483,plain,
% 1.11/1.30 (~m_main_v_state1(s76, c_c1)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[6482, 539, 6446])).
% 1.11/1.30 tff(6484,plain,
% 1.11/1.30 (((~![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(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)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6485,plain,
% 1.11/1.30 (((~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)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6486,plain,
% 1.11/1.30 (((~![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))))),
% 1.11/1.30 inference(monotonicity,[status(thm)],[6485])).
% 1.11/1.30 tff(6487,plain,
% 1.11/1.30 (((~![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)))),
% 1.11/1.30 inference(transitivity,[status(thm)],[6486, 6484])).
% 1.11/1.30 tff(6488,plain,
% 1.11/1.30 ((~![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)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(6489,plain,
% 1.11/1.30 ((~![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(s74, c_n2) | (~m_main_v_state2(s75, c_n2)) | (~node13(s74, s75))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[6488, 6487])).
% 1.11/1.30 tff(6490,plain,
% 1.11/1.30 (~m_main_v_state2(s75, c_n2)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[6489, 311, 6331, 6423])).
% 1.11/1.30 tff(6491,plain,
% 1.11/1.30 (((~![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)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6492,plain,
% 1.11/1.30 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s75, c_n2) | (~node9(s75)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(6493,plain,
% 1.11/1.30 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s75, c_n2) | (~node9(s75))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[6492, 6491])).
% 1.11/1.30 tff(6494,plain,
% 1.11/1.30 (~node9(s75)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[6493, 88, 6490])).
% 1.11/1.30 tff(6495,plain,
% 1.11/1.30 (((~![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)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6496,plain,
% 1.11/1.30 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s75, c_n2) | (~node10(s75)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(6497,plain,
% 1.11/1.30 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s75, c_n2) | (~node10(s75))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[6496, 6495])).
% 1.11/1.30 tff(6498,plain,
% 1.11/1.30 (~node10(s75)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[6497, 249, 6490])).
% 1.11/1.30 tff(6499,plain,
% 1.11/1.30 (((~![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)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6500,plain,
% 1.11/1.30 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s75, c_n2) | (~node8(s75)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(6501,plain,
% 1.11/1.30 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s75, c_n2) | (~node8(s75))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[6500, 6499])).
% 1.11/1.30 tff(6502,plain,
% 1.11/1.30 (~node8(s75)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[6501, 271, 6490])).
% 1.11/1.30 tff(6503,plain,
% 1.11/1.30 (((~![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))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6504,plain,
% 1.11/1.30 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s75, s76)) | node14(s75, s76))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(6505,plain,
% 1.11/1.30 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s75, s76)) | node14(s75, s76)),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[6504, 6503])).
% 1.11/1.30 tff(6506,plain,
% 1.11/1.30 (node14(s75, s76)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[6505, 46, 6437])).
% 1.11/1.30 tff(6507,plain,
% 1.11/1.30 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(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))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6508,plain,
% 1.11/1.30 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(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))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(6509,plain,
% 1.11/1.30 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(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)),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[6508, 6507])).
% 1.11/1.30 tff(6510,plain,
% 1.11/1.30 ((~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)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[6509, 617, 6506])).
% 1.11/1.30 tff(6511,plain,
% 1.11/1.30 (m_main_v_state2(s76, c_c2)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[6510, 6502, 6374, 6430, 6498, 6494])).
% 1.11/1.30 tff(6512,plain,
% 1.11/1.30 (((~![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)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6513,plain,
% 1.11/1.30 ((~![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)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(6514,plain,
% 1.11/1.30 ((~![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))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[6513, 6512])).
% 1.11/1.30 tff(6515,plain,
% 1.11/1.30 (~m_main_v_state2(s76, c_n2)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[6514, 697, 6511])).
% 1.11/1.30 tff(6516,plain,
% 1.11/1.30 (((~![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)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6517,plain,
% 1.11/1.30 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s76, c_n2) | (~node4(s76)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(6518,plain,
% 1.11/1.30 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s76, c_n2) | (~node4(s76))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[6517, 6516])).
% 1.11/1.30 tff(6519,plain,
% 1.11/1.30 (~node4(s76)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[6518, 388, 6515])).
% 1.11/1.30 tff(6520,plain,
% 1.11/1.30 (succ(s76, s77) <=> succ(s76, s77)),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6521,axiom,(succ(s76, s77)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound77')).
% 1.11/1.30 tff(6522,plain,
% 1.11/1.30 (succ(s76, s77)),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[6521, 6520])).
% 1.11/1.30 tff(6523,plain,
% 1.11/1.30 (((~![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))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6524,plain,
% 1.11/1.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s76, s77)) | trans(s76, s77))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(6525,plain,
% 1.11/1.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s76, s77)) | trans(s76, s77)),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[6524, 6523])).
% 1.11/1.30 tff(6526,plain,
% 1.11/1.30 (trans(s76, s77)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[6525, 6522, 32])).
% 1.11/1.30 tff(6527,plain,
% 1.11/1.30 (((~![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))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6528,plain,
% 1.11/1.30 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s76, s77)) | node7(s76, s77))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(6529,plain,
% 1.11/1.30 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s76, s77)) | node7(s76, s77)),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[6528, 6527])).
% 1.11/1.30 tff(6530,plain,
% 1.11/1.30 (node7(s76, s77)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[6529, 206, 6526])).
% 1.11/1.30 tff(6531,plain,
% 1.11/1.30 (((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(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)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6532,plain,
% 1.11/1.30 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s76, c_c1) | node1(s76) | node2(s76) | node3(s76) | node4(s76) | node5(s76) | node6(s76, s77) | (~node7(s76, s77)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(6533,plain,
% 1.11/1.30 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s76, c_c1) | node1(s76) | node2(s76) | node3(s76) | node4(s76) | node5(s76) | node6(s76, s77) | (~node7(s76, s77))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[6532, 6531])).
% 1.11/1.30 tff(6534,plain,
% 1.11/1.30 (m_main_v_state1(s76, c_c1) | node1(s76) | node2(s76) | node3(s76) | node4(s76) | node5(s76) | node6(s76, s77)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[6533, 820, 6530])).
% 1.11/1.30 tff(6535,plain,
% 1.11/1.30 (node6(s76, s77)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[6534, 6519, 6483, 6479, 6475, 6471, 6454])).
% 1.11/1.30 tff(6536,plain,
% 1.11/1.30 (((~![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(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)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6537,plain,
% 1.11/1.30 (((~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)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6538,plain,
% 1.11/1.30 (((~![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))))),
% 1.11/1.30 inference(monotonicity,[status(thm)],[6537])).
% 1.11/1.30 tff(6539,plain,
% 1.11/1.30 (((~![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)))),
% 1.11/1.30 inference(transitivity,[status(thm)],[6538, 6536])).
% 1.11/1.30 tff(6540,plain,
% 1.11/1.30 ((~![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))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(6541,plain,
% 1.11/1.30 ((~![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(s76, c_t1)) | m_main_v_state1(s77, c_t1) | (~node6(s76, s77))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[6540, 6539])).
% 1.11/1.30 tff(6542,plain,
% 1.11/1.30 (m_main_v_state1(s77, c_t1)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[6541, 856, 6446, 6535])).
% 1.11/1.30 tff(6543,plain,
% 1.11/1.30 (((~![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)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6544,plain,
% 1.11/1.30 ((~![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)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(6545,plain,
% 1.11/1.30 ((~![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))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[6544, 6543])).
% 1.11/1.30 tff(6546,plain,
% 1.11/1.30 (~m_main_v_state2(s76, c_t2)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[6545, 260, 6511])).
% 1.11/1.30 tff(6547,plain,
% 1.11/1.30 (((~![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)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6548,plain,
% 1.11/1.30 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s76, c_t2) | (~node12(s76)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(6549,plain,
% 1.11/1.30 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s76, c_t2) | (~node12(s76))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[6548, 6547])).
% 1.11/1.30 tff(6550,plain,
% 1.11/1.30 (~node12(s76)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[6549, 633, 6546])).
% 1.11/1.30 tff(6551,plain,
% 1.11/1.30 (((~![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)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6552,plain,
% 1.11/1.30 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s76, c_n1) | (~node11(s76)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(6553,plain,
% 1.11/1.30 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s76, c_n1) | (~node11(s76))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[6552, 6551])).
% 1.11/1.30 tff(6554,plain,
% 1.11/1.30 (~node11(s76)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[6553, 238, 6450])).
% 1.11/1.30 tff(6555,plain,
% 1.11/1.30 (((~![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)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6556,plain,
% 1.11/1.30 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s76, c_c1) | (~node10(s76)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(6557,plain,
% 1.11/1.30 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s76, c_c1) | (~node10(s76))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[6556, 6555])).
% 1.11/1.30 tff(6558,plain,
% 1.11/1.30 (~node10(s76)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[6557, 675, 6483])).
% 1.11/1.30 tff(6559,plain,
% 1.11/1.30 (((~![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)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6560,plain,
% 1.11/1.30 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s76, c_n1) | (~node9(s76)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(6561,plain,
% 1.11/1.30 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s76, c_n1) | (~node9(s76))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[6560, 6559])).
% 1.11/1.30 tff(6562,plain,
% 1.11/1.30 (~node9(s76)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[6561, 686, 6450])).
% 1.11/1.30 tff(6563,plain,
% 1.11/1.30 (((~![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)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6564,plain,
% 1.11/1.30 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s76, c_n2) | (~node8(s76)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(6565,plain,
% 1.11/1.30 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s76, c_n2) | (~node8(s76))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[6564, 6563])).
% 1.11/1.30 tff(6566,plain,
% 1.11/1.30 (~node8(s76)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[6565, 271, 6515])).
% 1.11/1.30 tff(6567,plain,
% 1.11/1.30 (((~![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))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6568,plain,
% 1.11/1.30 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s76, s77)) | node14(s76, s77))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(6569,plain,
% 1.11/1.30 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s76, s77)) | node14(s76, s77)),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[6568, 6567])).
% 1.11/1.30 tff(6570,plain,
% 1.11/1.30 (node14(s76, s77)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[6569, 46, 6526])).
% 1.11/1.30 tff(6571,plain,
% 1.11/1.30 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(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)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6572,plain,
% 1.11/1.30 (((~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)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6573,plain,
% 1.11/1.30 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(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))))),
% 1.11/1.30 inference(monotonicity,[status(thm)],[6572])).
% 1.11/1.30 tff(6574,plain,
% 1.11/1.30 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(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)))),
% 1.11/1.30 inference(transitivity,[status(thm)],[6573, 6571])).
% 1.11/1.30 tff(6575,plain,
% 1.11/1.30 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s76, c_c2)) | node9(s76) | node8(s76) | node10(s76) | node11(s76) | node12(s76) | (~node14(s76, s77)) | m_main_v_state2(s77, c_n2))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(6576,plain,
% 1.11/1.30 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s77, c_n2) | node9(s76) | node8(s76) | node10(s76) | node11(s76) | node12(s76) | (~node14(s76, s77)) | (~m_main_v_state2(s76, c_c2))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[6575, 6574])).
% 1.11/1.30 tff(6577,plain,
% 1.11/1.30 (m_main_v_state2(s77, c_n2) | node9(s76) | node8(s76) | node10(s76) | node11(s76) | node12(s76) | (~m_main_v_state2(s76, c_c2))),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[6576, 726, 6570])).
% 1.11/1.30 tff(6578,plain,
% 1.11/1.30 (m_main_v_state2(s77, c_n2)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[6577, 6566, 6511, 6562, 6558, 6554, 6550])).
% 1.11/1.30 tff(6579,plain,
% 1.11/1.30 (((~![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)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6580,plain,
% 1.11/1.30 ((~![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)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(6581,plain,
% 1.11/1.30 ((~![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))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[6580, 6579])).
% 1.11/1.30 tff(6582,plain,
% 1.11/1.30 (~m_main_v_state2(s77, c_t2)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[6581, 77, 6578])).
% 1.11/1.30 tff(6583,plain,
% 1.11/1.30 (((~![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)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6584,plain,
% 1.11/1.30 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s77, c_t2) | (~node15(s77)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(6585,plain,
% 1.11/1.30 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s77, c_t2) | (~node15(s77))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[6584, 6583])).
% 1.11/1.30 tff(6586,plain,
% 1.11/1.30 (~node15(s77)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[6585, 103, 6582])).
% 1.11/1.30 tff(6587,plain,
% 1.11/1.30 (succ(s77, s78) <=> succ(s77, s78)),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6588,axiom,(succ(s77, s78)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound78')).
% 1.11/1.30 tff(6589,plain,
% 1.11/1.30 (succ(s77, s78)),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[6588, 6587])).
% 1.11/1.30 tff(6590,plain,
% 1.11/1.30 (((~![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))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6591,plain,
% 1.11/1.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s77, s78)) | trans(s77, s78))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(6592,plain,
% 1.11/1.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s77, s78)) | trans(s77, s78)),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[6591, 6590])).
% 1.11/1.30 tff(6593,plain,
% 1.11/1.30 (trans(s77, s78)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[6592, 6589, 32])).
% 1.11/1.30 tff(6594,plain,
% 1.11/1.30 (((~![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))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(6595,plain,
% 1.11/1.30 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s77, s78)) | node18(s77, s78))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(6596,plain,
% 1.11/1.31 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s77, s78)) | node18(s77, s78)),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[6595, 6594])).
% 1.11/1.31 tff(6597,plain,
% 1.11/1.31 (node18(s77, s78)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[6596, 125, 6593])).
% 1.11/1.31 tff(6598,plain,
% 1.11/1.31 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | (node15(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))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(6599,plain,
% 1.11/1.31 (((~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))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(6600,plain,
% 1.11/1.31 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(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)))),
% 1.11/1.31 inference(monotonicity,[status(thm)],[6599])).
% 1.11/1.31 tff(6601,plain,
% 1.11/1.31 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(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))),
% 1.11/1.31 inference(transitivity,[status(thm)],[6600, 6598])).
% 1.11/1.31 tff(6602,plain,
% 1.11/1.31 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | ((~m_main_v_state1(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | node15(s77) | (~node18(s77, s78)) | m_main_v_turn(s78, c_1))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(6603,plain,
% 1.11/1.31 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node15(X) | (~node18(X, Y)) | m_main_v_turn(Y, c_1))) | node15(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)),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[6602, 6601])).
% 1.11/1.31 tff(6604,plain,
% 1.11/1.31 (node15(s77) | (~m_main_v_state1(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | m_main_v_turn(s78, c_1)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[6603, 992, 6597])).
% 1.11/1.31 tff(6605,plain,
% 1.11/1.31 (m_main_v_turn(s78, c_1)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[6604, 6586, 6578, 6542])).
% 1.11/1.31 tff(6606,plain,
% 1.11/1.31 (((~![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)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(6607,plain,
% 1.11/1.31 ((~![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)))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(6608,plain,
% 1.11/1.31 ((~![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))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[6607, 6606])).
% 1.11/1.31 tff(6609,plain,
% 1.11/1.31 (~m_main_v_turn(s78, c_2)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[6608, 156, 6605])).
% 1.11/1.31 tff(6610,plain,
% 1.11/1.31 (((~![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)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(6611,plain,
% 1.11/1.31 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s78, c_2) | (~node12(s78)))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(6612,plain,
% 1.11/1.31 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s78, c_2) | (~node12(s78))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[6611, 6610])).
% 1.11/1.31 tff(6613,plain,
% 1.11/1.31 (~node12(s78)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[6612, 184, 6609])).
% 1.11/1.31 tff(6614,plain,
% 1.11/1.31 (((~![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))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(6615,plain,
% 1.11/1.31 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s77, s78)) | node14(s77, s78))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(6616,plain,
% 1.11/1.31 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s77, s78)) | node14(s77, s78)),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[6615, 6614])).
% 1.11/1.31 tff(6617,plain,
% 1.11/1.31 (node14(s77, s78)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[6616, 46, 6593])).
% 1.11/1.31 tff(6618,plain,
% 1.11/1.31 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(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))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(6619,plain,
% 1.11/1.31 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | ((~m_main_v_state1(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | (~node14(s77, s78)) | m_main_v_state2(s78, c_t2))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(6620,plain,
% 1.11/1.31 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | (~node14(X, Y)) | m_main_v_state2(Y, c_t2))) | (~m_main_v_state1(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | (~node14(s77, s78)) | m_main_v_state2(s78, c_t2)),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[6619, 6618])).
% 1.11/1.31 tff(6621,plain,
% 1.11/1.31 ((~m_main_v_state1(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | m_main_v_state2(s78, c_t2)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[6620, 922, 6617])).
% 1.11/1.31 tff(6622,plain,
% 1.11/1.31 (m_main_v_state2(s78, c_t2)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[6621, 6542, 6578])).
% 1.11/1.31 tff(6623,plain,
% 1.11/1.31 (((~![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)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(6624,plain,
% 1.11/1.31 ((~![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)))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(6625,plain,
% 1.11/1.31 ((~![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))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[6624, 6623])).
% 1.11/1.31 tff(6626,plain,
% 1.11/1.31 (~m_main_v_state2(s78, c_n2)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[6625, 77, 6622])).
% 1.11/1.31 tff(6627,plain,
% 1.11/1.31 (((~![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)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(6628,plain,
% 1.11/1.31 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s78, c_n2) | (~node8(s78)))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(6629,plain,
% 1.11/1.31 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s78, c_n2) | (~node8(s78))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[6628, 6627])).
% 1.11/1.31 tff(6630,plain,
% 1.11/1.31 (~node8(s78)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[6629, 271, 6626])).
% 1.11/1.31 tff(6631,plain,
% 1.11/1.31 (((~![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)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(6632,plain,
% 1.11/1.31 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s78, c_n2) | (~node9(s78)))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(6633,plain,
% 1.11/1.31 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s78, c_n2) | (~node9(s78))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[6632, 6631])).
% 1.11/1.31 tff(6634,plain,
% 1.11/1.31 (~node9(s78)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[6633, 88, 6626])).
% 1.11/1.31 tff(6635,plain,
% 1.11/1.31 (((~![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)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(6636,plain,
% 1.11/1.31 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s78, c_n2) | (~node10(s78)))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(6637,plain,
% 1.11/1.31 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s78, c_n2) | (~node10(s78))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[6636, 6635])).
% 1.11/1.31 tff(6638,plain,
% 1.11/1.31 (~node10(s78)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[6637, 249, 6626])).
% 1.11/1.31 tff(6639,plain,
% 1.11/1.31 (((~![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)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(6640,plain,
% 1.11/1.31 ((~![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)))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(6641,plain,
% 1.11/1.31 ((~![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))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[6640, 6639])).
% 1.11/1.31 tff(6642,plain,
% 1.11/1.31 (~m_main_v_state2(s78, c_c2)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[6641, 260, 6622])).
% 1.11/1.31 tff(6643,plain,
% 1.11/1.31 (((~![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)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(6644,plain,
% 1.11/1.31 ((~![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)))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(6645,plain,
% 1.11/1.31 ((~![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))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[6644, 6643])).
% 1.11/1.31 tff(6646,plain,
% 1.11/1.31 (~m_main_v_state2(s77, c_c2)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[6645, 697, 6578])).
% 1.11/1.31 tff(6647,plain,
% 1.11/1.31 (((~![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)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(6648,plain,
% 1.11/1.31 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s77, c_c2) | (~node3(s77)))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(6649,plain,
% 1.11/1.31 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s77, c_c2) | (~node3(s77))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[6648, 6647])).
% 1.11/1.31 tff(6650,plain,
% 1.11/1.31 (~node3(s77)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[6649, 399, 6646])).
% 1.11/1.31 tff(6651,plain,
% 1.11/1.31 (((~![V: $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)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(6652,plain,
% 1.11/1.31 (((~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)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(6653,plain,
% 1.11/1.31 (((~![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))))),
% 1.11/1.31 inference(monotonicity,[status(thm)],[6652])).
% 1.11/1.31 tff(6654,plain,
% 1.11/1.31 (((~![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)))),
% 1.11/1.31 inference(transitivity,[status(thm)],[6653, 6651])).
% 1.11/1.31 tff(6655,plain,
% 1.11/1.31 ((~![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)))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(6656,plain,
% 1.11/1.31 ((~![V: $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))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[6655, 6654])).
% 1.11/1.31 tff(6657,plain,
% 1.11/1.31 (~m_main_v_state1(s77, c_n1)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[6656, 835, 6450, 6535])).
% 1.11/1.31 tff(6658,plain,
% 1.11/1.31 (((~![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)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(6659,plain,
% 1.11/1.31 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s77, c_n1) | (~node2(s77)))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(6660,plain,
% 1.11/1.31 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s77, c_n1) | (~node2(s77))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[6659, 6658])).
% 1.11/1.31 tff(6661,plain,
% 1.11/1.31 (~node2(s77)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[6660, 787, 6657])).
% 1.11/1.31 tff(6662,plain,
% 1.11/1.31 (((~![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)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(6663,plain,
% 1.11/1.31 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s77, c_t2) | (~node1(s77)))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(6664,plain,
% 1.11/1.31 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s77, c_t2) | (~node1(s77))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[6663, 6662])).
% 1.11/1.31 tff(6665,plain,
% 1.11/1.31 (~node1(s77)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[6664, 195, 6582])).
% 1.11/1.31 tff(6666,plain,
% 1.11/1.31 (((~![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))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(6667,plain,
% 1.11/1.31 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s77, s78)) | node7(s77, s78))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(6668,plain,
% 1.11/1.31 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s77, s78)) | node7(s77, s78)),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[6667, 6666])).
% 1.11/1.31 tff(6669,plain,
% 1.11/1.31 (node7(s77, s78)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[6668, 206, 6593])).
% 1.11/1.31 tff(6670,plain,
% 1.11/1.31 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(6671,plain,
% 1.11/1.31 (((~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)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(6672,plain,
% 1.11/1.31 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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))))),
% 1.11/1.31 inference(monotonicity,[status(thm)],[6671])).
% 1.11/1.31 tff(6673,plain,
% 1.11/1.31 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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)))),
% 1.11/1.31 inference(transitivity,[status(thm)],[6672, 6670])).
% 1.11/1.31 tff(6674,plain,
% 1.11/1.31 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(6675,plain,
% 1.11/1.31 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[6674, 6673])).
% 1.11/1.31 tff(6676,plain,
% 1.11/1.31 ((~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)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[6675, 892, 6669])).
% 1.11/1.31 tff(6677,plain,
% 1.11/1.31 (m_main_v_state1(s78, c_c1)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[6676, 6665, 6578, 6542, 6661, 6650])).
% 1.11/1.31 tff(6678,plain,
% 1.11/1.31 (((~![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)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(6679,plain,
% 1.11/1.31 ((~![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)))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(6680,plain,
% 1.11/1.31 ((~![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))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[6679, 6678])).
% 1.11/1.31 tff(6681,plain,
% 1.11/1.31 (~m_main_v_state1(s78, c_n1)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[6680, 454, 6677])).
% 1.11/1.31 tff(6682,plain,
% 1.11/1.31 (((~![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)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(6683,plain,
% 1.11/1.31 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s78, c_n1) | (~node11(s78)))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(6684,plain,
% 1.11/1.31 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s78, c_n1) | (~node11(s78))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[6683, 6682])).
% 1.11/1.31 tff(6685,plain,
% 1.11/1.31 (~node11(s78)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[6684, 238, 6681])).
% 1.11/1.31 tff(6686,plain,
% 1.11/1.31 (succ(s78, s79) <=> succ(s78, s79)),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(6687,axiom,(succ(s78, s79)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound79')).
% 1.11/1.31 tff(6688,plain,
% 1.11/1.31 (succ(s78, s79)),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[6687, 6686])).
% 1.11/1.31 tff(6689,plain,
% 1.11/1.31 (((~![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))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(6690,plain,
% 1.11/1.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s78, s79)) | trans(s78, s79))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(6691,plain,
% 1.11/1.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s78, s79)) | trans(s78, s79)),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[6690, 6689])).
% 1.11/1.31 tff(6692,plain,
% 1.11/1.31 (trans(s78, s79)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[6691, 6688, 32])).
% 1.11/1.31 tff(6693,plain,
% 1.11/1.31 (((~![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))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(6694,plain,
% 1.11/1.31 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s78, s79)) | node14(s78, s79))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(6695,plain,
% 1.11/1.31 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s78, s79)) | node14(s78, s79)),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[6694, 6693])).
% 1.11/1.31 tff(6696,plain,
% 1.11/1.31 (node14(s78, s79)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[6695, 46, 6692])).
% 1.11/1.31 tff(6697,plain,
% 1.11/1.31 (((~![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)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(6698,plain,
% 1.11/1.31 ((~![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)))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(6699,plain,
% 1.11/1.31 ((~![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))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[6698, 6697])).
% 1.11/1.31 tff(6700,plain,
% 1.11/1.31 (m_main_v_state2(s78, c_c2) | node9(s78) | node8(s78) | node10(s78) | node11(s78) | node12(s78) | node13(s78, s79)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[6699, 296, 6696])).
% 1.11/1.31 tff(6701,plain,
% 1.11/1.31 (node13(s78, s79)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[6700, 6685, 6642, 6638, 6634, 6630, 6613])).
% 1.11/1.31 tff(6702,plain,
% 1.11/1.31 (((~![V: $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)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(6703,plain,
% 1.11/1.31 (((~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)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(6704,plain,
% 1.11/1.31 (((~![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))))),
% 1.11/1.31 inference(monotonicity,[status(thm)],[6703])).
% 1.11/1.31 tff(6705,plain,
% 1.11/1.31 (((~![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)))),
% 1.11/1.31 inference(transitivity,[status(thm)],[6704, 6702])).
% 1.11/1.31 tff(6706,plain,
% 1.11/1.31 ((~![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)))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(6707,plain,
% 1.11/1.31 ((~![V: $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))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[6706, 6705])).
% 1.11/1.31 tff(6708,plain,
% 1.11/1.31 (~m_main_v_state2(s79, c_n2)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[6707, 311, 6626, 6701])).
% 1.11/1.31 tff(6709,plain,
% 1.11/1.31 (((~![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)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(6710,plain,
% 1.11/1.31 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s79, c_n2) | (~node9(s79)))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(6711,plain,
% 1.11/1.31 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s79, c_n2) | (~node9(s79))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[6710, 6709])).
% 1.11/1.31 tff(6712,plain,
% 1.11/1.31 (~node9(s79)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[6711, 88, 6708])).
% 1.11/1.31 tff(6713,plain,
% 1.11/1.31 (((~![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)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6714,plain,
% 1.11/1.32 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s79, c_n2) | (~node10(s79)))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(6715,plain,
% 1.11/1.32 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s79, c_n2) | (~node10(s79))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6714, 6713])).
% 1.11/1.32 tff(6716,plain,
% 1.11/1.32 (~node10(s79)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6715, 249, 6708])).
% 1.11/1.32 tff(6717,plain,
% 1.11/1.32 (((~![V: $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)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6718,plain,
% 1.11/1.32 (((~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)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6719,plain,
% 1.11/1.32 (((~![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))))),
% 1.11/1.32 inference(monotonicity,[status(thm)],[6718])).
% 1.11/1.32 tff(6720,plain,
% 1.11/1.32 (((~![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)))),
% 1.11/1.32 inference(transitivity,[status(thm)],[6719, 6717])).
% 1.11/1.32 tff(6721,plain,
% 1.11/1.32 ((~![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))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(6722,plain,
% 1.11/1.32 ((~![V: $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))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6721, 6720])).
% 1.11/1.32 tff(6723,plain,
% 1.11/1.32 (m_main_v_state2(s79, c_t2)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6722, 518, 6622, 6701])).
% 1.11/1.32 tff(6724,plain,
% 1.11/1.32 (((~![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)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6725,plain,
% 1.11/1.32 ((~![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)))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(6726,plain,
% 1.11/1.32 ((~![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))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6725, 6724])).
% 1.11/1.32 tff(6727,plain,
% 1.11/1.32 (~m_main_v_state1(s78, c_t1)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6726, 539, 6677])).
% 1.11/1.32 tff(6728,plain,
% 1.11/1.32 (((~![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)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6729,plain,
% 1.11/1.32 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s78, c_t1) | (~node5(s78)))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(6730,plain,
% 1.11/1.32 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s78, c_t1) | (~node5(s78))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6729, 6728])).
% 1.11/1.32 tff(6731,plain,
% 1.11/1.32 (~node5(s78)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6730, 550, 6727])).
% 1.11/1.32 tff(6732,plain,
% 1.11/1.32 (((~![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)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6733,plain,
% 1.11/1.32 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s78, c_n2) | (~node4(s78)))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(6734,plain,
% 1.11/1.32 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s78, c_n2) | (~node4(s78))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6733, 6732])).
% 1.11/1.32 tff(6735,plain,
% 1.11/1.32 (~node4(s78)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6734, 388, 6626])).
% 1.11/1.32 tff(6736,plain,
% 1.11/1.32 (((~![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)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6737,plain,
% 1.11/1.32 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s78, c_c2) | (~node3(s78)))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(6738,plain,
% 1.11/1.32 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s78, c_c2) | (~node3(s78))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6737, 6736])).
% 1.11/1.32 tff(6739,plain,
% 1.11/1.32 (~node3(s78)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6738, 399, 6642])).
% 1.11/1.32 tff(6740,plain,
% 1.11/1.32 (((~![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)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6741,plain,
% 1.11/1.32 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s78, c_n2) | (~node2(s78)))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(6742,plain,
% 1.11/1.32 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s78, c_n2) | (~node2(s78))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6741, 6740])).
% 1.11/1.32 tff(6743,plain,
% 1.11/1.32 (~node2(s78)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6742, 410, 6626])).
% 1.11/1.32 tff(6744,plain,
% 1.11/1.32 (((~![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)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6745,plain,
% 1.11/1.32 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s78, c_n1) | (~node1(s78)))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(6746,plain,
% 1.11/1.32 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s78, c_n1) | (~node1(s78))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6745, 6744])).
% 1.11/1.32 tff(6747,plain,
% 1.11/1.32 (~node1(s78)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6746, 421, 6681])).
% 1.11/1.32 tff(6748,plain,
% 1.11/1.32 (((~![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))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6749,plain,
% 1.11/1.32 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s78, s79)) | node7(s78, s79))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(6750,plain,
% 1.11/1.32 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s78, s79)) | node7(s78, s79)),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6749, 6748])).
% 1.11/1.32 tff(6751,plain,
% 1.11/1.32 (node7(s78, s79)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6750, 206, 6692])).
% 1.11/1.32 tff(6752,plain,
% 1.11/1.32 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6753,plain,
% 1.11/1.32 (((~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)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6754,plain,
% 1.11/1.32 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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))))),
% 1.11/1.32 inference(monotonicity,[status(thm)],[6753])).
% 1.11/1.32 tff(6755,plain,
% 1.11/1.32 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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)))),
% 1.11/1.32 inference(transitivity,[status(thm)],[6754, 6752])).
% 1.11/1.32 tff(6756,plain,
% 1.11/1.32 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(6757,plain,
% 1.11/1.32 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6756, 6755])).
% 1.11/1.32 tff(6758,plain,
% 1.11/1.32 (m_main_v_state1(s79, c_n1) | (~m_main_v_state1(s78, c_c1)) | node1(s78) | node2(s78) | node3(s78) | node4(s78) | node5(s78)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6757, 584, 6751])).
% 1.11/1.32 tff(6759,plain,
% 1.11/1.32 (m_main_v_state1(s79, c_n1)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6758, 6747, 6677, 6743, 6739, 6735, 6731])).
% 1.11/1.32 tff(6760,plain,
% 1.11/1.32 (((~![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)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6761,plain,
% 1.11/1.32 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s79, c_n2) | (~node8(s79)))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(6762,plain,
% 1.11/1.32 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s79, c_n2) | (~node8(s79))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6761, 6760])).
% 1.11/1.32 tff(6763,plain,
% 1.11/1.32 (~node8(s79)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6762, 271, 6708])).
% 1.11/1.32 tff(6764,plain,
% 1.11/1.32 (succ(s79, s80) <=> succ(s79, s80)),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6765,axiom,(succ(s79, s80)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound80')).
% 1.11/1.32 tff(6766,plain,
% 1.11/1.32 (succ(s79, s80)),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6765, 6764])).
% 1.11/1.32 tff(6767,plain,
% 1.11/1.32 (((~![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))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6768,plain,
% 1.11/1.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s79, s80)) | trans(s79, s80))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(6769,plain,
% 1.11/1.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s79, s80)) | trans(s79, s80)),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6768, 6767])).
% 1.11/1.32 tff(6770,plain,
% 1.11/1.32 (trans(s79, s80)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6769, 6766, 32])).
% 1.11/1.32 tff(6771,plain,
% 1.11/1.32 (((~![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))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6772,plain,
% 1.11/1.32 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s79, s80)) | node14(s79, s80))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(6773,plain,
% 1.11/1.32 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s79, s80)) | node14(s79, s80)),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6772, 6771])).
% 1.11/1.32 tff(6774,plain,
% 1.11/1.32 (node14(s79, s80)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6773, 46, 6770])).
% 1.11/1.32 tff(6775,plain,
% 1.11/1.32 (((~![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))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6776,plain,
% 1.11/1.32 ((~![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))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(6777,plain,
% 1.11/1.32 ((~![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)),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6776, 6775])).
% 1.11/1.32 tff(6778,plain,
% 1.11/1.32 ((~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)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6777, 617, 6774])).
% 1.11/1.32 tff(6779,plain,
% 1.11/1.32 (m_main_v_state2(s80, c_c2)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6778, 6763, 6759, 6723, 6716, 6712])).
% 1.11/1.32 tff(6780,plain,
% 1.11/1.32 (((~![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)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6781,plain,
% 1.11/1.32 ((~![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)))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(6782,plain,
% 1.11/1.32 ((~![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))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6781, 6780])).
% 1.11/1.32 tff(6783,plain,
% 1.11/1.32 (~m_main_v_state2(s80, c_t2)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6782, 260, 6779])).
% 1.11/1.32 tff(6784,plain,
% 1.11/1.32 (((~![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)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6785,plain,
% 1.11/1.32 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s80, c_t2) | (~node12(s80)))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(6786,plain,
% 1.11/1.32 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s80, c_t2) | (~node12(s80))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6785, 6784])).
% 1.11/1.32 tff(6787,plain,
% 1.11/1.32 (~node12(s80)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6786, 633, 6783])).
% 1.11/1.32 tff(6788,plain,
% 1.11/1.32 (((~![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))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6789,plain,
% 1.11/1.32 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s79, s80)) | node7(s79, s80))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(6790,plain,
% 1.11/1.32 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s79, s80)) | node7(s79, s80)),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6789, 6788])).
% 1.11/1.32 tff(6791,plain,
% 1.11/1.32 (node7(s79, s80)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6790, 206, 6770])).
% 1.11/1.32 tff(6792,plain,
% 1.11/1.32 (((~![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))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6793,plain,
% 1.11/1.32 ((~![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))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(6794,plain,
% 1.11/1.32 ((~![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)),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6793, 6792])).
% 1.11/1.32 tff(6795,plain,
% 1.11/1.32 ((~m_main_v_state1(s79, c_n1)) | (~m_main_v_state2(s79, c_t2)) | m_main_v_state1(s80, c_t1)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6794, 651, 6791])).
% 1.11/1.32 tff(6796,plain,
% 1.11/1.32 (m_main_v_state1(s80, c_t1)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6795, 6723, 6759])).
% 1.11/1.32 tff(6797,plain,
% 1.11/1.32 (((~![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)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6798,plain,
% 1.11/1.32 ((~![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)))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(6799,plain,
% 1.11/1.32 ((~![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))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6798, 6797])).
% 1.11/1.32 tff(6800,plain,
% 1.11/1.32 (~m_main_v_state1(s80, c_n1)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6799, 10, 6796])).
% 1.11/1.32 tff(6801,plain,
% 1.11/1.32 (((~![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)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6802,plain,
% 1.11/1.32 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s80, c_n1) | (~node11(s80)))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(6803,plain,
% 1.11/1.32 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s80, c_n1) | (~node11(s80))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6802, 6801])).
% 1.11/1.32 tff(6804,plain,
% 1.11/1.32 (~node11(s80)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6803, 238, 6800])).
% 1.11/1.32 tff(6805,plain,
% 1.11/1.32 (((~![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)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6806,plain,
% 1.11/1.32 ((~![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)))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(6807,plain,
% 1.11/1.32 ((~![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))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6806, 6805])).
% 1.11/1.32 tff(6808,plain,
% 1.11/1.32 (~m_main_v_state1(s80, c_c1)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6807, 539, 6796])).
% 1.11/1.32 tff(6809,plain,
% 1.11/1.32 (((~![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)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6810,plain,
% 1.11/1.32 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s80, c_c1) | (~node10(s80)))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(6811,plain,
% 1.11/1.32 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s80, c_c1) | (~node10(s80))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6810, 6809])).
% 1.11/1.32 tff(6812,plain,
% 1.11/1.32 (~node10(s80)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6811, 675, 6808])).
% 1.11/1.32 tff(6813,plain,
% 1.11/1.32 (((~![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)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6814,plain,
% 1.11/1.32 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s80, c_n1) | (~node9(s80)))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(6815,plain,
% 1.11/1.32 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s80, c_n1) | (~node9(s80))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6814, 6813])).
% 1.11/1.32 tff(6816,plain,
% 1.11/1.32 (~node9(s80)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6815, 686, 6800])).
% 1.11/1.32 tff(6817,plain,
% 1.11/1.32 (((~![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)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6818,plain,
% 1.11/1.32 ((~![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)))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(6819,plain,
% 1.11/1.32 ((~![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))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6818, 6817])).
% 1.11/1.32 tff(6820,plain,
% 1.11/1.32 (~m_main_v_state2(s80, c_n2)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6819, 697, 6779])).
% 1.11/1.32 tff(6821,plain,
% 1.11/1.32 (((~![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)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6822,plain,
% 1.11/1.32 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s80, c_n2) | (~node8(s80)))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(6823,plain,
% 1.11/1.32 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s80, c_n2) | (~node8(s80))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6822, 6821])).
% 1.11/1.32 tff(6824,plain,
% 1.11/1.32 (~node8(s80)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6823, 271, 6820])).
% 1.11/1.32 tff(6825,plain,
% 1.11/1.32 (succ(s80, s81) <=> succ(s80, s81)),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6826,axiom,(succ(s80, s81)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound81')).
% 1.11/1.32 tff(6827,plain,
% 1.11/1.32 (succ(s80, s81)),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6826, 6825])).
% 1.11/1.32 tff(6828,plain,
% 1.11/1.32 (((~![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))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6829,plain,
% 1.11/1.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s80, s81)) | trans(s80, s81))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(6830,plain,
% 1.11/1.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s80, s81)) | trans(s80, s81)),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6829, 6828])).
% 1.11/1.32 tff(6831,plain,
% 1.11/1.32 (trans(s80, s81)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6830, 6827, 32])).
% 1.11/1.32 tff(6832,plain,
% 1.11/1.32 (((~![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))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6833,plain,
% 1.11/1.32 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s80, s81)) | node14(s80, s81))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(6834,plain,
% 1.11/1.32 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s80, s81)) | node14(s80, s81)),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6833, 6832])).
% 1.11/1.32 tff(6835,plain,
% 1.11/1.32 (node14(s80, s81)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6834, 46, 6831])).
% 1.11/1.32 tff(6836,plain,
% 1.11/1.32 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | 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)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6837,plain,
% 1.11/1.32 (((~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)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6838,plain,
% 1.11/1.32 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | 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))))),
% 1.11/1.32 inference(monotonicity,[status(thm)],[6837])).
% 1.11/1.32 tff(6839,plain,
% 1.11/1.32 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | 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)))),
% 1.11/1.32 inference(transitivity,[status(thm)],[6838, 6836])).
% 1.11/1.32 tff(6840,plain,
% 1.11/1.32 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | 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))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(6841,plain,
% 1.11/1.32 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | 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))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6840, 6839])).
% 1.11/1.32 tff(6842,plain,
% 1.11/1.32 (m_main_v_state2(s81, c_n2) | node9(s80) | node8(s80) | node10(s80) | node11(s80) | node12(s80) | (~m_main_v_state2(s80, c_c2))),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6841, 726, 6835])).
% 1.11/1.32 tff(6843,plain,
% 1.11/1.32 (m_main_v_state2(s81, c_n2)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6842, 6824, 6779, 6816, 6812, 6804, 6787])).
% 1.11/1.32 tff(6844,plain,
% 1.11/1.32 (((~![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)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6845,plain,
% 1.11/1.32 ((~![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)))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(6846,plain,
% 1.11/1.32 ((~![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))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6845, 6844])).
% 1.11/1.32 tff(6847,plain,
% 1.11/1.32 (~m_main_v_state2(s81, c_c2)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6846, 697, 6843])).
% 1.11/1.32 tff(6848,plain,
% 1.11/1.32 (((~![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)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6849,plain,
% 1.11/1.32 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s81, c_c2) | (~node3(s81)))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(6850,plain,
% 1.11/1.32 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s81, c_c2) | (~node3(s81))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6849, 6848])).
% 1.11/1.32 tff(6851,plain,
% 1.11/1.32 (~node3(s81)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6850, 399, 6847])).
% 1.11/1.32 tff(6852,plain,
% 1.11/1.32 (((~![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)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(6853,plain,
% 1.11/1.32 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s80, c_n1) | (~node1(s80)))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(6854,plain,
% 1.11/1.32 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s80, c_n1) | (~node1(s80))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[6853, 6852])).
% 1.11/1.32 tff(6855,plain,
% 1.11/1.32 (~node1(s80)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[6854, 421, 6800])).
% 1.11/1.32 tff(6856,plain,
% 1.11/1.32 (((~![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))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(6857,plain,
% 1.11/1.33 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s79, s80)) | node18(s79, s80))),
% 1.11/1.33 inference(quant_inst,[status(thm)],[])).
% 1.11/1.33 tff(6858,plain,
% 1.11/1.33 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s79, s80)) | node18(s79, s80)),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[6857, 6856])).
% 1.11/1.33 tff(6859,plain,
% 1.11/1.33 (node18(s79, s80)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[6858, 125, 6770])).
% 1.11/1.33 tff(6860,plain,
% 1.11/1.33 (((~![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(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))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(6861,plain,
% 1.11/1.33 ((~![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(s79, c_n1)) | (~m_main_v_state2(s79, c_t2)) | (~node18(s79, s80)) | m_main_v_turn(s80, c_2))),
% 1.11/1.33 inference(quant_inst,[status(thm)],[])).
% 1.11/1.33 tff(6862,plain,
% 1.11/1.33 ((~![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(s79, c_n1)) | (~m_main_v_state2(s79, c_t2)) | (~node18(s79, s80)) | m_main_v_turn(s80, c_2)),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[6861, 6860])).
% 1.11/1.33 tff(6863,plain,
% 1.11/1.33 ((~m_main_v_state1(s79, c_n1)) | (~m_main_v_state2(s79, c_t2)) | m_main_v_turn(s80, c_2)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[6862, 760, 6859])).
% 1.11/1.33 tff(6864,plain,
% 1.11/1.33 (m_main_v_turn(s80, c_2)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[6863, 6723, 6759])).
% 1.11/1.33 tff(6865,plain,
% 1.11/1.33 (((~![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)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(6866,plain,
% 1.11/1.33 ((~![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)))),
% 1.11/1.33 inference(quant_inst,[status(thm)],[])).
% 1.11/1.33 tff(6867,plain,
% 1.11/1.33 ((~![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))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[6866, 6865])).
% 1.11/1.33 tff(6868,plain,
% 1.11/1.33 (~m_main_v_turn(s80, c_1)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[6867, 156, 6864])).
% 1.11/1.33 tff(6869,plain,
% 1.11/1.33 (((~![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)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(6870,plain,
% 1.11/1.33 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s80, c_1) | (~node5(s80)))),
% 1.11/1.33 inference(quant_inst,[status(thm)],[])).
% 1.11/1.33 tff(6871,plain,
% 1.11/1.33 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s80, c_1) | (~node5(s80))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[6870, 6869])).
% 1.11/1.33 tff(6872,plain,
% 1.11/1.33 (~node5(s80)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[6871, 776, 6868])).
% 1.11/1.33 tff(6873,plain,
% 1.11/1.33 (((~![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)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(6874,plain,
% 1.11/1.33 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s80, c_n1) | (~node2(s80)))),
% 1.11/1.33 inference(quant_inst,[status(thm)],[])).
% 1.11/1.33 tff(6875,plain,
% 1.11/1.33 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s80, c_n1) | (~node2(s80))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[6874, 6873])).
% 1.11/1.33 tff(6876,plain,
% 1.11/1.33 (~node2(s80)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[6875, 787, 6800])).
% 1.11/1.33 tff(6877,plain,
% 1.11/1.33 (((~![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)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(6878,plain,
% 1.11/1.33 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s80, c_n1) | (~node3(s80)))),
% 1.11/1.33 inference(quant_inst,[status(thm)],[])).
% 1.11/1.33 tff(6879,plain,
% 1.11/1.33 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s80, c_n1) | (~node3(s80))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[6878, 6877])).
% 1.11/1.33 tff(6880,plain,
% 1.11/1.33 (~node3(s80)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[6879, 798, 6800])).
% 1.11/1.33 tff(6881,plain,
% 1.11/1.33 (((~![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)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(6882,plain,
% 1.11/1.33 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s80, c_n2) | (~node4(s80)))),
% 1.11/1.33 inference(quant_inst,[status(thm)],[])).
% 1.11/1.33 tff(6883,plain,
% 1.11/1.33 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s80, c_n2) | (~node4(s80))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[6882, 6881])).
% 1.11/1.33 tff(6884,plain,
% 1.11/1.33 (~node4(s80)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[6883, 388, 6820])).
% 1.11/1.33 tff(6885,plain,
% 1.11/1.33 (((~![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))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(6886,plain,
% 1.11/1.33 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s80, s81)) | node7(s80, s81))),
% 1.11/1.33 inference(quant_inst,[status(thm)],[])).
% 1.11/1.33 tff(6887,plain,
% 1.11/1.33 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s80, s81)) | node7(s80, s81)),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[6886, 6885])).
% 1.11/1.33 tff(6888,plain,
% 1.11/1.33 (node7(s80, s81)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[6887, 206, 6831])).
% 1.11/1.33 tff(6889,plain,
% 1.11/1.33 (((~![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)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(6890,plain,
% 1.11/1.33 ((~![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)))),
% 1.11/1.33 inference(quant_inst,[status(thm)],[])).
% 1.11/1.33 tff(6891,plain,
% 1.11/1.33 ((~![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))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[6890, 6889])).
% 1.11/1.33 tff(6892,plain,
% 1.11/1.33 (m_main_v_state1(s80, c_c1) | node1(s80) | node2(s80) | node3(s80) | node4(s80) | node5(s80) | node6(s80, s81)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[6891, 820, 6888])).
% 1.11/1.33 tff(6893,plain,
% 1.11/1.33 (node6(s80, s81)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[6892, 6884, 6808, 6880, 6876, 6872, 6855])).
% 1.11/1.33 tff(6894,plain,
% 1.11/1.33 (((~![V: $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)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(6895,plain,
% 1.11/1.33 (((~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)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(6896,plain,
% 1.11/1.33 (((~![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))))),
% 1.11/1.33 inference(monotonicity,[status(thm)],[6895])).
% 1.11/1.33 tff(6897,plain,
% 1.11/1.33 (((~![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)))),
% 1.11/1.33 inference(transitivity,[status(thm)],[6896, 6894])).
% 1.11/1.33 tff(6898,plain,
% 1.11/1.33 ((~![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)))),
% 1.11/1.33 inference(quant_inst,[status(thm)],[])).
% 1.11/1.33 tff(6899,plain,
% 1.11/1.33 ((~![V: $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))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[6898, 6897])).
% 1.11/1.33 tff(6900,plain,
% 1.11/1.33 (~m_main_v_state1(s81, c_n1)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[6899, 835, 6800, 6893])).
% 1.11/1.33 tff(6901,plain,
% 1.11/1.33 (((~![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)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(6902,plain,
% 1.11/1.33 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s81, c_n1) | (~node2(s81)))),
% 1.11/1.33 inference(quant_inst,[status(thm)],[])).
% 1.11/1.33 tff(6903,plain,
% 1.11/1.33 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s81, c_n1) | (~node2(s81))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[6902, 6901])).
% 1.11/1.33 tff(6904,plain,
% 1.11/1.33 (~node2(s81)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[6903, 787, 6900])).
% 1.11/1.33 tff(6905,plain,
% 1.11/1.33 (((~![V: $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)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(6906,plain,
% 1.11/1.33 (((~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)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(6907,plain,
% 1.11/1.33 (((~![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))))),
% 1.11/1.33 inference(monotonicity,[status(thm)],[6906])).
% 1.11/1.33 tff(6908,plain,
% 1.11/1.33 (((~![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)))),
% 1.17/1.33 inference(transitivity,[status(thm)],[6907, 6905])).
% 1.17/1.33 tff(6909,plain,
% 1.17/1.33 ((~![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))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(6910,plain,
% 1.17/1.33 ((~![V: $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))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[6909, 6908])).
% 1.17/1.33 tff(6911,plain,
% 1.17/1.33 (m_main_v_state1(s81, c_t1)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[6910, 856, 6796, 6893])).
% 1.17/1.33 tff(6912,plain,
% 1.17/1.33 (((~![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)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(6913,plain,
% 1.17/1.33 ((~![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)))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(6914,plain,
% 1.17/1.33 ((~![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))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[6913, 6912])).
% 1.17/1.33 tff(6915,plain,
% 1.17/1.33 (~m_main_v_state2(s81, c_t2)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[6914, 77, 6843])).
% 1.17/1.33 tff(6916,plain,
% 1.17/1.33 (((~![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)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(6917,plain,
% 1.17/1.33 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s81, c_t2) | (~node1(s81)))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(6918,plain,
% 1.17/1.33 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s81, c_t2) | (~node1(s81))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[6917, 6916])).
% 1.17/1.33 tff(6919,plain,
% 1.17/1.33 (~node1(s81)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[6918, 195, 6915])).
% 1.17/1.33 tff(6920,plain,
% 1.17/1.33 (succ(s81, s82) <=> succ(s81, s82)),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(6921,axiom,(succ(s81, s82)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound82')).
% 1.17/1.33 tff(6922,plain,
% 1.17/1.33 (succ(s81, s82)),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[6921, 6920])).
% 1.17/1.33 tff(6923,plain,
% 1.17/1.33 (((~![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))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(6924,plain,
% 1.17/1.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s81, s82)) | trans(s81, s82))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(6925,plain,
% 1.17/1.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s81, s82)) | trans(s81, s82)),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[6924, 6923])).
% 1.17/1.33 tff(6926,plain,
% 1.17/1.33 (trans(s81, s82)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[6925, 6922, 32])).
% 1.17/1.33 tff(6927,plain,
% 1.17/1.33 (((~![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))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(6928,plain,
% 1.17/1.33 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s81, s82)) | node7(s81, s82))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(6929,plain,
% 1.17/1.33 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s81, s82)) | node7(s81, s82)),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[6928, 6927])).
% 1.17/1.33 tff(6930,plain,
% 1.17/1.33 (node7(s81, s82)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[6929, 206, 6926])).
% 1.17/1.33 tff(6931,plain,
% 1.17/1.33 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(6932,plain,
% 1.17/1.33 (((~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)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(6933,plain,
% 1.17/1.33 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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))))),
% 1.17/1.33 inference(monotonicity,[status(thm)],[6932])).
% 1.17/1.33 tff(6934,plain,
% 1.17/1.33 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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)))),
% 1.17/1.33 inference(transitivity,[status(thm)],[6933, 6931])).
% 1.17/1.33 tff(6935,plain,
% 1.17/1.33 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(6936,plain,
% 1.17/1.33 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[6935, 6934])).
% 1.17/1.33 tff(6937,plain,
% 1.17/1.33 ((~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)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[6936, 892, 6930])).
% 1.17/1.33 tff(6938,plain,
% 1.17/1.33 (m_main_v_state1(s82, c_c1)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[6937, 6919, 6843, 6911, 6904, 6851])).
% 1.17/1.33 tff(6939,plain,
% 1.17/1.33 (((~![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)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(6940,plain,
% 1.17/1.33 ((~![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)))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(6941,plain,
% 1.17/1.33 ((~![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))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[6940, 6939])).
% 1.17/1.33 tff(6942,plain,
% 1.17/1.33 (~m_main_v_state1(s82, c_t1)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[6941, 539, 6938])).
% 1.17/1.33 tff(6943,plain,
% 1.17/1.33 (((~![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)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(6944,plain,
% 1.17/1.33 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s82, c_t1) | (~node5(s82)))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(6945,plain,
% 1.17/1.33 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s82, c_t1) | (~node5(s82))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[6944, 6943])).
% 1.17/1.33 tff(6946,plain,
% 1.17/1.33 (~node5(s82)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[6945, 550, 6942])).
% 1.17/1.33 tff(6947,plain,
% 1.17/1.33 (((~![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))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(6948,plain,
% 1.17/1.33 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s81, s82)) | node14(s81, s82))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(6949,plain,
% 1.17/1.33 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s81, s82)) | node14(s81, s82)),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[6948, 6947])).
% 1.17/1.33 tff(6950,plain,
% 1.17/1.33 (node14(s81, s82)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[6949, 46, 6926])).
% 1.17/1.33 tff(6951,plain,
% 1.17/1.33 (((~![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))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(6952,plain,
% 1.17/1.33 ((~![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))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(6953,plain,
% 1.17/1.33 ((~![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)),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[6952, 6951])).
% 1.17/1.33 tff(6954,plain,
% 1.17/1.33 ((~m_main_v_state1(s81, c_t1)) | (~m_main_v_state2(s81, c_n2)) | m_main_v_state2(s82, c_t2)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[6953, 922, 6950])).
% 1.17/1.33 tff(6955,plain,
% 1.17/1.33 (m_main_v_state2(s82, c_t2)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[6954, 6911, 6843])).
% 1.17/1.33 tff(6956,plain,
% 1.17/1.33 (((~![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)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(6957,plain,
% 1.17/1.33 ((~![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)))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(6958,plain,
% 1.17/1.33 ((~![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))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[6957, 6956])).
% 1.17/1.33 tff(6959,plain,
% 1.17/1.33 (~m_main_v_state2(s82, c_n2)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[6958, 77, 6955])).
% 1.17/1.33 tff(6960,plain,
% 1.17/1.33 (((~![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)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(6961,plain,
% 1.17/1.33 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s82, c_n2) | (~node4(s82)))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(6962,plain,
% 1.17/1.33 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s82, c_n2) | (~node4(s82))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[6961, 6960])).
% 1.17/1.33 tff(6963,plain,
% 1.17/1.33 (~node4(s82)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[6962, 388, 6959])).
% 1.17/1.33 tff(6964,plain,
% 1.17/1.33 (((~![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)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(6965,plain,
% 1.17/1.33 ((~![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)))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(6966,plain,
% 1.17/1.33 ((~![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))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[6965, 6964])).
% 1.17/1.33 tff(6967,plain,
% 1.17/1.33 (~m_main_v_state2(s82, c_c2)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[6966, 260, 6955])).
% 1.17/1.33 tff(6968,plain,
% 1.17/1.33 (((~![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)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(6969,plain,
% 1.17/1.33 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s82, c_c2) | (~node3(s82)))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(6970,plain,
% 1.17/1.33 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s82, c_c2) | (~node3(s82))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[6969, 6968])).
% 1.17/1.33 tff(6971,plain,
% 1.17/1.33 (~node3(s82)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[6970, 399, 6967])).
% 1.17/1.33 tff(6972,plain,
% 1.17/1.33 (((~![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)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(6973,plain,
% 1.17/1.33 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s82, c_n2) | (~node2(s82)))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(6974,plain,
% 1.17/1.33 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s82, c_n2) | (~node2(s82))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[6973, 6972])).
% 1.17/1.33 tff(6975,plain,
% 1.17/1.33 (~node2(s82)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[6974, 410, 6959])).
% 1.17/1.33 tff(6976,plain,
% 1.17/1.33 (((~![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)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(6977,plain,
% 1.17/1.33 ((~![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)))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(6978,plain,
% 1.17/1.33 ((~![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))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[6977, 6976])).
% 1.17/1.34 tff(6979,plain,
% 1.17/1.34 (~m_main_v_state1(s82, c_n1)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[6978, 454, 6938])).
% 1.17/1.34 tff(6980,plain,
% 1.17/1.34 (((~![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)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(6981,plain,
% 1.17/1.34 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s82, c_n1) | (~node1(s82)))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(6982,plain,
% 1.17/1.34 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s82, c_n1) | (~node1(s82))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[6981, 6980])).
% 1.17/1.34 tff(6983,plain,
% 1.17/1.34 (~node1(s82)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[6982, 421, 6979])).
% 1.17/1.34 tff(6984,plain,
% 1.17/1.34 (succ(s82, s83) <=> succ(s82, s83)),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(6985,axiom,(succ(s82, s83)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound83')).
% 1.17/1.34 tff(6986,plain,
% 1.17/1.34 (succ(s82, s83)),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[6985, 6984])).
% 1.17/1.34 tff(6987,plain,
% 1.17/1.34 (((~![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))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(6988,plain,
% 1.17/1.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s82, s83)) | trans(s82, s83))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(6989,plain,
% 1.17/1.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s82, s83)) | trans(s82, s83)),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[6988, 6987])).
% 1.17/1.34 tff(6990,plain,
% 1.17/1.34 (trans(s82, s83)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[6989, 6986, 32])).
% 1.17/1.34 tff(6991,plain,
% 1.17/1.34 (((~![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))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(6992,plain,
% 1.17/1.34 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s82, s83)) | node7(s82, s83))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(6993,plain,
% 1.17/1.34 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s82, s83)) | node7(s82, s83)),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[6992, 6991])).
% 1.17/1.34 tff(6994,plain,
% 1.17/1.34 (node7(s82, s83)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[6993, 206, 6990])).
% 1.17/1.34 tff(6995,plain,
% 1.17/1.34 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(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)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(6996,plain,
% 1.17/1.34 (((~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)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(6997,plain,
% 1.17/1.34 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(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))))),
% 1.17/1.34 inference(monotonicity,[status(thm)],[6996])).
% 1.17/1.34 tff(6998,plain,
% 1.17/1.34 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(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)))),
% 1.17/1.34 inference(transitivity,[status(thm)],[6997, 6995])).
% 1.17/1.34 tff(6999,plain,
% 1.17/1.34 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s82, c_c1)) | node1(s82) | node2(s82) | node3(s82) | node4(s82) | node5(s82) | (~node7(s82, s83)) | m_main_v_state1(s83, c_n1))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(7000,plain,
% 1.17/1.34 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s83, c_n1) | (~m_main_v_state1(s82, c_c1)) | node1(s82) | node2(s82) | node3(s82) | node4(s82) | node5(s82) | (~node7(s82, s83))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[6999, 6998])).
% 1.17/1.34 tff(7001,plain,
% 1.17/1.34 (m_main_v_state1(s83, c_n1) | (~m_main_v_state1(s82, c_c1)) | node1(s82) | node2(s82) | node3(s82) | node4(s82) | node5(s82)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[7000, 584, 6994])).
% 1.17/1.34 tff(7002,plain,
% 1.17/1.34 (m_main_v_state1(s83, c_n1)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[7001, 6983, 6938, 6975, 6971, 6963, 6946])).
% 1.17/1.34 tff(7003,plain,
% 1.17/1.34 (((~![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)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(7004,plain,
% 1.17/1.34 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s81, c_t2) | (~node15(s81)))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(7005,plain,
% 1.17/1.34 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s81, c_t2) | (~node15(s81))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[7004, 7003])).
% 1.17/1.34 tff(7006,plain,
% 1.17/1.34 (~node15(s81)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[7005, 103, 6915])).
% 1.17/1.34 tff(7007,plain,
% 1.17/1.34 (((~![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))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(7008,plain,
% 1.17/1.34 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s81, s82)) | node18(s81, s82))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(7009,plain,
% 1.17/1.34 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s81, s82)) | node18(s81, s82)),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[7008, 7007])).
% 1.17/1.34 tff(7010,plain,
% 1.17/1.34 (node18(s81, s82)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[7009, 125, 6926])).
% 1.17/1.34 tff(7011,plain,
% 1.17/1.34 (((~![Y: $i, X: $i] : ((~m_main_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))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(7012,plain,
% 1.17/1.34 (((~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))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(7013,plain,
% 1.17/1.34 (((~![Y: $i, X: $i] : ((~m_main_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)))),
% 1.17/1.34 inference(monotonicity,[status(thm)],[7012])).
% 1.17/1.34 tff(7014,plain,
% 1.17/1.34 (((~![Y: $i, X: $i] : ((~m_main_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))),
% 1.17/1.34 inference(transitivity,[status(thm)],[7013, 7011])).
% 1.17/1.34 tff(7015,plain,
% 1.17/1.34 ((~![Y: $i, X: $i] : ((~m_main_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))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(7016,plain,
% 1.17/1.34 ((~![Y: $i, X: $i] : ((~m_main_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)),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[7015, 7014])).
% 1.17/1.34 tff(7017,plain,
% 1.17/1.34 (node15(s81) | (~m_main_v_state1(s81, c_t1)) | (~m_main_v_state2(s81, c_n2)) | m_main_v_turn(s82, c_1)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[7016, 992, 7010])).
% 1.17/1.34 tff(7018,plain,
% 1.17/1.34 (m_main_v_turn(s82, c_1)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[7017, 7006, 6843, 6911])).
% 1.17/1.34 tff(7019,plain,
% 1.17/1.34 (((~![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)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(7020,plain,
% 1.17/1.34 ((~![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)))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(7021,plain,
% 1.17/1.34 ((~![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))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[7020, 7019])).
% 1.17/1.34 tff(7022,plain,
% 1.17/1.34 (~m_main_v_turn(s82, c_2)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[7021, 156, 7018])).
% 1.17/1.34 tff(7023,plain,
% 1.17/1.34 (((~![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)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(7024,plain,
% 1.17/1.34 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s82, c_2) | (~node12(s82)))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(7025,plain,
% 1.17/1.34 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s82, c_2) | (~node12(s82))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[7024, 7023])).
% 1.17/1.34 tff(7026,plain,
% 1.17/1.34 (~node12(s82)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[7025, 184, 7022])).
% 1.17/1.34 tff(7027,plain,
% 1.17/1.34 (((~![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)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(7028,plain,
% 1.17/1.34 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s82, c_n2) | (~node8(s82)))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(7029,plain,
% 1.17/1.34 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s82, c_n2) | (~node8(s82))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[7028, 7027])).
% 1.17/1.34 tff(7030,plain,
% 1.17/1.34 (~node8(s82)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[7029, 271, 6959])).
% 1.17/1.34 tff(7031,plain,
% 1.17/1.34 (((~![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)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(7032,plain,
% 1.17/1.34 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s82, c_n2) | (~node9(s82)))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(7033,plain,
% 1.17/1.34 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s82, c_n2) | (~node9(s82))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[7032, 7031])).
% 1.17/1.34 tff(7034,plain,
% 1.17/1.34 (~node9(s82)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[7033, 88, 6959])).
% 1.17/1.34 tff(7035,plain,
% 1.17/1.34 (((~![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)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(7036,plain,
% 1.17/1.34 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s82, c_n2) | (~node10(s82)))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(7037,plain,
% 1.17/1.34 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s82, c_n2) | (~node10(s82))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[7036, 7035])).
% 1.17/1.34 tff(7038,plain,
% 1.17/1.34 (~node10(s82)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[7037, 249, 6959])).
% 1.17/1.34 tff(7039,plain,
% 1.17/1.34 (((~![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)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(7040,plain,
% 1.17/1.34 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s82, c_n1) | (~node11(s82)))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(7041,plain,
% 1.17/1.34 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s82, c_n1) | (~node11(s82))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[7040, 7039])).
% 1.17/1.34 tff(7042,plain,
% 1.17/1.34 (~node11(s82)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[7041, 238, 6979])).
% 1.17/1.34 tff(7043,plain,
% 1.17/1.34 (((~![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))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(7044,plain,
% 1.17/1.34 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s82, s83)) | node14(s82, s83))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(7045,plain,
% 1.17/1.34 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s82, s83)) | node14(s82, s83)),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[7044, 7043])).
% 1.17/1.34 tff(7046,plain,
% 1.17/1.34 (node14(s82, s83)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[7045, 46, 6990])).
% 1.17/1.34 tff(7047,plain,
% 1.17/1.34 (((~![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)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(7048,plain,
% 1.17/1.34 ((~![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)))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(7049,plain,
% 1.17/1.34 ((~![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))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[7048, 7047])).
% 1.17/1.34 tff(7050,plain,
% 1.17/1.34 (m_main_v_state2(s82, c_c2) | node9(s82) | node8(s82) | node10(s82) | node11(s82) | node12(s82) | node13(s82, s83)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[7049, 296, 7046])).
% 1.17/1.34 tff(7051,plain,
% 1.17/1.34 (node13(s82, s83)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[7050, 7042, 6967, 7038, 7034, 7030, 7026])).
% 1.17/1.34 tff(7052,plain,
% 1.17/1.34 (((~![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(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)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(7053,plain,
% 1.17/1.34 (((~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)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(7054,plain,
% 1.17/1.34 (((~![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))))),
% 1.17/1.34 inference(monotonicity,[status(thm)],[7053])).
% 1.17/1.34 tff(7055,plain,
% 1.17/1.34 (((~![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)))),
% 1.17/1.34 inference(transitivity,[status(thm)],[7054, 7052])).
% 1.17/1.34 tff(7056,plain,
% 1.17/1.34 ((~![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))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(7057,plain,
% 1.17/1.34 ((~![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(s82, c_t2)) | m_main_v_state2(s83, c_t2) | (~node13(s82, s83))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[7056, 7055])).
% 1.17/1.34 tff(7058,plain,
% 1.17/1.34 (m_main_v_state2(s83, c_t2)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[7057, 518, 6955, 7051])).
% 1.17/1.34 tff(7059,plain,
% 1.17/1.34 (succ(s83, s84) <=> succ(s83, s84)),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(7060,axiom,(succ(s83, s84)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound84')).
% 1.17/1.34 tff(7061,plain,
% 1.17/1.34 (succ(s83, s84)),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[7060, 7059])).
% 1.17/1.34 tff(7062,plain,
% 1.17/1.34 (((~![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))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(7063,plain,
% 1.17/1.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s83, s84)) | trans(s83, s84))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(7064,plain,
% 1.17/1.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s83, s84)) | trans(s83, s84)),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[7063, 7062])).
% 1.17/1.34 tff(7065,plain,
% 1.17/1.34 (trans(s83, s84)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[7064, 7061, 32])).
% 1.17/1.34 tff(7066,plain,
% 1.17/1.34 (((~![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))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(7067,plain,
% 1.17/1.34 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s83, s84)) | node7(s83, s84))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(7068,plain,
% 1.17/1.34 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s83, s84)) | node7(s83, s84)),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[7067, 7066])).
% 1.17/1.34 tff(7069,plain,
% 1.17/1.34 (node7(s83, s84)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[7068, 206, 7065])).
% 1.17/1.34 tff(7070,plain,
% 1.17/1.34 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(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))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(7071,plain,
% 1.17/1.34 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | ((~m_main_v_state1(s83, c_n1)) | (~m_main_v_state2(s83, c_t2)) | (~node7(s83, s84)) | m_main_v_state1(s84, c_t1))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(7072,plain,
% 1.17/1.34 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node7(X, Y)) | m_main_v_state1(Y, c_t1))) | (~m_main_v_state1(s83, c_n1)) | (~m_main_v_state2(s83, c_t2)) | (~node7(s83, s84)) | m_main_v_state1(s84, c_t1)),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[7071, 7070])).
% 1.17/1.34 tff(7073,plain,
% 1.17/1.34 ((~m_main_v_state1(s83, c_n1)) | (~m_main_v_state2(s83, c_t2)) | m_main_v_state1(s84, c_t1)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[7072, 651, 7069])).
% 1.17/1.34 tff(7074,plain,
% 1.17/1.34 (m_main_v_state1(s84, c_t1)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[7073, 7058, 7002])).
% 1.17/1.34 tff(7075,plain,
% 1.17/1.34 (((~![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)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(7076,plain,
% 1.17/1.34 ((~![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)))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(7077,plain,
% 1.17/1.34 ((~![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))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[7076, 7075])).
% 1.17/1.34 tff(7078,plain,
% 1.17/1.34 (~m_main_v_state1(s84, c_n1)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[7077, 10, 7074])).
% 1.17/1.34 tff(7079,plain,
% 1.17/1.34 (((~![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)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(7080,plain,
% 1.17/1.34 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s84, c_n1) | (~node1(s84)))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(7081,plain,
% 1.17/1.34 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s84, c_n1) | (~node1(s84))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[7080, 7079])).
% 1.17/1.34 tff(7082,plain,
% 1.17/1.34 (~node1(s84)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[7081, 421, 7078])).
% 1.17/1.34 tff(7083,plain,
% 1.17/1.34 (((~![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))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(7084,plain,
% 1.17/1.34 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s83, s84)) | node18(s83, s84))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(7085,plain,
% 1.17/1.34 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s83, s84)) | node18(s83, s84)),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[7084, 7083])).
% 1.17/1.34 tff(7086,plain,
% 1.17/1.34 (node18(s83, s84)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[7085, 125, 7065])).
% 1.17/1.34 tff(7087,plain,
% 1.17/1.34 (((~![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))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7088,plain,
% 1.17/1.35 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | ((~m_main_v_state1(s83, c_n1)) | (~m_main_v_state2(s83, c_t2)) | (~node18(s83, s84)) | m_main_v_turn(s84, c_2))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(7089,plain,
% 1.17/1.35 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s83, c_n1)) | (~m_main_v_state2(s83, c_t2)) | (~node18(s83, s84)) | m_main_v_turn(s84, c_2)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7088, 7087])).
% 1.17/1.35 tff(7090,plain,
% 1.17/1.35 ((~m_main_v_state1(s83, c_n1)) | (~m_main_v_state2(s83, c_t2)) | m_main_v_turn(s84, c_2)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7089, 760, 7086])).
% 1.17/1.35 tff(7091,plain,
% 1.17/1.35 (m_main_v_turn(s84, c_2)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7090, 7058, 7002])).
% 1.17/1.35 tff(7092,plain,
% 1.17/1.35 (((~![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)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7093,plain,
% 1.17/1.35 ((~![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)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(7094,plain,
% 1.17/1.35 ((~![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))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7093, 7092])).
% 1.17/1.35 tff(7095,plain,
% 1.17/1.35 (~m_main_v_turn(s84, c_1)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7094, 156, 7091])).
% 1.17/1.35 tff(7096,plain,
% 1.17/1.35 (((~![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)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7097,plain,
% 1.17/1.35 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s84, c_1) | (~node5(s84)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(7098,plain,
% 1.17/1.35 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s84, c_1) | (~node5(s84))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7097, 7096])).
% 1.17/1.35 tff(7099,plain,
% 1.17/1.35 (~node5(s84)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7098, 776, 7095])).
% 1.17/1.35 tff(7100,plain,
% 1.17/1.35 (((~![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)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7101,plain,
% 1.17/1.35 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s84, c_n1) | (~node2(s84)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(7102,plain,
% 1.17/1.35 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s84, c_n1) | (~node2(s84))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7101, 7100])).
% 1.17/1.35 tff(7103,plain,
% 1.17/1.35 (~node2(s84)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7102, 787, 7078])).
% 1.17/1.35 tff(7104,plain,
% 1.17/1.35 (((~![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)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7105,plain,
% 1.17/1.35 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s84, c_n1) | (~node3(s84)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(7106,plain,
% 1.17/1.35 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s84, c_n1) | (~node3(s84))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7105, 7104])).
% 1.17/1.35 tff(7107,plain,
% 1.17/1.35 (~node3(s84)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7106, 798, 7078])).
% 1.17/1.35 tff(7108,plain,
% 1.17/1.35 (((~![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)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7109,plain,
% 1.17/1.35 ((~![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)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(7110,plain,
% 1.17/1.35 ((~![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))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7109, 7108])).
% 1.17/1.35 tff(7111,plain,
% 1.17/1.35 (~m_main_v_state1(s84, c_c1)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7110, 539, 7074])).
% 1.17/1.35 tff(7112,plain,
% 1.17/1.35 (((~![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(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)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7113,plain,
% 1.17/1.35 (((~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)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7114,plain,
% 1.17/1.35 (((~![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))))),
% 1.17/1.35 inference(monotonicity,[status(thm)],[7113])).
% 1.17/1.35 tff(7115,plain,
% 1.17/1.35 (((~![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)))),
% 1.17/1.35 inference(transitivity,[status(thm)],[7114, 7112])).
% 1.17/1.35 tff(7116,plain,
% 1.17/1.35 ((~![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)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(7117,plain,
% 1.17/1.35 ((~![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(s82, c_n2) | (~m_main_v_state2(s83, c_n2)) | (~node13(s82, s83))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7116, 7115])).
% 1.17/1.35 tff(7118,plain,
% 1.17/1.35 (~m_main_v_state2(s83, c_n2)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7117, 311, 6959, 7051])).
% 1.17/1.35 tff(7119,plain,
% 1.17/1.35 (((~![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)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7120,plain,
% 1.17/1.35 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s83, c_n2) | (~node9(s83)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(7121,plain,
% 1.17/1.35 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s83, c_n2) | (~node9(s83))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7120, 7119])).
% 1.17/1.35 tff(7122,plain,
% 1.17/1.35 (~node9(s83)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7121, 88, 7118])).
% 1.17/1.35 tff(7123,plain,
% 1.17/1.35 (((~![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)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7124,plain,
% 1.17/1.35 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s83, c_n2) | (~node10(s83)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(7125,plain,
% 1.17/1.35 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s83, c_n2) | (~node10(s83))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7124, 7123])).
% 1.17/1.35 tff(7126,plain,
% 1.17/1.35 (~node10(s83)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7125, 249, 7118])).
% 1.17/1.35 tff(7127,plain,
% 1.17/1.35 (((~![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)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7128,plain,
% 1.17/1.35 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s83, c_n2) | (~node8(s83)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(7129,plain,
% 1.17/1.35 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s83, c_n2) | (~node8(s83))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7128, 7127])).
% 1.17/1.35 tff(7130,plain,
% 1.17/1.35 (~node8(s83)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7129, 271, 7118])).
% 1.17/1.35 tff(7131,plain,
% 1.17/1.35 (((~![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))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7132,plain,
% 1.17/1.35 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s83, s84)) | node14(s83, s84))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(7133,plain,
% 1.17/1.35 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s83, s84)) | node14(s83, s84)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7132, 7131])).
% 1.17/1.35 tff(7134,plain,
% 1.17/1.35 (node14(s83, s84)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7133, 46, 7065])).
% 1.17/1.35 tff(7135,plain,
% 1.17/1.35 (((~![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))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7136,plain,
% 1.17/1.35 ((~![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))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(7137,plain,
% 1.17/1.35 ((~![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)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7136, 7135])).
% 1.17/1.35 tff(7138,plain,
% 1.17/1.35 ((~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)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7137, 617, 7134])).
% 1.17/1.35 tff(7139,plain,
% 1.17/1.35 (m_main_v_state2(s84, c_c2)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7138, 7130, 7002, 7058, 7126, 7122])).
% 1.17/1.35 tff(7140,plain,
% 1.17/1.35 (((~![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)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7141,plain,
% 1.17/1.35 ((~![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)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(7142,plain,
% 1.17/1.35 ((~![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))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7141, 7140])).
% 1.17/1.35 tff(7143,plain,
% 1.17/1.35 (~m_main_v_state2(s84, c_n2)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7142, 697, 7139])).
% 1.17/1.35 tff(7144,plain,
% 1.17/1.35 (((~![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)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7145,plain,
% 1.17/1.35 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s84, c_n2) | (~node4(s84)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(7146,plain,
% 1.17/1.35 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s84, c_n2) | (~node4(s84))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7145, 7144])).
% 1.17/1.35 tff(7147,plain,
% 1.17/1.35 (~node4(s84)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7146, 388, 7143])).
% 1.17/1.35 tff(7148,plain,
% 1.17/1.35 (succ(s84, s85) <=> succ(s84, s85)),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7149,axiom,(succ(s84, s85)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound85')).
% 1.17/1.35 tff(7150,plain,
% 1.17/1.35 (succ(s84, s85)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7149, 7148])).
% 1.17/1.35 tff(7151,plain,
% 1.17/1.35 (((~![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))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7152,plain,
% 1.17/1.35 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s84, s85)) | trans(s84, s85))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(7153,plain,
% 1.17/1.35 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s84, s85)) | trans(s84, s85)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7152, 7151])).
% 1.17/1.35 tff(7154,plain,
% 1.17/1.35 (trans(s84, s85)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7153, 7150, 32])).
% 1.17/1.35 tff(7155,plain,
% 1.17/1.35 (((~![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))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7156,plain,
% 1.17/1.35 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s84, s85)) | node7(s84, s85))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(7157,plain,
% 1.17/1.35 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s84, s85)) | node7(s84, s85)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7156, 7155])).
% 1.17/1.35 tff(7158,plain,
% 1.17/1.35 (node7(s84, s85)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7157, 206, 7154])).
% 1.17/1.35 tff(7159,plain,
% 1.17/1.35 (((~![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)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7160,plain,
% 1.17/1.35 ((~![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)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(7161,plain,
% 1.17/1.35 ((~![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))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7160, 7159])).
% 1.17/1.35 tff(7162,plain,
% 1.17/1.35 (m_main_v_state1(s84, c_c1) | node1(s84) | node2(s84) | node3(s84) | node4(s84) | node5(s84) | node6(s84, s85)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7161, 820, 7158])).
% 1.17/1.35 tff(7163,plain,
% 1.17/1.35 (node6(s84, s85)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7162, 7147, 7111, 7107, 7103, 7099, 7082])).
% 1.17/1.35 tff(7164,plain,
% 1.17/1.35 (((~![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(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)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7165,plain,
% 1.17/1.35 (((~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)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7166,plain,
% 1.17/1.35 (((~![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))))),
% 1.17/1.35 inference(monotonicity,[status(thm)],[7165])).
% 1.17/1.35 tff(7167,plain,
% 1.17/1.35 (((~![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)))),
% 1.17/1.35 inference(transitivity,[status(thm)],[7166, 7164])).
% 1.17/1.35 tff(7168,plain,
% 1.17/1.35 ((~![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))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(7169,plain,
% 1.17/1.35 ((~![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(s84, c_t1)) | m_main_v_state1(s85, c_t1) | (~node6(s84, s85))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7168, 7167])).
% 1.17/1.35 tff(7170,plain,
% 1.17/1.35 (m_main_v_state1(s85, c_t1)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7169, 856, 7074, 7163])).
% 1.17/1.35 tff(7171,plain,
% 1.17/1.35 (((~![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)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7172,plain,
% 1.17/1.35 ((~![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)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(7173,plain,
% 1.17/1.35 ((~![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))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7172, 7171])).
% 1.17/1.35 tff(7174,plain,
% 1.17/1.35 (~m_main_v_state2(s84, c_t2)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7173, 260, 7139])).
% 1.17/1.35 tff(7175,plain,
% 1.17/1.35 (((~![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)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7176,plain,
% 1.17/1.35 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s84, c_t2) | (~node12(s84)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(7177,plain,
% 1.17/1.35 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s84, c_t2) | (~node12(s84))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7176, 7175])).
% 1.17/1.35 tff(7178,plain,
% 1.17/1.35 (~node12(s84)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7177, 633, 7174])).
% 1.17/1.35 tff(7179,plain,
% 1.17/1.35 (((~![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)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7180,plain,
% 1.17/1.35 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s84, c_n1) | (~node11(s84)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(7181,plain,
% 1.17/1.35 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s84, c_n1) | (~node11(s84))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7180, 7179])).
% 1.17/1.35 tff(7182,plain,
% 1.17/1.35 (~node11(s84)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7181, 238, 7078])).
% 1.17/1.35 tff(7183,plain,
% 1.17/1.35 (((~![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)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7184,plain,
% 1.17/1.35 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s84, c_c1) | (~node10(s84)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(7185,plain,
% 1.17/1.35 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s84, c_c1) | (~node10(s84))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7184, 7183])).
% 1.17/1.35 tff(7186,plain,
% 1.17/1.35 (~node10(s84)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7185, 675, 7111])).
% 1.17/1.35 tff(7187,plain,
% 1.17/1.35 (((~![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)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7188,plain,
% 1.17/1.35 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s84, c_n1) | (~node9(s84)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(7189,plain,
% 1.17/1.35 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s84, c_n1) | (~node9(s84))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7188, 7187])).
% 1.17/1.35 tff(7190,plain,
% 1.17/1.35 (~node9(s84)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7189, 686, 7078])).
% 1.17/1.35 tff(7191,plain,
% 1.17/1.35 (((~![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)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7192,plain,
% 1.17/1.35 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s84, c_n2) | (~node8(s84)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(7193,plain,
% 1.17/1.35 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s84, c_n2) | (~node8(s84))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7192, 7191])).
% 1.17/1.35 tff(7194,plain,
% 1.17/1.35 (~node8(s84)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7193, 271, 7143])).
% 1.17/1.35 tff(7195,plain,
% 1.17/1.35 (((~![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))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7196,plain,
% 1.17/1.35 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s84, s85)) | node14(s84, s85))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(7197,plain,
% 1.17/1.35 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s84, s85)) | node14(s84, s85)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7196, 7195])).
% 1.17/1.35 tff(7198,plain,
% 1.17/1.35 (node14(s84, s85)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7197, 46, 7154])).
% 1.17/1.35 tff(7199,plain,
% 1.17/1.35 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | (m_main_v_state2(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)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7200,plain,
% 1.17/1.35 (((~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)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7201,plain,
% 1.17/1.35 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(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))))),
% 1.17/1.35 inference(monotonicity,[status(thm)],[7200])).
% 1.17/1.35 tff(7202,plain,
% 1.17/1.35 (((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(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)))),
% 1.17/1.35 inference(transitivity,[status(thm)],[7201, 7199])).
% 1.17/1.35 tff(7203,plain,
% 1.17/1.35 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | ((~m_main_v_state2(s84, c_c2)) | node9(s84) | node8(s84) | node10(s84) | node11(s84) | node12(s84) | (~node14(s84, s85)) | m_main_v_state2(s85, c_n2))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(7204,plain,
% 1.17/1.35 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s85, c_n2) | node9(s84) | node8(s84) | node10(s84) | node11(s84) | node12(s84) | (~node14(s84, s85)) | (~m_main_v_state2(s84, c_c2))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7203, 7202])).
% 1.17/1.35 tff(7205,plain,
% 1.17/1.35 (m_main_v_state2(s85, c_n2) | node9(s84) | node8(s84) | node10(s84) | node11(s84) | node12(s84) | (~m_main_v_state2(s84, c_c2))),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7204, 726, 7198])).
% 1.17/1.35 tff(7206,plain,
% 1.17/1.35 (m_main_v_state2(s85, c_n2)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7205, 7194, 7139, 7190, 7186, 7182, 7178])).
% 1.17/1.35 tff(7207,plain,
% 1.17/1.35 (((~![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)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7208,plain,
% 1.17/1.35 ((~![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)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(7209,plain,
% 1.17/1.35 ((~![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))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7208, 7207])).
% 1.17/1.35 tff(7210,plain,
% 1.17/1.35 (~m_main_v_state2(s85, c_t2)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7209, 77, 7206])).
% 1.17/1.35 tff(7211,plain,
% 1.17/1.35 (((~![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)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7212,plain,
% 1.17/1.35 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s85, c_t2) | (~node15(s85)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(7213,plain,
% 1.17/1.35 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s85, c_t2) | (~node15(s85))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7212, 7211])).
% 1.17/1.35 tff(7214,plain,
% 1.17/1.35 (~node15(s85)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7213, 103, 7210])).
% 1.17/1.35 tff(7215,plain,
% 1.17/1.35 (succ(s85, s86) <=> succ(s85, s86)),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7216,axiom,(succ(s85, s86)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound86')).
% 1.17/1.35 tff(7217,plain,
% 1.17/1.35 (succ(s85, s86)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7216, 7215])).
% 1.17/1.35 tff(7218,plain,
% 1.17/1.35 (((~![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))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7219,plain,
% 1.17/1.35 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s85, s86)) | trans(s85, s86))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(7220,plain,
% 1.17/1.35 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s85, s86)) | trans(s85, s86)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7219, 7218])).
% 1.17/1.35 tff(7221,plain,
% 1.17/1.35 (trans(s85, s86)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7220, 7217, 32])).
% 1.17/1.35 tff(7222,plain,
% 1.17/1.35 (((~![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))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7223,plain,
% 1.17/1.35 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s85, s86)) | node18(s85, s86))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(7224,plain,
% 1.17/1.35 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s85, s86)) | node18(s85, s86)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[7223, 7222])).
% 1.17/1.35 tff(7225,plain,
% 1.17/1.35 (node18(s85, s86)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[7224, 125, 7221])).
% 1.17/1.35 tff(7226,plain,
% 1.17/1.35 (((~![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(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))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(7227,plain,
% 1.17/1.35 (((~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))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(7228,plain,
% 1.17/1.36 (((~![Y: $i, X: $i] : ((~m_main_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)))),
% 1.17/1.36 inference(monotonicity,[status(thm)],[7227])).
% 1.17/1.36 tff(7229,plain,
% 1.17/1.36 (((~![Y: $i, X: $i] : ((~m_main_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))),
% 1.17/1.36 inference(transitivity,[status(thm)],[7228, 7226])).
% 1.17/1.36 tff(7230,plain,
% 1.17/1.36 ((~![Y: $i, X: $i] : ((~m_main_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))),
% 1.17/1.36 inference(quant_inst,[status(thm)],[])).
% 1.17/1.36 tff(7231,plain,
% 1.17/1.36 ((~![Y: $i, X: $i] : ((~m_main_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)),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[7230, 7229])).
% 1.17/1.36 tff(7232,plain,
% 1.17/1.36 (node15(s85) | (~m_main_v_state1(s85, c_t1)) | (~m_main_v_state2(s85, c_n2)) | m_main_v_turn(s86, c_1)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[7231, 992, 7225])).
% 1.17/1.36 tff(7233,plain,
% 1.17/1.36 (m_main_v_turn(s86, c_1)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[7232, 7214, 7206, 7170])).
% 1.17/1.36 tff(7234,plain,
% 1.17/1.36 (((~![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)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(7235,plain,
% 1.17/1.36 ((~![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)))),
% 1.17/1.36 inference(quant_inst,[status(thm)],[])).
% 1.17/1.36 tff(7236,plain,
% 1.17/1.36 ((~![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))),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[7235, 7234])).
% 1.17/1.36 tff(7237,plain,
% 1.17/1.36 (~m_main_v_turn(s86, c_2)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[7236, 156, 7233])).
% 1.17/1.36 tff(7238,plain,
% 1.17/1.36 (((~![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)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(7239,plain,
% 1.17/1.36 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s86, c_2) | (~node12(s86)))),
% 1.17/1.36 inference(quant_inst,[status(thm)],[])).
% 1.17/1.36 tff(7240,plain,
% 1.17/1.36 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s86, c_2) | (~node12(s86))),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[7239, 7238])).
% 1.17/1.36 tff(7241,plain,
% 1.17/1.36 (~node12(s86)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[7240, 184, 7237])).
% 1.17/1.36 tff(7242,plain,
% 1.17/1.36 (((~![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))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(7243,plain,
% 1.17/1.36 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s85, s86)) | node14(s85, s86))),
% 1.17/1.36 inference(quant_inst,[status(thm)],[])).
% 1.17/1.36 tff(7244,plain,
% 1.17/1.36 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s85, s86)) | node14(s85, s86)),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[7243, 7242])).
% 1.17/1.36 tff(7245,plain,
% 1.17/1.36 (node14(s85, s86)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[7244, 46, 7221])).
% 1.17/1.36 tff(7246,plain,
% 1.17/1.36 (((~![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))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(7247,plain,
% 1.17/1.36 ((~![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))),
% 1.17/1.36 inference(quant_inst,[status(thm)],[])).
% 1.17/1.36 tff(7248,plain,
% 1.17/1.36 ((~![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)),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[7247, 7246])).
% 1.17/1.36 tff(7249,plain,
% 1.17/1.36 ((~m_main_v_state1(s85, c_t1)) | (~m_main_v_state2(s85, c_n2)) | m_main_v_state2(s86, c_t2)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[7248, 922, 7245])).
% 1.17/1.36 tff(7250,plain,
% 1.17/1.36 (m_main_v_state2(s86, c_t2)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[7249, 7170, 7206])).
% 1.17/1.36 tff(7251,plain,
% 1.17/1.36 (((~![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)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(7252,plain,
% 1.17/1.36 ((~![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)))),
% 1.17/1.36 inference(quant_inst,[status(thm)],[])).
% 1.17/1.36 tff(7253,plain,
% 1.17/1.36 ((~![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))),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[7252, 7251])).
% 1.17/1.36 tff(7254,plain,
% 1.17/1.36 (~m_main_v_state2(s86, c_n2)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[7253, 77, 7250])).
% 1.17/1.36 tff(7255,plain,
% 1.17/1.36 (((~![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)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(7256,plain,
% 1.17/1.36 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s86, c_n2) | (~node8(s86)))),
% 1.17/1.36 inference(quant_inst,[status(thm)],[])).
% 1.17/1.36 tff(7257,plain,
% 1.17/1.36 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s86, c_n2) | (~node8(s86))),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[7256, 7255])).
% 1.17/1.36 tff(7258,plain,
% 1.17/1.36 (~node8(s86)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[7257, 271, 7254])).
% 1.17/1.36 tff(7259,plain,
% 1.17/1.36 (((~![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)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(7260,plain,
% 1.17/1.36 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s86, c_n2) | (~node9(s86)))),
% 1.17/1.36 inference(quant_inst,[status(thm)],[])).
% 1.17/1.36 tff(7261,plain,
% 1.17/1.36 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s86, c_n2) | (~node9(s86))),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[7260, 7259])).
% 1.17/1.36 tff(7262,plain,
% 1.17/1.36 (~node9(s86)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[7261, 88, 7254])).
% 1.17/1.36 tff(7263,plain,
% 1.17/1.36 (((~![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)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(7264,plain,
% 1.17/1.36 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s86, c_n2) | (~node10(s86)))),
% 1.17/1.36 inference(quant_inst,[status(thm)],[])).
% 1.17/1.36 tff(7265,plain,
% 1.17/1.36 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s86, c_n2) | (~node10(s86))),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[7264, 7263])).
% 1.17/1.36 tff(7266,plain,
% 1.17/1.36 (~node10(s86)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[7265, 249, 7254])).
% 1.17/1.36 tff(7267,plain,
% 1.17/1.36 (((~![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)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(7268,plain,
% 1.17/1.36 ((~![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)))),
% 1.17/1.36 inference(quant_inst,[status(thm)],[])).
% 1.17/1.36 tff(7269,plain,
% 1.17/1.36 ((~![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))),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[7268, 7267])).
% 1.17/1.36 tff(7270,plain,
% 1.17/1.36 (~m_main_v_state2(s86, c_c2)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[7269, 260, 7250])).
% 1.17/1.36 tff(7271,plain,
% 1.17/1.36 (((~![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)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(7272,plain,
% 1.17/1.36 ((~![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)))),
% 1.17/1.36 inference(quant_inst,[status(thm)],[])).
% 1.17/1.36 tff(7273,plain,
% 1.17/1.36 ((~![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))),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[7272, 7271])).
% 1.17/1.36 tff(7274,plain,
% 1.17/1.36 (~m_main_v_state2(s85, c_c2)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[7273, 697, 7206])).
% 1.17/1.36 tff(7275,plain,
% 1.17/1.36 (((~![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)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(7276,plain,
% 1.17/1.36 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s85, c_c2) | (~node3(s85)))),
% 1.17/1.36 inference(quant_inst,[status(thm)],[])).
% 1.17/1.36 tff(7277,plain,
% 1.17/1.36 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s85, c_c2) | (~node3(s85))),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[7276, 7275])).
% 1.17/1.36 tff(7278,plain,
% 1.17/1.36 (~node3(s85)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[7277, 399, 7274])).
% 1.17/1.36 tff(7279,plain,
% 1.17/1.36 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | (m_main_v_state1(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)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(7280,plain,
% 1.17/1.36 (((~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)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.20/1.36 tff(7281,plain,
% 1.20/1.36 (((~![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))))),
% 1.20/1.36 inference(monotonicity,[status(thm)],[7280])).
% 1.20/1.36 tff(7282,plain,
% 1.20/1.36 (((~![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)))),
% 1.20/1.36 inference(transitivity,[status(thm)],[7281, 7279])).
% 1.20/1.36 tff(7283,plain,
% 1.20/1.36 ((~![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)))),
% 1.20/1.36 inference(quant_inst,[status(thm)],[])).
% 1.20/1.36 tff(7284,plain,
% 1.20/1.36 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | m_main_v_state1(s84, c_n1) | (~m_main_v_state1(s85, c_n1)) | (~node6(s84, s85))),
% 1.20/1.36 inference(modus_ponens,[status(thm)],[7283, 7282])).
% 1.20/1.36 tff(7285,plain,
% 1.20/1.36 (~m_main_v_state1(s85, c_n1)),
% 1.20/1.36 inference(unit_resolution,[status(thm)],[7284, 835, 7078, 7163])).
% 1.20/1.36 tff(7286,plain,
% 1.20/1.36 (((~![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)))),
% 1.20/1.36 inference(rewrite,[status(thm)],[])).
% 1.20/1.36 tff(7287,plain,
% 1.20/1.36 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s85, c_n1) | (~node2(s85)))),
% 1.20/1.36 inference(quant_inst,[status(thm)],[])).
% 1.20/1.36 tff(7288,plain,
% 1.20/1.36 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s85, c_n1) | (~node2(s85))),
% 1.20/1.36 inference(modus_ponens,[status(thm)],[7287, 7286])).
% 1.20/1.36 tff(7289,plain,
% 1.20/1.36 (~node2(s85)),
% 1.20/1.36 inference(unit_resolution,[status(thm)],[7288, 787, 7285])).
% 1.20/1.36 tff(7290,plain,
% 1.20/1.36 (((~![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)))),
% 1.20/1.36 inference(rewrite,[status(thm)],[])).
% 1.20/1.36 tff(7291,plain,
% 1.20/1.36 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s85, c_t2) | (~node1(s85)))),
% 1.20/1.36 inference(quant_inst,[status(thm)],[])).
% 1.20/1.36 tff(7292,plain,
% 1.20/1.36 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s85, c_t2) | (~node1(s85))),
% 1.20/1.36 inference(modus_ponens,[status(thm)],[7291, 7290])).
% 1.20/1.36 tff(7293,plain,
% 1.20/1.36 (~node1(s85)),
% 1.20/1.36 inference(unit_resolution,[status(thm)],[7292, 195, 7210])).
% 1.20/1.36 tff(7294,plain,
% 1.20/1.36 (((~![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))),
% 1.20/1.36 inference(rewrite,[status(thm)],[])).
% 1.20/1.36 tff(7295,plain,
% 1.20/1.36 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s85, s86)) | node7(s85, s86))),
% 1.20/1.36 inference(quant_inst,[status(thm)],[])).
% 1.20/1.36 tff(7296,plain,
% 1.20/1.36 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s85, s86)) | node7(s85, s86)),
% 1.20/1.36 inference(modus_ponens,[status(thm)],[7295, 7294])).
% 1.20/1.36 tff(7297,plain,
% 1.20/1.36 (node7(s85, s86)),
% 1.20/1.36 inference(unit_resolution,[status(thm)],[7296, 206, 7221])).
% 1.20/1.36 tff(7298,plain,
% 1.20/1.36 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(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)))),
% 1.20/1.36 inference(rewrite,[status(thm)],[])).
% 1.20/1.36 tff(7299,plain,
% 1.20/1.36 (((~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)))),
% 1.20/1.36 inference(rewrite,[status(thm)],[])).
% 1.20/1.36 tff(7300,plain,
% 1.20/1.36 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(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))))),
% 1.20/1.36 inference(monotonicity,[status(thm)],[7299])).
% 1.20/1.36 tff(7301,plain,
% 1.20/1.36 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(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)))),
% 1.20/1.36 inference(transitivity,[status(thm)],[7300, 7298])).
% 1.20/1.36 tff(7302,plain,
% 1.20/1.36 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | ((~m_main_v_state1(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))),
% 1.20/1.36 inference(quant_inst,[status(thm)],[])).
% 1.20/1.36 tff(7303,plain,
% 1.20/1.36 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state2(X, c_n2)) | node1(X) | node2(X) | node3(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_c1))) | (~m_main_v_state1(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))),
% 1.20/1.36 inference(modus_ponens,[status(thm)],[7302, 7301])).
% 1.20/1.36 tff(7304,plain,
% 1.20/1.36 ((~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)),
% 1.20/1.36 inference(unit_resolution,[status(thm)],[7303, 892, 7297])).
% 1.20/1.36 tff(7305,plain,
% 1.20/1.36 (m_main_v_state1(s86, c_c1)),
% 1.20/1.36 inference(unit_resolution,[status(thm)],[7304, 7293, 7206, 7170, 7289, 7278])).
% 1.20/1.36 tff(7306,plain,
% 1.20/1.36 (((~![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)))),
% 1.20/1.36 inference(rewrite,[status(thm)],[])).
% 1.20/1.36 tff(7307,plain,
% 1.20/1.36 ((~![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)))),
% 1.20/1.36 inference(quant_inst,[status(thm)],[])).
% 1.20/1.36 tff(7308,plain,
% 1.20/1.36 ((~![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))),
% 1.20/1.36 inference(modus_ponens,[status(thm)],[7307, 7306])).
% 1.20/1.36 tff(7309,plain,
% 1.20/1.36 (~m_main_v_state1(s86, c_n1)),
% 1.20/1.36 inference(unit_resolution,[status(thm)],[7308, 454, 7305])).
% 1.20/1.36 tff(7310,plain,
% 1.20/1.36 (((~![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)))),
% 1.20/1.36 inference(rewrite,[status(thm)],[])).
% 1.20/1.36 tff(7311,plain,
% 1.20/1.36 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s86, c_n1) | (~node11(s86)))),
% 1.20/1.36 inference(quant_inst,[status(thm)],[])).
% 1.20/1.36 tff(7312,plain,
% 1.20/1.36 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s86, c_n1) | (~node11(s86))),
% 1.20/1.36 inference(modus_ponens,[status(thm)],[7311, 7310])).
% 1.20/1.36 tff(7313,plain,
% 1.20/1.36 (~node11(s86)),
% 1.20/1.36 inference(unit_resolution,[status(thm)],[7312, 238, 7309])).
% 1.20/1.36 tff(7314,plain,
% 1.20/1.36 (succ(s86, s87) <=> succ(s86, s87)),
% 1.20/1.36 inference(rewrite,[status(thm)],[])).
% 1.20/1.36 tff(7315,axiom,(succ(s86, s87)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound87')).
% 1.20/1.36 tff(7316,plain,
% 1.20/1.36 (succ(s86, s87)),
% 1.20/1.36 inference(modus_ponens,[status(thm)],[7315, 7314])).
% 1.20/1.36 tff(7317,plain,
% 1.20/1.36 (((~![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))),
% 1.20/1.36 inference(rewrite,[status(thm)],[])).
% 1.20/1.36 tff(7318,plain,
% 1.20/1.36 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s86, s87)) | trans(s86, s87))),
% 1.20/1.36 inference(quant_inst,[status(thm)],[])).
% 1.20/1.36 tff(7319,plain,
% 1.20/1.36 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s86, s87)) | trans(s86, s87)),
% 1.20/1.36 inference(modus_ponens,[status(thm)],[7318, 7317])).
% 1.20/1.36 tff(7320,plain,
% 1.20/1.36 (trans(s86, s87)),
% 1.20/1.36 inference(unit_resolution,[status(thm)],[7319, 7316, 32])).
% 1.20/1.36 tff(7321,plain,
% 1.20/1.36 (((~![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))),
% 1.20/1.36 inference(rewrite,[status(thm)],[])).
% 1.20/1.36 tff(7322,plain,
% 1.20/1.36 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s86, s87)) | node14(s86, s87))),
% 1.20/1.36 inference(quant_inst,[status(thm)],[])).
% 1.20/1.36 tff(7323,plain,
% 1.20/1.36 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s86, s87)) | node14(s86, s87)),
% 1.20/1.36 inference(modus_ponens,[status(thm)],[7322, 7321])).
% 1.20/1.36 tff(7324,plain,
% 1.20/1.36 (node14(s86, s87)),
% 1.20/1.36 inference(unit_resolution,[status(thm)],[7323, 46, 7320])).
% 1.20/1.36 tff(7325,plain,
% 1.20/1.36 (((~![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)))),
% 1.20/1.36 inference(rewrite,[status(thm)],[])).
% 1.20/1.36 tff(7326,plain,
% 1.20/1.36 ((~![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)))),
% 1.20/1.36 inference(quant_inst,[status(thm)],[])).
% 1.20/1.36 tff(7327,plain,
% 1.20/1.36 ((~![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))),
% 1.20/1.36 inference(modus_ponens,[status(thm)],[7326, 7325])).
% 1.20/1.36 tff(7328,plain,
% 1.20/1.36 (m_main_v_state2(s86, c_c2) | node9(s86) | node8(s86) | node10(s86) | node11(s86) | node12(s86) | node13(s86, s87)),
% 1.20/1.36 inference(unit_resolution,[status(thm)],[7327, 296, 7324])).
% 1.20/1.36 tff(7329,plain,
% 1.20/1.36 (node13(s86, s87)),
% 1.20/1.36 inference(unit_resolution,[status(thm)],[7328, 7313, 7270, 7266, 7262, 7258, 7241])).
% 1.20/1.36 tff(7330,plain,
% 1.20/1.36 (((~![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(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)))),
% 1.20/1.36 inference(rewrite,[status(thm)],[])).
% 1.20/1.36 tff(7331,plain,
% 1.20/1.36 (((~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)))),
% 1.20/1.36 inference(rewrite,[status(thm)],[])).
% 1.20/1.36 tff(7332,plain,
% 1.20/1.36 (((~![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))))),
% 1.20/1.36 inference(monotonicity,[status(thm)],[7331])).
% 1.20/1.36 tff(7333,plain,
% 1.20/1.36 (((~![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)))),
% 1.20/1.36 inference(transitivity,[status(thm)],[7332, 7330])).
% 1.20/1.36 tff(7334,plain,
% 1.20/1.36 ((~![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)))),
% 1.20/1.36 inference(quant_inst,[status(thm)],[])).
% 1.20/1.36 tff(7335,plain,
% 1.20/1.36 ((~![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(s86, c_n2) | (~m_main_v_state2(s87, c_n2)) | (~node13(s86, s87))),
% 1.20/1.36 inference(modus_ponens,[status(thm)],[7334, 7333])).
% 1.20/1.36 tff(7336,plain,
% 1.20/1.36 (~m_main_v_state2(s87, c_n2)),
% 1.20/1.36 inference(unit_resolution,[status(thm)],[7335, 311, 7254, 7329])).
% 1.20/1.36 tff(7337,plain,
% 1.20/1.36 (((~![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)))),
% 1.20/1.36 inference(rewrite,[status(thm)],[])).
% 1.20/1.36 tff(7338,plain,
% 1.20/1.36 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s87, c_n2) | (~node9(s87)))),
% 1.20/1.36 inference(quant_inst,[status(thm)],[])).
% 1.20/1.36 tff(7339,plain,
% 1.20/1.36 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s87, c_n2) | (~node9(s87))),
% 1.20/1.36 inference(modus_ponens,[status(thm)],[7338, 7337])).
% 1.20/1.36 tff(7340,plain,
% 1.20/1.36 (~node9(s87)),
% 1.20/1.36 inference(unit_resolution,[status(thm)],[7339, 88, 7336])).
% 1.20/1.36 tff(7341,plain,
% 1.20/1.36 (((~![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)))),
% 1.20/1.36 inference(rewrite,[status(thm)],[])).
% 1.20/1.36 tff(7342,plain,
% 1.20/1.36 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s87, c_n2) | (~node10(s87)))),
% 1.20/1.36 inference(quant_inst,[status(thm)],[])).
% 1.20/1.36 tff(7343,plain,
% 1.20/1.36 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s87, c_n2) | (~node10(s87))),
% 1.20/1.36 inference(modus_ponens,[status(thm)],[7342, 7341])).
% 1.20/1.36 tff(7344,plain,
% 1.20/1.36 (~node10(s87)),
% 1.20/1.36 inference(unit_resolution,[status(thm)],[7343, 249, 7336])).
% 1.20/1.36 tff(7345,plain,
% 1.20/1.36 (((~![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(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)))),
% 1.20/1.36 inference(rewrite,[status(thm)],[])).
% 1.20/1.36 tff(7346,plain,
% 1.20/1.36 (((~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)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7347,plain,
% 1.20/1.37 (((~![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))))),
% 1.20/1.37 inference(monotonicity,[status(thm)],[7346])).
% 1.20/1.37 tff(7348,plain,
% 1.20/1.37 (((~![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)))),
% 1.20/1.37 inference(transitivity,[status(thm)],[7347, 7345])).
% 1.20/1.37 tff(7349,plain,
% 1.20/1.37 ((~![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))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(7350,plain,
% 1.20/1.37 ((~![V: $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))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7349, 7348])).
% 1.20/1.37 tff(7351,plain,
% 1.20/1.37 (m_main_v_state2(s87, c_t2)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7350, 518, 7250, 7329])).
% 1.20/1.37 tff(7352,plain,
% 1.20/1.37 (((~![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)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7353,plain,
% 1.20/1.37 ((~![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)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(7354,plain,
% 1.20/1.37 ((~![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))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7353, 7352])).
% 1.20/1.37 tff(7355,plain,
% 1.20/1.37 (~m_main_v_state1(s86, c_t1)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7354, 539, 7305])).
% 1.20/1.37 tff(7356,plain,
% 1.20/1.37 (((~![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)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7357,plain,
% 1.20/1.37 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s86, c_t1) | (~node5(s86)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(7358,plain,
% 1.20/1.37 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s86, c_t1) | (~node5(s86))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7357, 7356])).
% 1.20/1.37 tff(7359,plain,
% 1.20/1.37 (~node5(s86)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7358, 550, 7355])).
% 1.20/1.37 tff(7360,plain,
% 1.20/1.37 (((~![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)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7361,plain,
% 1.20/1.37 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s86, c_n2) | (~node4(s86)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(7362,plain,
% 1.20/1.37 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s86, c_n2) | (~node4(s86))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7361, 7360])).
% 1.20/1.37 tff(7363,plain,
% 1.20/1.37 (~node4(s86)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7362, 388, 7254])).
% 1.20/1.37 tff(7364,plain,
% 1.20/1.37 (((~![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)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7365,plain,
% 1.20/1.37 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s86, c_c2) | (~node3(s86)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(7366,plain,
% 1.20/1.37 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s86, c_c2) | (~node3(s86))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7365, 7364])).
% 1.20/1.37 tff(7367,plain,
% 1.20/1.37 (~node3(s86)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7366, 399, 7270])).
% 1.20/1.37 tff(7368,plain,
% 1.20/1.37 (((~![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)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7369,plain,
% 1.20/1.37 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s86, c_n2) | (~node2(s86)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(7370,plain,
% 1.20/1.37 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s86, c_n2) | (~node2(s86))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7369, 7368])).
% 1.20/1.37 tff(7371,plain,
% 1.20/1.37 (~node2(s86)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7370, 410, 7254])).
% 1.20/1.37 tff(7372,plain,
% 1.20/1.37 (((~![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)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7373,plain,
% 1.20/1.37 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s86, c_n1) | (~node1(s86)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(7374,plain,
% 1.20/1.37 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s86, c_n1) | (~node1(s86))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7373, 7372])).
% 1.20/1.37 tff(7375,plain,
% 1.20/1.37 (~node1(s86)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7374, 421, 7309])).
% 1.20/1.37 tff(7376,plain,
% 1.20/1.37 (((~![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))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7377,plain,
% 1.20/1.37 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s86, s87)) | node7(s86, s87))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(7378,plain,
% 1.20/1.37 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s86, s87)) | node7(s86, s87)),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7377, 7376])).
% 1.20/1.37 tff(7379,plain,
% 1.20/1.37 (node7(s86, s87)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7378, 206, 7320])).
% 1.20/1.37 tff(7380,plain,
% 1.20/1.37 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | (m_main_v_state1(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)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7381,plain,
% 1.20/1.37 (((~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)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7382,plain,
% 1.20/1.37 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(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))))),
% 1.20/1.37 inference(monotonicity,[status(thm)],[7381])).
% 1.20/1.37 tff(7383,plain,
% 1.20/1.37 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(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)))),
% 1.20/1.37 inference(transitivity,[status(thm)],[7382, 7380])).
% 1.20/1.37 tff(7384,plain,
% 1.20/1.37 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | ((~m_main_v_state1(s86, c_c1)) | node1(s86) | node2(s86) | node3(s86) | node4(s86) | node5(s86) | (~node7(s86, s87)) | m_main_v_state1(s87, c_n1))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(7385,plain,
% 1.20/1.37 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | (~node7(X, Y)) | m_main_v_state1(Y, c_n1))) | m_main_v_state1(s87, c_n1) | (~m_main_v_state1(s86, c_c1)) | node1(s86) | node2(s86) | node3(s86) | node4(s86) | node5(s86) | (~node7(s86, s87))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7384, 7383])).
% 1.20/1.37 tff(7386,plain,
% 1.20/1.37 (m_main_v_state1(s87, c_n1) | (~m_main_v_state1(s86, c_c1)) | node1(s86) | node2(s86) | node3(s86) | node4(s86) | node5(s86)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7385, 584, 7379])).
% 1.20/1.37 tff(7387,plain,
% 1.20/1.37 (m_main_v_state1(s87, c_n1)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7386, 7375, 7305, 7371, 7367, 7363, 7359])).
% 1.20/1.37 tff(7388,plain,
% 1.20/1.37 (((~![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)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7389,plain,
% 1.20/1.37 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s87, c_n2) | (~node8(s87)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(7390,plain,
% 1.20/1.37 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s87, c_n2) | (~node8(s87))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7389, 7388])).
% 1.20/1.37 tff(7391,plain,
% 1.20/1.37 (~node8(s87)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7390, 271, 7336])).
% 1.20/1.37 tff(7392,plain,
% 1.20/1.37 (succ(s87, s88) <=> succ(s87, s88)),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7393,axiom,(succ(s87, s88)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound88')).
% 1.20/1.37 tff(7394,plain,
% 1.20/1.37 (succ(s87, s88)),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7393, 7392])).
% 1.20/1.37 tff(7395,plain,
% 1.20/1.37 (((~![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))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7396,plain,
% 1.20/1.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s87, s88)) | trans(s87, s88))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(7397,plain,
% 1.20/1.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s87, s88)) | trans(s87, s88)),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7396, 7395])).
% 1.20/1.37 tff(7398,plain,
% 1.20/1.37 (trans(s87, s88)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7397, 7394, 32])).
% 1.20/1.37 tff(7399,plain,
% 1.20/1.37 (((~![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))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7400,plain,
% 1.20/1.37 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s87, s88)) | node14(s87, s88))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(7401,plain,
% 1.20/1.37 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s87, s88)) | node14(s87, s88)),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7400, 7399])).
% 1.20/1.37 tff(7402,plain,
% 1.20/1.37 (node14(s87, s88)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7401, 46, 7398])).
% 1.20/1.37 tff(7403,plain,
% 1.20/1.37 (((~![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))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7404,plain,
% 1.20/1.37 ((~![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))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(7405,plain,
% 1.20/1.37 ((~![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)),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7404, 7403])).
% 1.20/1.37 tff(7406,plain,
% 1.20/1.37 ((~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)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7405, 617, 7402])).
% 1.20/1.37 tff(7407,plain,
% 1.20/1.37 (m_main_v_state2(s88, c_c2)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7406, 7391, 7387, 7351, 7344, 7340])).
% 1.20/1.37 tff(7408,plain,
% 1.20/1.37 (((~![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)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7409,plain,
% 1.20/1.37 ((~![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)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(7410,plain,
% 1.20/1.37 ((~![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))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7409, 7408])).
% 1.20/1.37 tff(7411,plain,
% 1.20/1.37 (~m_main_v_state2(s88, c_t2)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7410, 260, 7407])).
% 1.20/1.37 tff(7412,plain,
% 1.20/1.37 (((~![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)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7413,plain,
% 1.20/1.37 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s88, c_t2) | (~node12(s88)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(7414,plain,
% 1.20/1.37 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s88, c_t2) | (~node12(s88))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7413, 7412])).
% 1.20/1.37 tff(7415,plain,
% 1.20/1.37 (~node12(s88)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7414, 633, 7411])).
% 1.20/1.37 tff(7416,plain,
% 1.20/1.37 (((~![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))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7417,plain,
% 1.20/1.37 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s87, s88)) | node7(s87, s88))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(7418,plain,
% 1.20/1.37 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s87, s88)) | node7(s87, s88)),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7417, 7416])).
% 1.20/1.37 tff(7419,plain,
% 1.20/1.37 (node7(s87, s88)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7418, 206, 7398])).
% 1.20/1.37 tff(7420,plain,
% 1.20/1.37 (((~![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))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7421,plain,
% 1.20/1.37 ((~![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))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(7422,plain,
% 1.20/1.37 ((~![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)),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7421, 7420])).
% 1.20/1.37 tff(7423,plain,
% 1.20/1.37 ((~m_main_v_state1(s87, c_n1)) | (~m_main_v_state2(s87, c_t2)) | m_main_v_state1(s88, c_t1)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7422, 651, 7419])).
% 1.20/1.37 tff(7424,plain,
% 1.20/1.37 (m_main_v_state1(s88, c_t1)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7423, 7351, 7387])).
% 1.20/1.37 tff(7425,plain,
% 1.20/1.37 (((~![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)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7426,plain,
% 1.20/1.37 ((~![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)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(7427,plain,
% 1.20/1.37 ((~![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))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7426, 7425])).
% 1.20/1.37 tff(7428,plain,
% 1.20/1.37 (~m_main_v_state1(s88, c_n1)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7427, 10, 7424])).
% 1.20/1.37 tff(7429,plain,
% 1.20/1.37 (((~![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)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7430,plain,
% 1.20/1.37 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s88, c_n1) | (~node11(s88)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(7431,plain,
% 1.20/1.37 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s88, c_n1) | (~node11(s88))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7430, 7429])).
% 1.20/1.37 tff(7432,plain,
% 1.20/1.37 (~node11(s88)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7431, 238, 7428])).
% 1.20/1.37 tff(7433,plain,
% 1.20/1.37 (((~![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)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7434,plain,
% 1.20/1.37 ((~![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)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(7435,plain,
% 1.20/1.37 ((~![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))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7434, 7433])).
% 1.20/1.37 tff(7436,plain,
% 1.20/1.37 (~m_main_v_state1(s88, c_c1)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7435, 539, 7424])).
% 1.20/1.37 tff(7437,plain,
% 1.20/1.37 (((~![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)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7438,plain,
% 1.20/1.37 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s88, c_c1) | (~node10(s88)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(7439,plain,
% 1.20/1.37 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s88, c_c1) | (~node10(s88))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7438, 7437])).
% 1.20/1.37 tff(7440,plain,
% 1.20/1.37 (~node10(s88)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7439, 675, 7436])).
% 1.20/1.37 tff(7441,plain,
% 1.20/1.37 (((~![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)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7442,plain,
% 1.20/1.37 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s88, c_n1) | (~node9(s88)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(7443,plain,
% 1.20/1.37 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s88, c_n1) | (~node9(s88))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7442, 7441])).
% 1.20/1.37 tff(7444,plain,
% 1.20/1.37 (~node9(s88)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7443, 686, 7428])).
% 1.20/1.37 tff(7445,plain,
% 1.20/1.37 (((~![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)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7446,plain,
% 1.20/1.37 ((~![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)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(7447,plain,
% 1.20/1.37 ((~![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))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7446, 7445])).
% 1.20/1.37 tff(7448,plain,
% 1.20/1.37 (~m_main_v_state2(s88, c_n2)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7447, 697, 7407])).
% 1.20/1.37 tff(7449,plain,
% 1.20/1.37 (((~![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)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7450,plain,
% 1.20/1.37 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s88, c_n2) | (~node8(s88)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(7451,plain,
% 1.20/1.37 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s88, c_n2) | (~node8(s88))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7450, 7449])).
% 1.20/1.37 tff(7452,plain,
% 1.20/1.37 (~node8(s88)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7451, 271, 7448])).
% 1.20/1.37 tff(7453,plain,
% 1.20/1.37 (succ(s88, s89) <=> succ(s88, s89)),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7454,axiom,(succ(s88, s89)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound89')).
% 1.20/1.37 tff(7455,plain,
% 1.20/1.37 (succ(s88, s89)),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7454, 7453])).
% 1.20/1.37 tff(7456,plain,
% 1.20/1.37 (((~![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))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7457,plain,
% 1.20/1.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s88, s89)) | trans(s88, s89))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(7458,plain,
% 1.20/1.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s88, s89)) | trans(s88, s89)),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7457, 7456])).
% 1.20/1.37 tff(7459,plain,
% 1.20/1.37 (trans(s88, s89)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7458, 7455, 32])).
% 1.20/1.37 tff(7460,plain,
% 1.20/1.37 (((~![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))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7461,plain,
% 1.20/1.37 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s88, s89)) | node14(s88, s89))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(7462,plain,
% 1.20/1.37 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s88, s89)) | node14(s88, s89)),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7461, 7460])).
% 1.20/1.37 tff(7463,plain,
% 1.20/1.37 (node14(s88, s89)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7462, 46, 7459])).
% 1.20/1.37 tff(7464,plain,
% 1.20/1.37 (((~![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(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)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7465,plain,
% 1.20/1.37 (((~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)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7466,plain,
% 1.20/1.37 (((~![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(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))))),
% 1.20/1.37 inference(monotonicity,[status(thm)],[7465])).
% 1.20/1.37 tff(7467,plain,
% 1.20/1.37 (((~![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(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)))),
% 1.20/1.37 inference(transitivity,[status(thm)],[7466, 7464])).
% 1.20/1.37 tff(7468,plain,
% 1.20/1.37 ((~![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(s88, c_c2)) | node9(s88) | node8(s88) | node10(s88) | node11(s88) | node12(s88) | (~node14(s88, s89)) | m_main_v_state2(s89, c_n2))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(7469,plain,
% 1.20/1.37 ((~![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(s89, c_n2) | node9(s88) | node8(s88) | node10(s88) | node11(s88) | node12(s88) | (~node14(s88, s89)) | (~m_main_v_state2(s88, c_c2))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7468, 7467])).
% 1.20/1.37 tff(7470,plain,
% 1.20/1.37 (m_main_v_state2(s89, c_n2) | node9(s88) | node8(s88) | node10(s88) | node11(s88) | node12(s88) | (~m_main_v_state2(s88, c_c2))),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7469, 726, 7463])).
% 1.20/1.37 tff(7471,plain,
% 1.20/1.37 (m_main_v_state2(s89, c_n2)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7470, 7452, 7407, 7444, 7440, 7432, 7415])).
% 1.20/1.37 tff(7472,plain,
% 1.20/1.37 (((~![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)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7473,plain,
% 1.20/1.37 ((~![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)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(7474,plain,
% 1.20/1.37 ((~![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))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7473, 7472])).
% 1.20/1.37 tff(7475,plain,
% 1.20/1.37 (~m_main_v_state2(s89, c_c2)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7474, 697, 7471])).
% 1.20/1.37 tff(7476,plain,
% 1.20/1.37 (((~![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)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7477,plain,
% 1.20/1.37 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s89, c_c2) | (~node3(s89)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(7478,plain,
% 1.20/1.37 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s89, c_c2) | (~node3(s89))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7477, 7476])).
% 1.20/1.37 tff(7479,plain,
% 1.20/1.37 (~node3(s89)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7478, 399, 7475])).
% 1.20/1.37 tff(7480,plain,
% 1.20/1.37 (((~![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)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(7481,plain,
% 1.20/1.37 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s88, c_n1) | (~node1(s88)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(7482,plain,
% 1.20/1.37 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s88, c_n1) | (~node1(s88))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[7481, 7480])).
% 1.20/1.37 tff(7483,plain,
% 1.20/1.37 (~node1(s88)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[7482, 421, 7428])).
% 1.20/1.37 tff(7484,plain,
% 1.20/1.37 (((~![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))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7485,plain,
% 1.20/1.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s87, s88)) | node18(s87, s88))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(7486,plain,
% 1.20/1.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s87, s88)) | node18(s87, s88)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[7485, 7484])).
% 1.20/1.38 tff(7487,plain,
% 1.20/1.38 (node18(s87, s88)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7486, 125, 7398])).
% 1.20/1.38 tff(7488,plain,
% 1.20/1.38 (((~![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))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7489,plain,
% 1.20/1.38 ((~![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))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(7490,plain,
% 1.20/1.38 ((~![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)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[7489, 7488])).
% 1.20/1.38 tff(7491,plain,
% 1.20/1.38 ((~m_main_v_state1(s87, c_n1)) | (~m_main_v_state2(s87, c_t2)) | m_main_v_turn(s88, c_2)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7490, 760, 7487])).
% 1.20/1.38 tff(7492,plain,
% 1.20/1.38 (m_main_v_turn(s88, c_2)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7491, 7351, 7387])).
% 1.20/1.38 tff(7493,plain,
% 1.20/1.38 (((~![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)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7494,plain,
% 1.20/1.38 ((~![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)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(7495,plain,
% 1.20/1.38 ((~![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))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[7494, 7493])).
% 1.20/1.38 tff(7496,plain,
% 1.20/1.38 (~m_main_v_turn(s88, c_1)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7495, 156, 7492])).
% 1.20/1.38 tff(7497,plain,
% 1.20/1.38 (((~![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)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7498,plain,
% 1.20/1.38 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s88, c_1) | (~node5(s88)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(7499,plain,
% 1.20/1.38 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s88, c_1) | (~node5(s88))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[7498, 7497])).
% 1.20/1.38 tff(7500,plain,
% 1.20/1.38 (~node5(s88)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7499, 776, 7496])).
% 1.20/1.38 tff(7501,plain,
% 1.20/1.38 (((~![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)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7502,plain,
% 1.20/1.38 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s88, c_n1) | (~node2(s88)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(7503,plain,
% 1.20/1.38 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s88, c_n1) | (~node2(s88))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[7502, 7501])).
% 1.20/1.38 tff(7504,plain,
% 1.20/1.38 (~node2(s88)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7503, 787, 7428])).
% 1.20/1.38 tff(7505,plain,
% 1.20/1.38 (((~![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)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7506,plain,
% 1.20/1.38 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s88, c_n1) | (~node3(s88)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(7507,plain,
% 1.20/1.38 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s88, c_n1) | (~node3(s88))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[7506, 7505])).
% 1.20/1.38 tff(7508,plain,
% 1.20/1.38 (~node3(s88)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7507, 798, 7428])).
% 1.20/1.38 tff(7509,plain,
% 1.20/1.38 (((~![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)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7510,plain,
% 1.20/1.38 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s88, c_n2) | (~node4(s88)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(7511,plain,
% 1.20/1.38 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s88, c_n2) | (~node4(s88))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[7510, 7509])).
% 1.20/1.38 tff(7512,plain,
% 1.20/1.38 (~node4(s88)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7511, 388, 7448])).
% 1.20/1.38 tff(7513,plain,
% 1.20/1.38 (((~![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))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7514,plain,
% 1.20/1.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s88, s89)) | node7(s88, s89))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(7515,plain,
% 1.20/1.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s88, s89)) | node7(s88, s89)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[7514, 7513])).
% 1.20/1.38 tff(7516,plain,
% 1.20/1.38 (node7(s88, s89)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7515, 206, 7459])).
% 1.20/1.38 tff(7517,plain,
% 1.20/1.38 (((~![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)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7518,plain,
% 1.20/1.38 ((~![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)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(7519,plain,
% 1.20/1.38 ((~![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))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[7518, 7517])).
% 1.20/1.38 tff(7520,plain,
% 1.20/1.38 (m_main_v_state1(s88, c_c1) | node1(s88) | node2(s88) | node3(s88) | node4(s88) | node5(s88) | node6(s88, s89)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7519, 820, 7516])).
% 1.20/1.38 tff(7521,plain,
% 1.20/1.38 (node6(s88, s89)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7520, 7512, 7436, 7508, 7504, 7500, 7483])).
% 1.20/1.38 tff(7522,plain,
% 1.20/1.38 (((~![V: $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)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7523,plain,
% 1.20/1.38 (((~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)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7524,plain,
% 1.20/1.38 (((~![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))))),
% 1.20/1.38 inference(monotonicity,[status(thm)],[7523])).
% 1.20/1.38 tff(7525,plain,
% 1.20/1.38 (((~![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)))),
% 1.20/1.38 inference(transitivity,[status(thm)],[7524, 7522])).
% 1.20/1.38 tff(7526,plain,
% 1.20/1.38 ((~![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)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(7527,plain,
% 1.20/1.38 ((~![V: $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))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[7526, 7525])).
% 1.20/1.38 tff(7528,plain,
% 1.20/1.38 (~m_main_v_state1(s89, c_n1)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7527, 835, 7428, 7521])).
% 1.20/1.38 tff(7529,plain,
% 1.20/1.38 (((~![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)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7530,plain,
% 1.20/1.38 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s89, c_n1) | (~node2(s89)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(7531,plain,
% 1.20/1.38 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s89, c_n1) | (~node2(s89))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[7530, 7529])).
% 1.20/1.38 tff(7532,plain,
% 1.20/1.38 (~node2(s89)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7531, 787, 7528])).
% 1.20/1.38 tff(7533,plain,
% 1.20/1.38 (((~![V: $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)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7534,plain,
% 1.20/1.38 (((~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)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7535,plain,
% 1.20/1.38 (((~![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))))),
% 1.20/1.38 inference(monotonicity,[status(thm)],[7534])).
% 1.20/1.38 tff(7536,plain,
% 1.20/1.38 (((~![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)))),
% 1.20/1.38 inference(transitivity,[status(thm)],[7535, 7533])).
% 1.20/1.38 tff(7537,plain,
% 1.20/1.38 ((~![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))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(7538,plain,
% 1.20/1.38 ((~![V: $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))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[7537, 7536])).
% 1.20/1.38 tff(7539,plain,
% 1.20/1.38 (m_main_v_state1(s89, c_t1)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7538, 856, 7424, 7521])).
% 1.20/1.38 tff(7540,plain,
% 1.20/1.38 (((~![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)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7541,plain,
% 1.20/1.38 ((~![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)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(7542,plain,
% 1.20/1.38 ((~![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))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[7541, 7540])).
% 1.20/1.38 tff(7543,plain,
% 1.20/1.38 (~m_main_v_state2(s89, c_t2)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7542, 77, 7471])).
% 1.20/1.38 tff(7544,plain,
% 1.20/1.38 (((~![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)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7545,plain,
% 1.20/1.38 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s89, c_t2) | (~node1(s89)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(7546,plain,
% 1.20/1.38 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s89, c_t2) | (~node1(s89))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[7545, 7544])).
% 1.20/1.38 tff(7547,plain,
% 1.20/1.38 (~node1(s89)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7546, 195, 7543])).
% 1.20/1.38 tff(7548,plain,
% 1.20/1.38 (succ(s89, s90) <=> succ(s89, s90)),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7549,axiom,(succ(s89, s90)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound90')).
% 1.20/1.38 tff(7550,plain,
% 1.20/1.38 (succ(s89, s90)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[7549, 7548])).
% 1.20/1.38 tff(7551,plain,
% 1.20/1.38 (((~![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))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7552,plain,
% 1.20/1.38 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s89, s90)) | trans(s89, s90))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(7553,plain,
% 1.20/1.38 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s89, s90)) | trans(s89, s90)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[7552, 7551])).
% 1.20/1.38 tff(7554,plain,
% 1.20/1.38 (trans(s89, s90)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7553, 7550, 32])).
% 1.20/1.38 tff(7555,plain,
% 1.20/1.38 (((~![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))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7556,plain,
% 1.20/1.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s89, s90)) | node7(s89, s90))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(7557,plain,
% 1.20/1.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s89, s90)) | node7(s89, s90)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[7556, 7555])).
% 1.20/1.38 tff(7558,plain,
% 1.20/1.38 (node7(s89, s90)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7557, 206, 7554])).
% 1.20/1.38 tff(7559,plain,
% 1.20/1.38 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7560,plain,
% 1.20/1.38 (((~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)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7561,plain,
% 1.20/1.38 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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))))),
% 1.20/1.38 inference(monotonicity,[status(thm)],[7560])).
% 1.20/1.38 tff(7562,plain,
% 1.20/1.38 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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)))),
% 1.20/1.38 inference(transitivity,[status(thm)],[7561, 7559])).
% 1.20/1.38 tff(7563,plain,
% 1.20/1.38 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(7564,plain,
% 1.20/1.38 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[7563, 7562])).
% 1.20/1.38 tff(7565,plain,
% 1.20/1.38 ((~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)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7564, 892, 7558])).
% 1.20/1.38 tff(7566,plain,
% 1.20/1.38 (m_main_v_state1(s90, c_c1)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7565, 7547, 7471, 7539, 7532, 7479])).
% 1.20/1.38 tff(7567,plain,
% 1.20/1.38 (((~![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)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7568,plain,
% 1.20/1.38 ((~![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)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(7569,plain,
% 1.20/1.38 ((~![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))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[7568, 7567])).
% 1.20/1.38 tff(7570,plain,
% 1.20/1.38 (~m_main_v_state1(s90, c_t1)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7569, 539, 7566])).
% 1.20/1.38 tff(7571,plain,
% 1.20/1.38 (((~![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)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7572,plain,
% 1.20/1.38 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s90, c_t1) | (~node5(s90)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(7573,plain,
% 1.20/1.38 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s90, c_t1) | (~node5(s90))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[7572, 7571])).
% 1.20/1.38 tff(7574,plain,
% 1.20/1.38 (~node5(s90)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7573, 550, 7570])).
% 1.20/1.38 tff(7575,plain,
% 1.20/1.38 (((~![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))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7576,plain,
% 1.20/1.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s89, s90)) | node14(s89, s90))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(7577,plain,
% 1.20/1.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s89, s90)) | node14(s89, s90)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[7576, 7575])).
% 1.20/1.38 tff(7578,plain,
% 1.20/1.38 (node14(s89, s90)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7577, 46, 7554])).
% 1.20/1.38 tff(7579,plain,
% 1.20/1.38 (((~![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(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))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7580,plain,
% 1.20/1.38 ((~![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(s89, c_t1)) | (~m_main_v_state2(s89, c_n2)) | (~node14(s89, s90)) | m_main_v_state2(s90, c_t2))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(7581,plain,
% 1.20/1.38 ((~![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(s89, c_t1)) | (~m_main_v_state2(s89, c_n2)) | (~node14(s89, s90)) | m_main_v_state2(s90, c_t2)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[7580, 7579])).
% 1.20/1.38 tff(7582,plain,
% 1.20/1.38 ((~m_main_v_state1(s89, c_t1)) | (~m_main_v_state2(s89, c_n2)) | m_main_v_state2(s90, c_t2)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7581, 922, 7578])).
% 1.20/1.38 tff(7583,plain,
% 1.20/1.38 (m_main_v_state2(s90, c_t2)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7582, 7539, 7471])).
% 1.20/1.38 tff(7584,plain,
% 1.20/1.38 (((~![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)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7585,plain,
% 1.20/1.38 ((~![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)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(7586,plain,
% 1.20/1.38 ((~![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))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[7585, 7584])).
% 1.20/1.38 tff(7587,plain,
% 1.20/1.38 (~m_main_v_state2(s90, c_n2)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7586, 77, 7583])).
% 1.20/1.38 tff(7588,plain,
% 1.20/1.38 (((~![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)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7589,plain,
% 1.20/1.38 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s90, c_n2) | (~node4(s90)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(7590,plain,
% 1.20/1.38 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s90, c_n2) | (~node4(s90))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[7589, 7588])).
% 1.20/1.38 tff(7591,plain,
% 1.20/1.38 (~node4(s90)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7590, 388, 7587])).
% 1.20/1.38 tff(7592,plain,
% 1.20/1.38 (((~![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)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7593,plain,
% 1.20/1.38 ((~![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)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(7594,plain,
% 1.20/1.38 ((~![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))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[7593, 7592])).
% 1.20/1.38 tff(7595,plain,
% 1.20/1.38 (~m_main_v_state2(s90, c_c2)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7594, 260, 7583])).
% 1.20/1.38 tff(7596,plain,
% 1.20/1.38 (((~![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)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7597,plain,
% 1.20/1.38 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s90, c_c2) | (~node3(s90)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(7598,plain,
% 1.20/1.38 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s90, c_c2) | (~node3(s90))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[7597, 7596])).
% 1.20/1.38 tff(7599,plain,
% 1.20/1.38 (~node3(s90)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7598, 399, 7595])).
% 1.20/1.38 tff(7600,plain,
% 1.20/1.38 (((~![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)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7601,plain,
% 1.20/1.38 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s90, c_n2) | (~node2(s90)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(7602,plain,
% 1.20/1.38 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s90, c_n2) | (~node2(s90))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[7601, 7600])).
% 1.20/1.38 tff(7603,plain,
% 1.20/1.38 (~node2(s90)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7602, 410, 7587])).
% 1.20/1.38 tff(7604,plain,
% 1.20/1.38 (((~![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)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7605,plain,
% 1.20/1.38 ((~![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)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(7606,plain,
% 1.20/1.38 ((~![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))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[7605, 7604])).
% 1.20/1.38 tff(7607,plain,
% 1.20/1.38 (~m_main_v_state1(s90, c_n1)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7606, 454, 7566])).
% 1.20/1.38 tff(7608,plain,
% 1.20/1.38 (((~![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)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7609,plain,
% 1.20/1.38 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s90, c_n1) | (~node1(s90)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(7610,plain,
% 1.20/1.38 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s90, c_n1) | (~node1(s90))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[7609, 7608])).
% 1.20/1.38 tff(7611,plain,
% 1.20/1.38 (~node1(s90)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[7610, 421, 7607])).
% 1.20/1.38 tff(7612,plain,
% 1.20/1.38 (succ(s90, s91) <=> succ(s90, s91)),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(7613,axiom,(succ(s90, s91)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound91')).
% 1.20/1.38 tff(7614,plain,
% 1.20/1.39 (succ(s90, s91)),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[7613, 7612])).
% 1.20/1.39 tff(7615,plain,
% 1.20/1.39 (((~![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))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(7616,plain,
% 1.20/1.39 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s90, s91)) | trans(s90, s91))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(7617,plain,
% 1.20/1.39 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s90, s91)) | trans(s90, s91)),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[7616, 7615])).
% 1.20/1.39 tff(7618,plain,
% 1.20/1.39 (trans(s90, s91)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7617, 7614, 32])).
% 1.20/1.39 tff(7619,plain,
% 1.20/1.39 (((~![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))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(7620,plain,
% 1.20/1.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s90, s91)) | node7(s90, s91))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(7621,plain,
% 1.20/1.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s90, s91)) | node7(s90, s91)),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[7620, 7619])).
% 1.20/1.39 tff(7622,plain,
% 1.20/1.39 (node7(s90, s91)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7621, 206, 7618])).
% 1.20/1.39 tff(7623,plain,
% 1.20/1.39 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(7624,plain,
% 1.20/1.39 (((~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)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(7625,plain,
% 1.20/1.39 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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))))),
% 1.20/1.39 inference(monotonicity,[status(thm)],[7624])).
% 1.20/1.39 tff(7626,plain,
% 1.20/1.39 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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)))),
% 1.20/1.39 inference(transitivity,[status(thm)],[7625, 7623])).
% 1.20/1.39 tff(7627,plain,
% 1.20/1.39 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(7628,plain,
% 1.20/1.39 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[7627, 7626])).
% 1.20/1.39 tff(7629,plain,
% 1.20/1.39 (m_main_v_state1(s91, c_n1) | (~m_main_v_state1(s90, c_c1)) | node1(s90) | node2(s90) | node3(s90) | node4(s90) | node5(s90)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7628, 584, 7622])).
% 1.20/1.39 tff(7630,plain,
% 1.20/1.39 (m_main_v_state1(s91, c_n1)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7629, 7611, 7566, 7603, 7599, 7591, 7574])).
% 1.20/1.39 tff(7631,plain,
% 1.20/1.39 (((~![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)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(7632,plain,
% 1.20/1.39 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s89, c_t2) | (~node15(s89)))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(7633,plain,
% 1.20/1.39 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s89, c_t2) | (~node15(s89))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[7632, 7631])).
% 1.20/1.39 tff(7634,plain,
% 1.20/1.39 (~node15(s89)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7633, 103, 7543])).
% 1.20/1.39 tff(7635,plain,
% 1.20/1.39 (((~![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))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(7636,plain,
% 1.20/1.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s89, s90)) | node18(s89, s90))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(7637,plain,
% 1.20/1.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s89, s90)) | node18(s89, s90)),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[7636, 7635])).
% 1.20/1.39 tff(7638,plain,
% 1.20/1.39 (node18(s89, s90)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7637, 125, 7554])).
% 1.20/1.39 tff(7639,plain,
% 1.20/1.39 (((~![Y: $i, X: $i] : ((~m_main_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))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(7640,plain,
% 1.20/1.39 (((~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))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(7641,plain,
% 1.20/1.39 (((~![Y: $i, X: $i] : ((~m_main_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)))),
% 1.20/1.39 inference(monotonicity,[status(thm)],[7640])).
% 1.20/1.39 tff(7642,plain,
% 1.20/1.39 (((~![Y: $i, X: $i] : ((~m_main_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))),
% 1.20/1.39 inference(transitivity,[status(thm)],[7641, 7639])).
% 1.20/1.39 tff(7643,plain,
% 1.20/1.39 ((~![Y: $i, X: $i] : ((~m_main_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))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(7644,plain,
% 1.20/1.39 ((~![Y: $i, X: $i] : ((~m_main_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)),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[7643, 7642])).
% 1.20/1.39 tff(7645,plain,
% 1.20/1.39 (node15(s89) | (~m_main_v_state1(s89, c_t1)) | (~m_main_v_state2(s89, c_n2)) | m_main_v_turn(s90, c_1)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7644, 992, 7638])).
% 1.20/1.39 tff(7646,plain,
% 1.20/1.39 (m_main_v_turn(s90, c_1)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7645, 7634, 7471, 7539])).
% 1.20/1.39 tff(7647,plain,
% 1.20/1.39 (((~![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)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(7648,plain,
% 1.20/1.39 ((~![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)))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(7649,plain,
% 1.20/1.39 ((~![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))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[7648, 7647])).
% 1.20/1.39 tff(7650,plain,
% 1.20/1.39 (~m_main_v_turn(s90, c_2)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7649, 156, 7646])).
% 1.20/1.39 tff(7651,plain,
% 1.20/1.39 (((~![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)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(7652,plain,
% 1.20/1.39 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s90, c_2) | (~node12(s90)))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(7653,plain,
% 1.20/1.39 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s90, c_2) | (~node12(s90))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[7652, 7651])).
% 1.20/1.39 tff(7654,plain,
% 1.20/1.39 (~node12(s90)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7653, 184, 7650])).
% 1.20/1.39 tff(7655,plain,
% 1.20/1.39 (((~![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)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(7656,plain,
% 1.20/1.39 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s90, c_n2) | (~node8(s90)))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(7657,plain,
% 1.20/1.39 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s90, c_n2) | (~node8(s90))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[7656, 7655])).
% 1.20/1.39 tff(7658,plain,
% 1.20/1.39 (~node8(s90)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7657, 271, 7587])).
% 1.20/1.39 tff(7659,plain,
% 1.20/1.39 (((~![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)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(7660,plain,
% 1.20/1.39 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s90, c_n2) | (~node9(s90)))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(7661,plain,
% 1.20/1.39 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s90, c_n2) | (~node9(s90))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[7660, 7659])).
% 1.20/1.39 tff(7662,plain,
% 1.20/1.39 (~node9(s90)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7661, 88, 7587])).
% 1.20/1.39 tff(7663,plain,
% 1.20/1.39 (((~![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)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(7664,plain,
% 1.20/1.39 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s90, c_n2) | (~node10(s90)))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(7665,plain,
% 1.20/1.39 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s90, c_n2) | (~node10(s90))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[7664, 7663])).
% 1.20/1.39 tff(7666,plain,
% 1.20/1.39 (~node10(s90)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7665, 249, 7587])).
% 1.20/1.39 tff(7667,plain,
% 1.20/1.39 (((~![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)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(7668,plain,
% 1.20/1.39 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s90, c_n1) | (~node11(s90)))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(7669,plain,
% 1.20/1.39 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s90, c_n1) | (~node11(s90))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[7668, 7667])).
% 1.20/1.39 tff(7670,plain,
% 1.20/1.39 (~node11(s90)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7669, 238, 7607])).
% 1.20/1.39 tff(7671,plain,
% 1.20/1.39 (((~![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))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(7672,plain,
% 1.20/1.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s90, s91)) | node14(s90, s91))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(7673,plain,
% 1.20/1.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s90, s91)) | node14(s90, s91)),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[7672, 7671])).
% 1.20/1.39 tff(7674,plain,
% 1.20/1.39 (node14(s90, s91)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7673, 46, 7618])).
% 1.20/1.39 tff(7675,plain,
% 1.20/1.39 (((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(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)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(7676,plain,
% 1.20/1.39 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | (m_main_v_state2(s90, c_c2) | node9(s90) | node8(s90) | node10(s90) | node11(s90) | node12(s90) | node13(s90, s91) | (~node14(s90, s91)))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(7677,plain,
% 1.20/1.39 ((~![Y: $i, X: $i] : (m_main_v_state2(X, c_c2) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | node13(X, Y) | (~node14(X, Y)))) | m_main_v_state2(s90, c_c2) | node9(s90) | node8(s90) | node10(s90) | node11(s90) | node12(s90) | node13(s90, s91) | (~node14(s90, s91))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[7676, 7675])).
% 1.20/1.39 tff(7678,plain,
% 1.20/1.39 (m_main_v_state2(s90, c_c2) | node9(s90) | node8(s90) | node10(s90) | node11(s90) | node12(s90) | node13(s90, s91)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7677, 296, 7674])).
% 1.20/1.39 tff(7679,plain,
% 1.20/1.39 (node13(s90, s91)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7678, 7670, 7595, 7666, 7662, 7658, 7654])).
% 1.20/1.39 tff(7680,plain,
% 1.20/1.39 (((~![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(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)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(7681,plain,
% 1.20/1.39 (((~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)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(7682,plain,
% 1.20/1.39 (((~![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))))),
% 1.20/1.39 inference(monotonicity,[status(thm)],[7681])).
% 1.20/1.39 tff(7683,plain,
% 1.20/1.39 (((~![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)))),
% 1.20/1.39 inference(transitivity,[status(thm)],[7682, 7680])).
% 1.20/1.39 tff(7684,plain,
% 1.20/1.39 ((~![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))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(7685,plain,
% 1.20/1.39 ((~![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(s90, c_t2)) | m_main_v_state2(s91, c_t2) | (~node13(s90, s91))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[7684, 7683])).
% 1.20/1.39 tff(7686,plain,
% 1.20/1.39 (m_main_v_state2(s91, c_t2)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7685, 518, 7583, 7679])).
% 1.20/1.39 tff(7687,plain,
% 1.20/1.39 (succ(s91, s92) <=> succ(s91, s92)),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(7688,axiom,(succ(s91, s92)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound92')).
% 1.20/1.39 tff(7689,plain,
% 1.20/1.39 (succ(s91, s92)),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[7688, 7687])).
% 1.20/1.39 tff(7690,plain,
% 1.20/1.39 (((~![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))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(7691,plain,
% 1.20/1.39 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s91, s92)) | trans(s91, s92))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(7692,plain,
% 1.20/1.39 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s91, s92)) | trans(s91, s92)),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[7691, 7690])).
% 1.20/1.39 tff(7693,plain,
% 1.20/1.39 (trans(s91, s92)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7692, 7689, 32])).
% 1.20/1.39 tff(7694,plain,
% 1.20/1.39 (((~![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))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(7695,plain,
% 1.20/1.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s91, s92)) | node7(s91, s92))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(7696,plain,
% 1.20/1.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s91, s92)) | node7(s91, s92)),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[7695, 7694])).
% 1.20/1.39 tff(7697,plain,
% 1.20/1.39 (node7(s91, s92)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7696, 206, 7693])).
% 1.20/1.39 tff(7698,plain,
% 1.20/1.39 (((~![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(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))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(7699,plain,
% 1.20/1.39 ((~![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(s91, c_n1)) | (~m_main_v_state2(s91, c_t2)) | (~node7(s91, s92)) | m_main_v_state1(s92, c_t1))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(7700,plain,
% 1.20/1.39 ((~![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(s91, c_n1)) | (~m_main_v_state2(s91, c_t2)) | (~node7(s91, s92)) | m_main_v_state1(s92, c_t1)),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[7699, 7698])).
% 1.20/1.39 tff(7701,plain,
% 1.20/1.39 ((~m_main_v_state1(s91, c_n1)) | (~m_main_v_state2(s91, c_t2)) | m_main_v_state1(s92, c_t1)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7700, 651, 7697])).
% 1.20/1.39 tff(7702,plain,
% 1.20/1.39 (m_main_v_state1(s92, c_t1)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7701, 7686, 7630])).
% 1.20/1.39 tff(7703,plain,
% 1.20/1.39 (((~![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)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(7704,plain,
% 1.20/1.39 ((~![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)))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(7705,plain,
% 1.20/1.39 ((~![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))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[7704, 7703])).
% 1.20/1.39 tff(7706,plain,
% 1.20/1.39 (~m_main_v_state1(s92, c_n1)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7705, 10, 7702])).
% 1.20/1.39 tff(7707,plain,
% 1.20/1.39 (((~![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)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(7708,plain,
% 1.20/1.39 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s92, c_n1) | (~node1(s92)))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(7709,plain,
% 1.20/1.39 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s92, c_n1) | (~node1(s92))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[7708, 7707])).
% 1.20/1.39 tff(7710,plain,
% 1.20/1.39 (~node1(s92)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7709, 421, 7706])).
% 1.20/1.39 tff(7711,plain,
% 1.20/1.39 (((~![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))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(7712,plain,
% 1.20/1.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s91, s92)) | node18(s91, s92))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(7713,plain,
% 1.20/1.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s91, s92)) | node18(s91, s92)),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[7712, 7711])).
% 1.20/1.39 tff(7714,plain,
% 1.20/1.39 (node18(s91, s92)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7713, 125, 7693])).
% 1.20/1.39 tff(7715,plain,
% 1.20/1.39 (((~![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(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))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(7716,plain,
% 1.20/1.39 ((~![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(s91, c_n1)) | (~m_main_v_state2(s91, c_t2)) | (~node18(s91, s92)) | m_main_v_turn(s92, c_2))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(7717,plain,
% 1.20/1.39 ((~![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(s91, c_n1)) | (~m_main_v_state2(s91, c_t2)) | (~node18(s91, s92)) | m_main_v_turn(s92, c_2)),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[7716, 7715])).
% 1.20/1.39 tff(7718,plain,
% 1.20/1.39 ((~m_main_v_state1(s91, c_n1)) | (~m_main_v_state2(s91, c_t2)) | m_main_v_turn(s92, c_2)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7717, 760, 7714])).
% 1.20/1.39 tff(7719,plain,
% 1.20/1.39 (m_main_v_turn(s92, c_2)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7718, 7686, 7630])).
% 1.20/1.39 tff(7720,plain,
% 1.20/1.39 (((~![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)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(7721,plain,
% 1.20/1.39 ((~![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)))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(7722,plain,
% 1.20/1.39 ((~![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))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[7721, 7720])).
% 1.20/1.39 tff(7723,plain,
% 1.20/1.39 (~m_main_v_turn(s92, c_1)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7722, 156, 7719])).
% 1.20/1.39 tff(7724,plain,
% 1.20/1.39 (((~![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)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(7725,plain,
% 1.20/1.39 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s92, c_1) | (~node5(s92)))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(7726,plain,
% 1.20/1.39 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s92, c_1) | (~node5(s92))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[7725, 7724])).
% 1.20/1.39 tff(7727,plain,
% 1.20/1.39 (~node5(s92)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7726, 776, 7723])).
% 1.20/1.39 tff(7728,plain,
% 1.20/1.39 (((~![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)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(7729,plain,
% 1.20/1.39 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s92, c_n1) | (~node2(s92)))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(7730,plain,
% 1.20/1.39 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s92, c_n1) | (~node2(s92))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[7729, 7728])).
% 1.20/1.39 tff(7731,plain,
% 1.20/1.39 (~node2(s92)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7730, 787, 7706])).
% 1.20/1.39 tff(7732,plain,
% 1.20/1.39 (((~![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)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(7733,plain,
% 1.20/1.39 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s92, c_n1) | (~node3(s92)))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(7734,plain,
% 1.20/1.39 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s92, c_n1) | (~node3(s92))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[7733, 7732])).
% 1.20/1.39 tff(7735,plain,
% 1.20/1.39 (~node3(s92)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7734, 798, 7706])).
% 1.20/1.39 tff(7736,plain,
% 1.20/1.39 (((~![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)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(7737,plain,
% 1.20/1.39 ((~![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)))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(7738,plain,
% 1.20/1.39 ((~![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))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[7737, 7736])).
% 1.20/1.39 tff(7739,plain,
% 1.20/1.39 (~m_main_v_state1(s92, c_c1)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[7738, 539, 7702])).
% 1.20/1.39 tff(7740,plain,
% 1.20/1.39 (((~![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(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)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7741,plain,
% 1.20/1.40 (((~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)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7742,plain,
% 1.20/1.40 (((~![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))))),
% 1.20/1.40 inference(monotonicity,[status(thm)],[7741])).
% 1.20/1.40 tff(7743,plain,
% 1.20/1.40 (((~![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)))),
% 1.20/1.40 inference(transitivity,[status(thm)],[7742, 7740])).
% 1.20/1.40 tff(7744,plain,
% 1.20/1.40 ((~![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)))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(7745,plain,
% 1.20/1.40 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | m_main_v_state2(s90, c_n2) | (~m_main_v_state2(s91, c_n2)) | (~node13(s90, s91))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[7744, 7743])).
% 1.20/1.40 tff(7746,plain,
% 1.20/1.40 (~m_main_v_state2(s91, c_n2)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7745, 311, 7587, 7679])).
% 1.20/1.40 tff(7747,plain,
% 1.20/1.40 (((~![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)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7748,plain,
% 1.20/1.40 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s91, c_n2) | (~node9(s91)))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(7749,plain,
% 1.20/1.40 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s91, c_n2) | (~node9(s91))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[7748, 7747])).
% 1.20/1.40 tff(7750,plain,
% 1.20/1.40 (~node9(s91)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7749, 88, 7746])).
% 1.20/1.40 tff(7751,plain,
% 1.20/1.40 (((~![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)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7752,plain,
% 1.20/1.40 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s91, c_n2) | (~node10(s91)))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(7753,plain,
% 1.20/1.40 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s91, c_n2) | (~node10(s91))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[7752, 7751])).
% 1.20/1.40 tff(7754,plain,
% 1.20/1.40 (~node10(s91)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7753, 249, 7746])).
% 1.20/1.40 tff(7755,plain,
% 1.20/1.40 (((~![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)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7756,plain,
% 1.20/1.40 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s91, c_n2) | (~node8(s91)))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(7757,plain,
% 1.20/1.40 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s91, c_n2) | (~node8(s91))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[7756, 7755])).
% 1.20/1.40 tff(7758,plain,
% 1.20/1.40 (~node8(s91)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7757, 271, 7746])).
% 1.20/1.40 tff(7759,plain,
% 1.20/1.40 (((~![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))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7760,plain,
% 1.20/1.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s91, s92)) | node14(s91, s92))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(7761,plain,
% 1.20/1.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s91, s92)) | node14(s91, s92)),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[7760, 7759])).
% 1.20/1.40 tff(7762,plain,
% 1.20/1.40 (node14(s91, s92)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7761, 46, 7693])).
% 1.20/1.40 tff(7763,plain,
% 1.20/1.40 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(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))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7764,plain,
% 1.20/1.40 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | ((~m_main_v_state1(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))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(7765,plain,
% 1.20/1.40 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (~m_main_v_state1(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)),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[7764, 7763])).
% 1.20/1.40 tff(7766,plain,
% 1.20/1.40 ((~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)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7765, 617, 7762])).
% 1.20/1.40 tff(7767,plain,
% 1.20/1.40 (m_main_v_state2(s92, c_c2)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7766, 7758, 7630, 7686, 7754, 7750])).
% 1.20/1.40 tff(7768,plain,
% 1.20/1.40 (((~![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)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7769,plain,
% 1.20/1.40 ((~![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)))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(7770,plain,
% 1.20/1.40 ((~![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))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[7769, 7768])).
% 1.20/1.40 tff(7771,plain,
% 1.20/1.40 (~m_main_v_state2(s92, c_n2)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7770, 697, 7767])).
% 1.20/1.40 tff(7772,plain,
% 1.20/1.40 (((~![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)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7773,plain,
% 1.20/1.40 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s92, c_n2) | (~node4(s92)))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(7774,plain,
% 1.20/1.40 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s92, c_n2) | (~node4(s92))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[7773, 7772])).
% 1.20/1.40 tff(7775,plain,
% 1.20/1.40 (~node4(s92)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7774, 388, 7771])).
% 1.20/1.40 tff(7776,plain,
% 1.20/1.40 (succ(s92, s93) <=> succ(s92, s93)),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7777,axiom,(succ(s92, s93)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound93')).
% 1.20/1.40 tff(7778,plain,
% 1.20/1.40 (succ(s92, s93)),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[7777, 7776])).
% 1.20/1.40 tff(7779,plain,
% 1.20/1.40 (((~![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))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7780,plain,
% 1.20/1.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s92, s93)) | trans(s92, s93))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(7781,plain,
% 1.20/1.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s92, s93)) | trans(s92, s93)),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[7780, 7779])).
% 1.20/1.40 tff(7782,plain,
% 1.20/1.40 (trans(s92, s93)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7781, 7778, 32])).
% 1.20/1.40 tff(7783,plain,
% 1.20/1.40 (((~![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))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7784,plain,
% 1.20/1.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s92, s93)) | node7(s92, s93))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(7785,plain,
% 1.20/1.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s92, s93)) | node7(s92, s93)),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[7784, 7783])).
% 1.20/1.40 tff(7786,plain,
% 1.20/1.40 (node7(s92, s93)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7785, 206, 7782])).
% 1.20/1.40 tff(7787,plain,
% 1.20/1.40 (((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(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)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7788,plain,
% 1.20/1.40 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | (m_main_v_state1(s92, c_c1) | node1(s92) | node2(s92) | node3(s92) | node4(s92) | node5(s92) | node6(s92, s93) | (~node7(s92, s93)))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(7789,plain,
% 1.20/1.40 ((~![Y: $i, X: $i] : (m_main_v_state1(X, c_c1) | node1(X) | node2(X) | node3(X) | node4(X) | node5(X) | node6(X, Y) | (~node7(X, Y)))) | m_main_v_state1(s92, c_c1) | node1(s92) | node2(s92) | node3(s92) | node4(s92) | node5(s92) | node6(s92, s93) | (~node7(s92, s93))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[7788, 7787])).
% 1.20/1.40 tff(7790,plain,
% 1.20/1.40 (m_main_v_state1(s92, c_c1) | node1(s92) | node2(s92) | node3(s92) | node4(s92) | node5(s92) | node6(s92, s93)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7789, 820, 7786])).
% 1.20/1.40 tff(7791,plain,
% 1.20/1.40 (node6(s92, s93)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7790, 7775, 7739, 7735, 7731, 7727, 7710])).
% 1.20/1.40 tff(7792,plain,
% 1.20/1.40 (((~![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(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)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7793,plain,
% 1.20/1.40 (((~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)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7794,plain,
% 1.20/1.40 (((~![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))))),
% 1.20/1.40 inference(monotonicity,[status(thm)],[7793])).
% 1.20/1.40 tff(7795,plain,
% 1.20/1.40 (((~![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)))),
% 1.20/1.40 inference(transitivity,[status(thm)],[7794, 7792])).
% 1.20/1.40 tff(7796,plain,
% 1.20/1.40 ((~![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))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(7797,plain,
% 1.20/1.40 ((~![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(s92, c_t1)) | m_main_v_state1(s93, c_t1) | (~node6(s92, s93))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[7796, 7795])).
% 1.20/1.40 tff(7798,plain,
% 1.20/1.40 (m_main_v_state1(s93, c_t1)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7797, 856, 7702, 7791])).
% 1.20/1.40 tff(7799,plain,
% 1.20/1.40 (((~![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)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7800,plain,
% 1.20/1.40 ((~![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)))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(7801,plain,
% 1.20/1.40 ((~![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))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[7800, 7799])).
% 1.20/1.40 tff(7802,plain,
% 1.20/1.40 (~m_main_v_state2(s92, c_t2)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7801, 260, 7767])).
% 1.20/1.40 tff(7803,plain,
% 1.20/1.40 (((~![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)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7804,plain,
% 1.20/1.40 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s92, c_t2) | (~node12(s92)))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(7805,plain,
% 1.20/1.40 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s92, c_t2) | (~node12(s92))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[7804, 7803])).
% 1.20/1.40 tff(7806,plain,
% 1.20/1.40 (~node12(s92)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7805, 633, 7802])).
% 1.20/1.40 tff(7807,plain,
% 1.20/1.40 (((~![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)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7808,plain,
% 1.20/1.40 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s92, c_n1) | (~node11(s92)))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(7809,plain,
% 1.20/1.40 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s92, c_n1) | (~node11(s92))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[7808, 7807])).
% 1.20/1.40 tff(7810,plain,
% 1.20/1.40 (~node11(s92)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7809, 238, 7706])).
% 1.20/1.40 tff(7811,plain,
% 1.20/1.40 (((~![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)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7812,plain,
% 1.20/1.40 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s92, c_c1) | (~node10(s92)))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(7813,plain,
% 1.20/1.40 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s92, c_c1) | (~node10(s92))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[7812, 7811])).
% 1.20/1.40 tff(7814,plain,
% 1.20/1.40 (~node10(s92)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7813, 675, 7739])).
% 1.20/1.40 tff(7815,plain,
% 1.20/1.40 (((~![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)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7816,plain,
% 1.20/1.40 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s92, c_n1) | (~node9(s92)))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(7817,plain,
% 1.20/1.40 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s92, c_n1) | (~node9(s92))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[7816, 7815])).
% 1.20/1.40 tff(7818,plain,
% 1.20/1.40 (~node9(s92)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7817, 686, 7706])).
% 1.20/1.40 tff(7819,plain,
% 1.20/1.40 (((~![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)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7820,plain,
% 1.20/1.40 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s92, c_n2) | (~node8(s92)))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(7821,plain,
% 1.20/1.40 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s92, c_n2) | (~node8(s92))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[7820, 7819])).
% 1.20/1.40 tff(7822,plain,
% 1.20/1.40 (~node8(s92)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7821, 271, 7771])).
% 1.20/1.40 tff(7823,plain,
% 1.20/1.40 (((~![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))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7824,plain,
% 1.20/1.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s92, s93)) | node14(s92, s93))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(7825,plain,
% 1.20/1.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s92, s93)) | node14(s92, s93)),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[7824, 7823])).
% 1.20/1.40 tff(7826,plain,
% 1.20/1.40 (node14(s92, s93)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7825, 46, 7782])).
% 1.20/1.40 tff(7827,plain,
% 1.20/1.40 (((~![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(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)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7828,plain,
% 1.20/1.40 (((~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)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7829,plain,
% 1.20/1.40 (((~![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(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))))),
% 1.20/1.40 inference(monotonicity,[status(thm)],[7828])).
% 1.20/1.40 tff(7830,plain,
% 1.20/1.40 (((~![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(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)))),
% 1.20/1.40 inference(transitivity,[status(thm)],[7829, 7827])).
% 1.20/1.40 tff(7831,plain,
% 1.20/1.40 ((~![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(s92, c_c2)) | node9(s92) | node8(s92) | node10(s92) | node11(s92) | node12(s92) | (~node14(s92, s93)) | m_main_v_state2(s93, c_n2))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(7832,plain,
% 1.20/1.40 ((~![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(s93, c_n2) | node9(s92) | node8(s92) | node10(s92) | node11(s92) | node12(s92) | (~node14(s92, s93)) | (~m_main_v_state2(s92, c_c2))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[7831, 7830])).
% 1.20/1.40 tff(7833,plain,
% 1.20/1.40 (m_main_v_state2(s93, c_n2) | node9(s92) | node8(s92) | node10(s92) | node11(s92) | node12(s92) | (~m_main_v_state2(s92, c_c2))),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7832, 726, 7826])).
% 1.20/1.40 tff(7834,plain,
% 1.20/1.40 (m_main_v_state2(s93, c_n2)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7833, 7822, 7767, 7818, 7814, 7810, 7806])).
% 1.20/1.40 tff(7835,plain,
% 1.20/1.40 (((~![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)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7836,plain,
% 1.20/1.40 ((~![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)))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(7837,plain,
% 1.20/1.40 ((~![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))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[7836, 7835])).
% 1.20/1.40 tff(7838,plain,
% 1.20/1.40 (~m_main_v_state2(s93, c_t2)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7837, 77, 7834])).
% 1.20/1.40 tff(7839,plain,
% 1.20/1.40 (((~![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)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7840,plain,
% 1.20/1.40 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s93, c_t2) | (~node15(s93)))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(7841,plain,
% 1.20/1.40 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s93, c_t2) | (~node15(s93))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[7840, 7839])).
% 1.20/1.40 tff(7842,plain,
% 1.20/1.40 (~node15(s93)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7841, 103, 7838])).
% 1.20/1.40 tff(7843,plain,
% 1.20/1.40 (succ(s93, s94) <=> succ(s93, s94)),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7844,axiom,(succ(s93, s94)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound94')).
% 1.20/1.40 tff(7845,plain,
% 1.20/1.40 (succ(s93, s94)),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[7844, 7843])).
% 1.20/1.40 tff(7846,plain,
% 1.20/1.40 (((~![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))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7847,plain,
% 1.20/1.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s93, s94)) | trans(s93, s94))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(7848,plain,
% 1.20/1.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s93, s94)) | trans(s93, s94)),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[7847, 7846])).
% 1.20/1.40 tff(7849,plain,
% 1.20/1.40 (trans(s93, s94)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7848, 7845, 32])).
% 1.20/1.40 tff(7850,plain,
% 1.20/1.40 (((~![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))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7851,plain,
% 1.20/1.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s93, s94)) | node18(s93, s94))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(7852,plain,
% 1.20/1.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s93, s94)) | node18(s93, s94)),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[7851, 7850])).
% 1.20/1.40 tff(7853,plain,
% 1.20/1.40 (node18(s93, s94)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7852, 125, 7849])).
% 1.20/1.40 tff(7854,plain,
% 1.20/1.40 (((~![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(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))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7855,plain,
% 1.20/1.40 (((~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))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7856,plain,
% 1.20/1.40 (((~![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(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)))),
% 1.20/1.40 inference(monotonicity,[status(thm)],[7855])).
% 1.20/1.40 tff(7857,plain,
% 1.20/1.40 (((~![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(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))),
% 1.20/1.40 inference(transitivity,[status(thm)],[7856, 7854])).
% 1.20/1.40 tff(7858,plain,
% 1.20/1.40 ((~![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(s93, c_t1)) | (~m_main_v_state2(s93, c_n2)) | node15(s93) | (~node18(s93, s94)) | m_main_v_turn(s94, c_1))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(7859,plain,
% 1.20/1.40 ((~![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(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)),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[7858, 7857])).
% 1.20/1.40 tff(7860,plain,
% 1.20/1.40 (node15(s93) | (~m_main_v_state1(s93, c_t1)) | (~m_main_v_state2(s93, c_n2)) | m_main_v_turn(s94, c_1)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7859, 992, 7853])).
% 1.20/1.40 tff(7861,plain,
% 1.20/1.40 (m_main_v_turn(s94, c_1)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7860, 7842, 7834, 7798])).
% 1.20/1.40 tff(7862,plain,
% 1.20/1.40 (((~![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)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7863,plain,
% 1.20/1.40 ((~![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)))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(7864,plain,
% 1.20/1.40 ((~![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))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[7863, 7862])).
% 1.20/1.40 tff(7865,plain,
% 1.20/1.40 (~m_main_v_turn(s94, c_2)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7864, 156, 7861])).
% 1.20/1.40 tff(7866,plain,
% 1.20/1.40 (((~![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)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7867,plain,
% 1.20/1.40 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s94, c_2) | (~node12(s94)))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(7868,plain,
% 1.20/1.40 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s94, c_2) | (~node12(s94))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[7867, 7866])).
% 1.20/1.40 tff(7869,plain,
% 1.20/1.40 (~node12(s94)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7868, 184, 7865])).
% 1.20/1.40 tff(7870,plain,
% 1.20/1.40 (((~![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))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7871,plain,
% 1.20/1.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s93, s94)) | node14(s93, s94))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(7872,plain,
% 1.20/1.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s93, s94)) | node14(s93, s94)),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[7871, 7870])).
% 1.20/1.40 tff(7873,plain,
% 1.20/1.40 (node14(s93, s94)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[7872, 46, 7849])).
% 1.20/1.40 tff(7874,plain,
% 1.20/1.40 (((~![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(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))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(7875,plain,
% 1.20/1.40 ((~![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(s93, c_t1)) | (~m_main_v_state2(s93, c_n2)) | (~node14(s93, s94)) | m_main_v_state2(s94, c_t2))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(7876,plain,
% 1.20/1.41 ((~![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)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[7875, 7874])).
% 1.20/1.41 tff(7877,plain,
% 1.20/1.41 ((~m_main_v_state1(s93, c_t1)) | (~m_main_v_state2(s93, c_n2)) | m_main_v_state2(s94, c_t2)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[7876, 922, 7873])).
% 1.20/1.41 tff(7878,plain,
% 1.20/1.41 (m_main_v_state2(s94, c_t2)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[7877, 7798, 7834])).
% 1.20/1.41 tff(7879,plain,
% 1.20/1.41 (((~![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)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(7880,plain,
% 1.20/1.41 ((~![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)))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(7881,plain,
% 1.20/1.41 ((~![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))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[7880, 7879])).
% 1.20/1.41 tff(7882,plain,
% 1.20/1.41 (~m_main_v_state2(s94, c_n2)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[7881, 77, 7878])).
% 1.20/1.41 tff(7883,plain,
% 1.20/1.41 (((~![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)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(7884,plain,
% 1.20/1.41 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s94, c_n2) | (~node8(s94)))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(7885,plain,
% 1.20/1.41 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s94, c_n2) | (~node8(s94))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[7884, 7883])).
% 1.20/1.41 tff(7886,plain,
% 1.20/1.41 (~node8(s94)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[7885, 271, 7882])).
% 1.20/1.41 tff(7887,plain,
% 1.20/1.41 (((~![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)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(7888,plain,
% 1.20/1.41 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s94, c_n2) | (~node9(s94)))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(7889,plain,
% 1.20/1.41 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s94, c_n2) | (~node9(s94))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[7888, 7887])).
% 1.20/1.41 tff(7890,plain,
% 1.20/1.41 (~node9(s94)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[7889, 88, 7882])).
% 1.20/1.41 tff(7891,plain,
% 1.20/1.41 (((~![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)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(7892,plain,
% 1.20/1.41 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s94, c_n2) | (~node10(s94)))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(7893,plain,
% 1.20/1.41 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s94, c_n2) | (~node10(s94))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[7892, 7891])).
% 1.20/1.41 tff(7894,plain,
% 1.20/1.41 (~node10(s94)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[7893, 249, 7882])).
% 1.20/1.41 tff(7895,plain,
% 1.20/1.41 (((~![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)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(7896,plain,
% 1.20/1.41 ((~![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)))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(7897,plain,
% 1.20/1.41 ((~![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))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[7896, 7895])).
% 1.20/1.41 tff(7898,plain,
% 1.20/1.41 (~m_main_v_state2(s94, c_c2)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[7897, 260, 7878])).
% 1.20/1.41 tff(7899,plain,
% 1.20/1.41 (((~![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)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(7900,plain,
% 1.20/1.41 ((~![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)))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(7901,plain,
% 1.20/1.41 ((~![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))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[7900, 7899])).
% 1.20/1.41 tff(7902,plain,
% 1.20/1.41 (~m_main_v_state2(s93, c_c2)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[7901, 697, 7834])).
% 1.20/1.41 tff(7903,plain,
% 1.20/1.41 (((~![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)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(7904,plain,
% 1.20/1.41 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s93, c_c2) | (~node3(s93)))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(7905,plain,
% 1.20/1.41 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s93, c_c2) | (~node3(s93))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[7904, 7903])).
% 1.20/1.41 tff(7906,plain,
% 1.20/1.41 (~node3(s93)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[7905, 399, 7902])).
% 1.20/1.41 tff(7907,plain,
% 1.20/1.41 (((~![V: $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)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(7908,plain,
% 1.20/1.41 (((~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)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(7909,plain,
% 1.20/1.41 (((~![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))))),
% 1.20/1.41 inference(monotonicity,[status(thm)],[7908])).
% 1.20/1.41 tff(7910,plain,
% 1.20/1.41 (((~![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)))),
% 1.20/1.41 inference(transitivity,[status(thm)],[7909, 7907])).
% 1.20/1.41 tff(7911,plain,
% 1.20/1.41 ((~![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)))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(7912,plain,
% 1.20/1.41 ((~![V: $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))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[7911, 7910])).
% 1.20/1.41 tff(7913,plain,
% 1.20/1.41 (~m_main_v_state1(s93, c_n1)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[7912, 835, 7706, 7791])).
% 1.20/1.41 tff(7914,plain,
% 1.20/1.41 (((~![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)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(7915,plain,
% 1.20/1.41 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s93, c_n1) | (~node2(s93)))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(7916,plain,
% 1.20/1.41 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s93, c_n1) | (~node2(s93))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[7915, 7914])).
% 1.20/1.41 tff(7917,plain,
% 1.20/1.41 (~node2(s93)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[7916, 787, 7913])).
% 1.20/1.41 tff(7918,plain,
% 1.20/1.41 (((~![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)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(7919,plain,
% 1.20/1.41 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s93, c_t2) | (~node1(s93)))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(7920,plain,
% 1.20/1.41 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s93, c_t2) | (~node1(s93))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[7919, 7918])).
% 1.20/1.41 tff(7921,plain,
% 1.20/1.41 (~node1(s93)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[7920, 195, 7838])).
% 1.20/1.41 tff(7922,plain,
% 1.20/1.41 (((~![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))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(7923,plain,
% 1.20/1.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s93, s94)) | node7(s93, s94))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(7924,plain,
% 1.20/1.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s93, s94)) | node7(s93, s94)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[7923, 7922])).
% 1.20/1.41 tff(7925,plain,
% 1.20/1.41 (node7(s93, s94)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[7924, 206, 7849])).
% 1.20/1.41 tff(7926,plain,
% 1.20/1.41 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(7927,plain,
% 1.20/1.41 (((~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)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(7928,plain,
% 1.20/1.41 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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))))),
% 1.20/1.41 inference(monotonicity,[status(thm)],[7927])).
% 1.20/1.41 tff(7929,plain,
% 1.20/1.41 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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)))),
% 1.20/1.41 inference(transitivity,[status(thm)],[7928, 7926])).
% 1.20/1.41 tff(7930,plain,
% 1.20/1.41 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(7931,plain,
% 1.20/1.41 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[7930, 7929])).
% 1.20/1.41 tff(7932,plain,
% 1.20/1.41 ((~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)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[7931, 892, 7925])).
% 1.20/1.41 tff(7933,plain,
% 1.20/1.41 (m_main_v_state1(s94, c_c1)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[7932, 7921, 7834, 7798, 7917, 7906])).
% 1.20/1.41 tff(7934,plain,
% 1.20/1.41 (((~![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)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(7935,plain,
% 1.20/1.41 ((~![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)))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(7936,plain,
% 1.20/1.41 ((~![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))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[7935, 7934])).
% 1.20/1.41 tff(7937,plain,
% 1.20/1.41 (~m_main_v_state1(s94, c_n1)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[7936, 454, 7933])).
% 1.20/1.41 tff(7938,plain,
% 1.20/1.41 (((~![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)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(7939,plain,
% 1.20/1.41 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s94, c_n1) | (~node11(s94)))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(7940,plain,
% 1.20/1.41 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s94, c_n1) | (~node11(s94))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[7939, 7938])).
% 1.20/1.41 tff(7941,plain,
% 1.20/1.41 (~node11(s94)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[7940, 238, 7937])).
% 1.20/1.41 tff(7942,plain,
% 1.20/1.41 (succ(s94, s95) <=> succ(s94, s95)),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(7943,axiom,(succ(s94, s95)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound95')).
% 1.20/1.41 tff(7944,plain,
% 1.20/1.41 (succ(s94, s95)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[7943, 7942])).
% 1.20/1.41 tff(7945,plain,
% 1.20/1.41 (((~![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))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(7946,plain,
% 1.20/1.41 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s94, s95)) | trans(s94, s95))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(7947,plain,
% 1.20/1.41 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s94, s95)) | trans(s94, s95)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[7946, 7945])).
% 1.20/1.41 tff(7948,plain,
% 1.20/1.41 (trans(s94, s95)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[7947, 7944, 32])).
% 1.20/1.41 tff(7949,plain,
% 1.20/1.41 (((~![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))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(7950,plain,
% 1.20/1.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s94, s95)) | node14(s94, s95))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(7951,plain,
% 1.20/1.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s94, s95)) | node14(s94, s95)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[7950, 7949])).
% 1.20/1.41 tff(7952,plain,
% 1.20/1.41 (node14(s94, s95)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[7951, 46, 7948])).
% 1.20/1.41 tff(7953,plain,
% 1.20/1.41 (((~![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(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)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(7954,plain,
% 1.20/1.41 ((~![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(s94, c_c2) | node9(s94) | node8(s94) | node10(s94) | node11(s94) | node12(s94) | node13(s94, s95) | (~node14(s94, s95)))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(7955,plain,
% 1.20/1.41 ((~![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(s94, c_c2) | node9(s94) | node8(s94) | node10(s94) | node11(s94) | node12(s94) | node13(s94, s95) | (~node14(s94, s95))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[7954, 7953])).
% 1.20/1.41 tff(7956,plain,
% 1.20/1.41 (m_main_v_state2(s94, c_c2) | node9(s94) | node8(s94) | node10(s94) | node11(s94) | node12(s94) | node13(s94, s95)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[7955, 296, 7952])).
% 1.20/1.41 tff(7957,plain,
% 1.20/1.41 (node13(s94, s95)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[7956, 7941, 7898, 7894, 7890, 7886, 7869])).
% 1.20/1.41 tff(7958,plain,
% 1.20/1.41 (((~![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(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)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(7959,plain,
% 1.20/1.41 (((~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)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(7960,plain,
% 1.20/1.41 (((~![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))))),
% 1.20/1.41 inference(monotonicity,[status(thm)],[7959])).
% 1.20/1.41 tff(7961,plain,
% 1.20/1.41 (((~![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)))),
% 1.20/1.41 inference(transitivity,[status(thm)],[7960, 7958])).
% 1.20/1.41 tff(7962,plain,
% 1.20/1.41 ((~![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)))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(7963,plain,
% 1.20/1.41 ((~![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(s94, c_n2) | (~m_main_v_state2(s95, c_n2)) | (~node13(s94, s95))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[7962, 7961])).
% 1.20/1.41 tff(7964,plain,
% 1.20/1.41 (~m_main_v_state2(s95, c_n2)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[7963, 311, 7882, 7957])).
% 1.20/1.41 tff(7965,plain,
% 1.20/1.41 (((~![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)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(7966,plain,
% 1.20/1.41 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s95, c_n2) | (~node9(s95)))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(7967,plain,
% 1.20/1.41 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s95, c_n2) | (~node9(s95))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[7966, 7965])).
% 1.20/1.41 tff(7968,plain,
% 1.20/1.41 (~node9(s95)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[7967, 88, 7964])).
% 1.20/1.41 tff(7969,plain,
% 1.20/1.41 (((~![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)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(7970,plain,
% 1.20/1.41 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s95, c_n2) | (~node10(s95)))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(7971,plain,
% 1.20/1.41 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s95, c_n2) | (~node10(s95))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[7970, 7969])).
% 1.20/1.41 tff(7972,plain,
% 1.20/1.41 (~node10(s95)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[7971, 249, 7964])).
% 1.20/1.41 tff(7973,plain,
% 1.20/1.41 (((~![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(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)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(7974,plain,
% 1.20/1.41 (((~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)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(7975,plain,
% 1.20/1.41 (((~![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))))),
% 1.20/1.41 inference(monotonicity,[status(thm)],[7974])).
% 1.20/1.41 tff(7976,plain,
% 1.20/1.41 (((~![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)))),
% 1.20/1.41 inference(transitivity,[status(thm)],[7975, 7973])).
% 1.20/1.41 tff(7977,plain,
% 1.20/1.41 ((~![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))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(7978,plain,
% 1.20/1.41 ((~![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(s94, c_t2)) | m_main_v_state2(s95, c_t2) | (~node13(s94, s95))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[7977, 7976])).
% 1.20/1.41 tff(7979,plain,
% 1.20/1.41 (m_main_v_state2(s95, c_t2)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[7978, 518, 7878, 7957])).
% 1.20/1.41 tff(7980,plain,
% 1.20/1.41 (((~![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)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(7981,plain,
% 1.20/1.41 ((~![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)))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(7982,plain,
% 1.20/1.41 ((~![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))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[7981, 7980])).
% 1.20/1.41 tff(7983,plain,
% 1.20/1.41 (~m_main_v_state1(s94, c_t1)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[7982, 539, 7933])).
% 1.20/1.41 tff(7984,plain,
% 1.20/1.41 (((~![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)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(7985,plain,
% 1.20/1.41 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s94, c_t1) | (~node5(s94)))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(7986,plain,
% 1.20/1.41 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s94, c_t1) | (~node5(s94))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[7985, 7984])).
% 1.20/1.41 tff(7987,plain,
% 1.20/1.41 (~node5(s94)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[7986, 550, 7983])).
% 1.20/1.41 tff(7988,plain,
% 1.20/1.41 (((~![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)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(7989,plain,
% 1.20/1.41 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s94, c_n2) | (~node4(s94)))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(7990,plain,
% 1.20/1.41 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s94, c_n2) | (~node4(s94))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[7989, 7988])).
% 1.20/1.41 tff(7991,plain,
% 1.20/1.41 (~node4(s94)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[7990, 388, 7882])).
% 1.20/1.41 tff(7992,plain,
% 1.20/1.41 (((~![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)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(7993,plain,
% 1.20/1.41 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s94, c_c2) | (~node3(s94)))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(7994,plain,
% 1.20/1.41 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s94, c_c2) | (~node3(s94))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[7993, 7992])).
% 1.20/1.41 tff(7995,plain,
% 1.20/1.41 (~node3(s94)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[7994, 399, 7898])).
% 1.20/1.41 tff(7996,plain,
% 1.20/1.41 (((~![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)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(7997,plain,
% 1.20/1.41 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s94, c_n2) | (~node2(s94)))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(7998,plain,
% 1.20/1.42 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s94, c_n2) | (~node2(s94))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[7997, 7996])).
% 1.20/1.42 tff(7999,plain,
% 1.20/1.42 (~node2(s94)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[7998, 410, 7882])).
% 1.20/1.42 tff(8000,plain,
% 1.20/1.42 (((~![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)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8001,plain,
% 1.20/1.42 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s94, c_n1) | (~node1(s94)))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(8002,plain,
% 1.20/1.42 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s94, c_n1) | (~node1(s94))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8001, 8000])).
% 1.20/1.42 tff(8003,plain,
% 1.20/1.42 (~node1(s94)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8002, 421, 7937])).
% 1.20/1.42 tff(8004,plain,
% 1.20/1.42 (((~![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))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8005,plain,
% 1.20/1.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s94, s95)) | node7(s94, s95))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(8006,plain,
% 1.20/1.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s94, s95)) | node7(s94, s95)),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8005, 8004])).
% 1.20/1.42 tff(8007,plain,
% 1.20/1.42 (node7(s94, s95)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8006, 206, 7948])).
% 1.20/1.42 tff(8008,plain,
% 1.20/1.42 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8009,plain,
% 1.20/1.42 (((~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)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8010,plain,
% 1.20/1.42 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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))))),
% 1.20/1.42 inference(monotonicity,[status(thm)],[8009])).
% 1.20/1.42 tff(8011,plain,
% 1.20/1.42 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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)))),
% 1.20/1.42 inference(transitivity,[status(thm)],[8010, 8008])).
% 1.20/1.42 tff(8012,plain,
% 1.20/1.42 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(8013,plain,
% 1.20/1.42 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8012, 8011])).
% 1.20/1.42 tff(8014,plain,
% 1.20/1.42 (m_main_v_state1(s95, c_n1) | (~m_main_v_state1(s94, c_c1)) | node1(s94) | node2(s94) | node3(s94) | node4(s94) | node5(s94)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8013, 584, 8007])).
% 1.20/1.42 tff(8015,plain,
% 1.20/1.42 (m_main_v_state1(s95, c_n1)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8014, 8003, 7933, 7999, 7995, 7991, 7987])).
% 1.20/1.42 tff(8016,plain,
% 1.20/1.42 (((~![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)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8017,plain,
% 1.20/1.42 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s95, c_n2) | (~node8(s95)))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(8018,plain,
% 1.20/1.42 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s95, c_n2) | (~node8(s95))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8017, 8016])).
% 1.20/1.42 tff(8019,plain,
% 1.20/1.42 (~node8(s95)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8018, 271, 7964])).
% 1.20/1.42 tff(8020,plain,
% 1.20/1.42 (succ(s95, s96) <=> succ(s95, s96)),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8021,axiom,(succ(s95, s96)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound96')).
% 1.20/1.42 tff(8022,plain,
% 1.20/1.42 (succ(s95, s96)),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8021, 8020])).
% 1.20/1.42 tff(8023,plain,
% 1.20/1.42 (((~![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))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8024,plain,
% 1.20/1.42 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s95, s96)) | trans(s95, s96))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(8025,plain,
% 1.20/1.42 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s95, s96)) | trans(s95, s96)),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8024, 8023])).
% 1.20/1.42 tff(8026,plain,
% 1.20/1.42 (trans(s95, s96)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8025, 8022, 32])).
% 1.20/1.42 tff(8027,plain,
% 1.20/1.42 (((~![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))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8028,plain,
% 1.20/1.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s95, s96)) | node14(s95, s96))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(8029,plain,
% 1.20/1.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s95, s96)) | node14(s95, s96)),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8028, 8027])).
% 1.20/1.42 tff(8030,plain,
% 1.20/1.42 (node14(s95, s96)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8029, 46, 8026])).
% 1.20/1.42 tff(8031,plain,
% 1.20/1.42 (((~![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))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8032,plain,
% 1.20/1.42 ((~![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))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(8033,plain,
% 1.20/1.42 ((~![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)),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8032, 8031])).
% 1.20/1.42 tff(8034,plain,
% 1.20/1.42 ((~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)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8033, 617, 8030])).
% 1.20/1.42 tff(8035,plain,
% 1.20/1.42 (m_main_v_state2(s96, c_c2)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8034, 8019, 8015, 7979, 7972, 7968])).
% 1.20/1.42 tff(8036,plain,
% 1.20/1.42 (((~![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)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8037,plain,
% 1.20/1.42 ((~![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)))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(8038,plain,
% 1.20/1.42 ((~![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))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8037, 8036])).
% 1.20/1.42 tff(8039,plain,
% 1.20/1.42 (~m_main_v_state2(s96, c_t2)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8038, 260, 8035])).
% 1.20/1.42 tff(8040,plain,
% 1.20/1.42 (((~![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)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8041,plain,
% 1.20/1.42 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s96, c_t2) | (~node12(s96)))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(8042,plain,
% 1.20/1.42 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s96, c_t2) | (~node12(s96))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8041, 8040])).
% 1.20/1.42 tff(8043,plain,
% 1.20/1.42 (~node12(s96)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8042, 633, 8039])).
% 1.20/1.42 tff(8044,plain,
% 1.20/1.42 (((~![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))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8045,plain,
% 1.20/1.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s95, s96)) | node7(s95, s96))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(8046,plain,
% 1.20/1.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s95, s96)) | node7(s95, s96)),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8045, 8044])).
% 1.20/1.42 tff(8047,plain,
% 1.20/1.42 (node7(s95, s96)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8046, 206, 8026])).
% 1.20/1.42 tff(8048,plain,
% 1.20/1.42 (((~![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))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8049,plain,
% 1.20/1.42 ((~![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))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(8050,plain,
% 1.20/1.42 ((~![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)),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8049, 8048])).
% 1.20/1.42 tff(8051,plain,
% 1.20/1.42 ((~m_main_v_state1(s95, c_n1)) | (~m_main_v_state2(s95, c_t2)) | m_main_v_state1(s96, c_t1)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8050, 651, 8047])).
% 1.20/1.42 tff(8052,plain,
% 1.20/1.42 (m_main_v_state1(s96, c_t1)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8051, 7979, 8015])).
% 1.20/1.42 tff(8053,plain,
% 1.20/1.42 (((~![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)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8054,plain,
% 1.20/1.42 ((~![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)))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(8055,plain,
% 1.20/1.42 ((~![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))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8054, 8053])).
% 1.20/1.42 tff(8056,plain,
% 1.20/1.42 (~m_main_v_state1(s96, c_n1)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8055, 10, 8052])).
% 1.20/1.42 tff(8057,plain,
% 1.20/1.42 (((~![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)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8058,plain,
% 1.20/1.42 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s96, c_n1) | (~node11(s96)))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(8059,plain,
% 1.20/1.42 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s96, c_n1) | (~node11(s96))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8058, 8057])).
% 1.20/1.42 tff(8060,plain,
% 1.20/1.42 (~node11(s96)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8059, 238, 8056])).
% 1.20/1.42 tff(8061,plain,
% 1.20/1.42 (((~![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)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8062,plain,
% 1.20/1.42 ((~![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)))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(8063,plain,
% 1.20/1.42 ((~![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))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8062, 8061])).
% 1.20/1.42 tff(8064,plain,
% 1.20/1.42 (~m_main_v_state1(s96, c_c1)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8063, 539, 8052])).
% 1.20/1.42 tff(8065,plain,
% 1.20/1.42 (((~![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)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8066,plain,
% 1.20/1.42 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s96, c_c1) | (~node10(s96)))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(8067,plain,
% 1.20/1.42 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s96, c_c1) | (~node10(s96))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8066, 8065])).
% 1.20/1.42 tff(8068,plain,
% 1.20/1.42 (~node10(s96)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8067, 675, 8064])).
% 1.20/1.42 tff(8069,plain,
% 1.20/1.42 (((~![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)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8070,plain,
% 1.20/1.42 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s96, c_n1) | (~node9(s96)))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(8071,plain,
% 1.20/1.42 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s96, c_n1) | (~node9(s96))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8070, 8069])).
% 1.20/1.42 tff(8072,plain,
% 1.20/1.42 (~node9(s96)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8071, 686, 8056])).
% 1.20/1.42 tff(8073,plain,
% 1.20/1.42 (((~![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)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8074,plain,
% 1.20/1.42 ((~![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)))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(8075,plain,
% 1.20/1.42 ((~![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))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8074, 8073])).
% 1.20/1.42 tff(8076,plain,
% 1.20/1.42 (~m_main_v_state2(s96, c_n2)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8075, 697, 8035])).
% 1.20/1.42 tff(8077,plain,
% 1.20/1.42 (((~![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)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8078,plain,
% 1.20/1.42 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s96, c_n2) | (~node8(s96)))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(8079,plain,
% 1.20/1.42 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s96, c_n2) | (~node8(s96))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8078, 8077])).
% 1.20/1.42 tff(8080,plain,
% 1.20/1.42 (~node8(s96)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8079, 271, 8076])).
% 1.20/1.42 tff(8081,plain,
% 1.20/1.42 (succ(s96, s97) <=> succ(s96, s97)),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8082,axiom,(succ(s96, s97)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound97')).
% 1.20/1.42 tff(8083,plain,
% 1.20/1.42 (succ(s96, s97)),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8082, 8081])).
% 1.20/1.42 tff(8084,plain,
% 1.20/1.42 (((~![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))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8085,plain,
% 1.20/1.42 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s96, s97)) | trans(s96, s97))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(8086,plain,
% 1.20/1.42 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s96, s97)) | trans(s96, s97)),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8085, 8084])).
% 1.20/1.42 tff(8087,plain,
% 1.20/1.42 (trans(s96, s97)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8086, 8083, 32])).
% 1.20/1.42 tff(8088,plain,
% 1.20/1.42 (((~![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))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8089,plain,
% 1.20/1.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s96, s97)) | node14(s96, s97))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(8090,plain,
% 1.20/1.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s96, s97)) | node14(s96, s97)),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8089, 8088])).
% 1.20/1.42 tff(8091,plain,
% 1.20/1.42 (node14(s96, s97)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8090, 46, 8087])).
% 1.20/1.42 tff(8092,plain,
% 1.20/1.42 (((~![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(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)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8093,plain,
% 1.20/1.42 (((~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)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8094,plain,
% 1.20/1.42 (((~![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(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))))),
% 1.20/1.42 inference(monotonicity,[status(thm)],[8093])).
% 1.20/1.42 tff(8095,plain,
% 1.20/1.42 (((~![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(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)))),
% 1.20/1.42 inference(transitivity,[status(thm)],[8094, 8092])).
% 1.20/1.42 tff(8096,plain,
% 1.20/1.42 ((~![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(s96, c_c2)) | node9(s96) | node8(s96) | node10(s96) | node11(s96) | node12(s96) | (~node14(s96, s97)) | m_main_v_state2(s97, c_n2))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(8097,plain,
% 1.20/1.42 ((~![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(s97, c_n2) | node9(s96) | node8(s96) | node10(s96) | node11(s96) | node12(s96) | (~node14(s96, s97)) | (~m_main_v_state2(s96, c_c2))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8096, 8095])).
% 1.20/1.42 tff(8098,plain,
% 1.20/1.42 (m_main_v_state2(s97, c_n2) | node9(s96) | node8(s96) | node10(s96) | node11(s96) | node12(s96) | (~m_main_v_state2(s96, c_c2))),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8097, 726, 8091])).
% 1.20/1.42 tff(8099,plain,
% 1.20/1.42 (m_main_v_state2(s97, c_n2)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8098, 8080, 8035, 8072, 8068, 8060, 8043])).
% 1.20/1.42 tff(8100,plain,
% 1.20/1.42 (((~![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)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8101,plain,
% 1.20/1.42 ((~![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)))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(8102,plain,
% 1.20/1.42 ((~![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))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8101, 8100])).
% 1.20/1.42 tff(8103,plain,
% 1.20/1.42 (~m_main_v_state2(s97, c_t2)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8102, 77, 8099])).
% 1.20/1.42 tff(8104,plain,
% 1.20/1.42 (^[X: $i] : refl((m_main_v_state2(X, c_t2) | (~node26(X))) <=> (m_main_v_state2(X, c_t2) | (~node26(X))))),
% 1.20/1.42 inference(bind,[status(th)],[])).
% 1.20/1.42 tff(8105,plain,
% 1.20/1.42 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X))) <=> ![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))),
% 1.20/1.42 inference(quant_intro,[status(thm)],[8104])).
% 1.20/1.42 tff(8106,plain,
% 1.20/1.42 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X))) <=> ![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8107,axiom,(![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty17')).
% 1.20/1.42 tff(8108,plain,
% 1.20/1.42 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8107, 8106])).
% 1.20/1.42 tff(8109,plain,(
% 1.20/1.42 ![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))),
% 1.20/1.42 inference(skolemize,[status(sab)],[8108])).
% 1.20/1.42 tff(8110,plain,
% 1.20/1.42 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8109, 8105])).
% 1.20/1.42 tff(8111,plain,
% 1.20/1.42 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s97, c_t2) | (~node26(s97)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s97, c_t2) | (~node26(s97)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8112,plain,
% 1.20/1.42 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s97, c_t2) | (~node26(s97)))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(8113,plain,
% 1.20/1.42 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s97, c_t2) | (~node26(s97))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8112, 8111])).
% 1.20/1.42 tff(8114,plain,
% 1.20/1.42 (~node26(s97)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8113, 8110, 8103])).
% 1.20/1.42 tff(8115,plain,
% 1.20/1.42 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s96)) | (~m_main_v_state2(s96, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s96)) | (~m_main_v_state2(s96, c_c2)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8116,plain,
% 1.20/1.42 (((~m_main_v_state2(s96, c_c2)) | (~always25(s96))) <=> ((~always25(s96)) | (~m_main_v_state2(s96, c_c2)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8117,plain,
% 1.20/1.42 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s96, c_c2)) | (~always25(s96)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s96)) | (~m_main_v_state2(s96, c_c2))))),
% 1.20/1.42 inference(monotonicity,[status(thm)],[8116])).
% 1.20/1.42 tff(8118,plain,
% 1.20/1.42 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s96, c_c2)) | (~always25(s96)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s96)) | (~m_main_v_state2(s96, c_c2)))),
% 1.20/1.42 inference(transitivity,[status(thm)],[8117, 8115])).
% 1.20/1.42 tff(8119,plain,
% 1.20/1.42 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s96, c_c2)) | (~always25(s96)))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(8120,plain,
% 1.20/1.42 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s96)) | (~m_main_v_state2(s96, c_c2))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8119, 8118])).
% 1.20/1.42 tff(8121,plain,
% 1.20/1.42 (~always25(s96)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8120, 3908, 8035])).
% 1.20/1.42 tff(8122,plain,
% 1.20/1.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s95, s96)) | (~always25(s95)) | always25(s96))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s95, s96)) | (~always25(s95)) | always25(s96))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8123,plain,
% 1.20/1.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s95, s96)) | (~always25(s95)) | always25(s96))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(8124,plain,
% 1.20/1.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s95, s96)) | (~always25(s95)) | always25(s96)),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8123, 8122])).
% 1.20/1.42 tff(8125,plain,
% 1.20/1.42 ((~always25(s95)) | always25(s96)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8124, 3934, 8026])).
% 1.20/1.42 tff(8126,plain,
% 1.20/1.42 (~always25(s95)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8125, 8121])).
% 1.20/1.42 tff(8127,plain,
% 1.20/1.42 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s95) | (~node26(s95)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s95) | (~node26(s95)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8128,plain,
% 1.20/1.42 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s95) | (~node26(s95)))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(8129,plain,
% 1.20/1.42 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s95) | (~node26(s95))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8128, 8127])).
% 1.20/1.42 tff(8130,plain,
% 1.20/1.42 (~node26(s95)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8129, 3949, 8126])).
% 1.20/1.42 tff(8131,plain,
% 1.20/1.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s94, s95)) | (~always25(s94)) | always25(s95))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s94, s95)) | (~always25(s94)) | always25(s95))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8132,plain,
% 1.20/1.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s94, s95)) | (~always25(s94)) | always25(s95))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(8133,plain,
% 1.20/1.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s94, s95)) | (~always25(s94)) | always25(s95)),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8132, 8131])).
% 1.20/1.42 tff(8134,plain,
% 1.20/1.42 ((~always25(s94)) | always25(s95)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8133, 3934, 7948])).
% 1.20/1.42 tff(8135,plain,
% 1.20/1.42 (~always25(s94)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8134, 8126])).
% 1.20/1.42 tff(8136,plain,
% 1.20/1.42 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s94) | (~node26(s94)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s94) | (~node26(s94)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8137,plain,
% 1.20/1.42 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s94) | (~node26(s94)))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(8138,plain,
% 1.20/1.42 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s94) | (~node26(s94))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8137, 8136])).
% 1.20/1.42 tff(8139,plain,
% 1.20/1.42 (~node26(s94)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8138, 3949, 8135])).
% 1.20/1.42 tff(8140,plain,
% 1.20/1.42 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s93, c_t2) | (~node26(s93)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s93, c_t2) | (~node26(s93)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8141,plain,
% 1.20/1.42 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s93, c_t2) | (~node26(s93)))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(8142,plain,
% 1.20/1.42 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s93, c_t2) | (~node26(s93))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[8141, 8140])).
% 1.20/1.42 tff(8143,plain,
% 1.20/1.42 (~node26(s93)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[8142, 8110, 7838])).
% 1.20/1.42 tff(8144,plain,
% 1.20/1.42 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s92)) | (~m_main_v_state2(s92, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s92)) | (~m_main_v_state2(s92, c_c2)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(8145,plain,
% 1.20/1.42 (((~m_main_v_state2(s92, c_c2)) | (~always25(s92))) <=> ((~always25(s92)) | (~m_main_v_state2(s92, c_c2)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8146,plain,
% 1.26/1.43 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s92, c_c2)) | (~always25(s92)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s92)) | (~m_main_v_state2(s92, c_c2))))),
% 1.26/1.43 inference(monotonicity,[status(thm)],[8145])).
% 1.26/1.43 tff(8147,plain,
% 1.26/1.43 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s92, c_c2)) | (~always25(s92)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s92)) | (~m_main_v_state2(s92, c_c2)))),
% 1.26/1.43 inference(transitivity,[status(thm)],[8146, 8144])).
% 1.26/1.43 tff(8148,plain,
% 1.26/1.43 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s92, c_c2)) | (~always25(s92)))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8149,plain,
% 1.26/1.43 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s92)) | (~m_main_v_state2(s92, c_c2))),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8148, 8147])).
% 1.26/1.43 tff(8150,plain,
% 1.26/1.43 (~always25(s92)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8149, 3908, 7767])).
% 1.26/1.43 tff(8151,plain,
% 1.26/1.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s91, s92)) | (~always25(s91)) | always25(s92))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s91, s92)) | (~always25(s91)) | always25(s92))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8152,plain,
% 1.26/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s91, s92)) | (~always25(s91)) | always25(s92))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8153,plain,
% 1.26/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s91, s92)) | (~always25(s91)) | always25(s92)),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8152, 8151])).
% 1.26/1.43 tff(8154,plain,
% 1.26/1.43 ((~always25(s91)) | always25(s92)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8153, 3934, 7693])).
% 1.26/1.43 tff(8155,plain,
% 1.26/1.43 (~always25(s91)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8154, 8150])).
% 1.26/1.43 tff(8156,plain,
% 1.26/1.43 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s91) | (~node26(s91)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s91) | (~node26(s91)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8157,plain,
% 1.26/1.43 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s91) | (~node26(s91)))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8158,plain,
% 1.26/1.43 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s91) | (~node26(s91))),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8157, 8156])).
% 1.26/1.43 tff(8159,plain,
% 1.26/1.43 (~node26(s91)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8158, 3949, 8155])).
% 1.26/1.43 tff(8160,plain,
% 1.26/1.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s90, s91)) | (~always25(s90)) | always25(s91))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s90, s91)) | (~always25(s90)) | always25(s91))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8161,plain,
% 1.26/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s90, s91)) | (~always25(s90)) | always25(s91))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8162,plain,
% 1.26/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s90, s91)) | (~always25(s90)) | always25(s91)),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8161, 8160])).
% 1.26/1.43 tff(8163,plain,
% 1.26/1.43 ((~always25(s90)) | always25(s91)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8162, 3934, 7618])).
% 1.26/1.43 tff(8164,plain,
% 1.26/1.43 (~always25(s90)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8163, 8155])).
% 1.26/1.43 tff(8165,plain,
% 1.26/1.43 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s90) | (~node26(s90)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s90) | (~node26(s90)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8166,plain,
% 1.26/1.43 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s90) | (~node26(s90)))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8167,plain,
% 1.26/1.43 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s90) | (~node26(s90))),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8166, 8165])).
% 1.26/1.43 tff(8168,plain,
% 1.26/1.43 (~node26(s90)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8167, 3949, 8164])).
% 1.26/1.43 tff(8169,plain,
% 1.26/1.43 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s89, c_t2) | (~node26(s89)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s89, c_t2) | (~node26(s89)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8170,plain,
% 1.26/1.43 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s89, c_t2) | (~node26(s89)))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8171,plain,
% 1.26/1.43 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s89, c_t2) | (~node26(s89))),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8170, 8169])).
% 1.26/1.43 tff(8172,plain,
% 1.26/1.43 (~node26(s89)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8171, 8110, 7543])).
% 1.26/1.43 tff(8173,plain,
% 1.26/1.43 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s88)) | (~m_main_v_state2(s88, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s88)) | (~m_main_v_state2(s88, c_c2)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8174,plain,
% 1.26/1.43 (((~m_main_v_state2(s88, c_c2)) | (~always25(s88))) <=> ((~always25(s88)) | (~m_main_v_state2(s88, c_c2)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8175,plain,
% 1.26/1.43 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s88, c_c2)) | (~always25(s88)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s88)) | (~m_main_v_state2(s88, c_c2))))),
% 1.26/1.43 inference(monotonicity,[status(thm)],[8174])).
% 1.26/1.43 tff(8176,plain,
% 1.26/1.43 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s88, c_c2)) | (~always25(s88)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s88)) | (~m_main_v_state2(s88, c_c2)))),
% 1.26/1.43 inference(transitivity,[status(thm)],[8175, 8173])).
% 1.26/1.43 tff(8177,plain,
% 1.26/1.43 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s88, c_c2)) | (~always25(s88)))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8178,plain,
% 1.26/1.43 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s88)) | (~m_main_v_state2(s88, c_c2))),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8177, 8176])).
% 1.26/1.43 tff(8179,plain,
% 1.26/1.43 (~always25(s88)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8178, 3908, 7407])).
% 1.26/1.43 tff(8180,plain,
% 1.26/1.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s87, s88)) | (~always25(s87)) | always25(s88))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s87, s88)) | (~always25(s87)) | always25(s88))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8181,plain,
% 1.26/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s87, s88)) | (~always25(s87)) | always25(s88))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8182,plain,
% 1.26/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s87, s88)) | (~always25(s87)) | always25(s88)),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8181, 8180])).
% 1.26/1.43 tff(8183,plain,
% 1.26/1.43 ((~always25(s87)) | always25(s88)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8182, 3934, 7398])).
% 1.26/1.43 tff(8184,plain,
% 1.26/1.43 (~always25(s87)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8183, 8179])).
% 1.26/1.43 tff(8185,plain,
% 1.26/1.43 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s87) | (~node26(s87)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s87) | (~node26(s87)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8186,plain,
% 1.26/1.43 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s87) | (~node26(s87)))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8187,plain,
% 1.26/1.43 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s87) | (~node26(s87))),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8186, 8185])).
% 1.26/1.43 tff(8188,plain,
% 1.26/1.43 (~node26(s87)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8187, 3949, 8184])).
% 1.26/1.43 tff(8189,plain,
% 1.26/1.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s86, s87)) | (~always25(s86)) | always25(s87))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s86, s87)) | (~always25(s86)) | always25(s87))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8190,plain,
% 1.26/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s86, s87)) | (~always25(s86)) | always25(s87))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8191,plain,
% 1.26/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s86, s87)) | (~always25(s86)) | always25(s87)),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8190, 8189])).
% 1.26/1.43 tff(8192,plain,
% 1.26/1.43 ((~always25(s86)) | always25(s87)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8191, 3934, 7320])).
% 1.26/1.43 tff(8193,plain,
% 1.26/1.43 (~always25(s86)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8192, 8184])).
% 1.26/1.43 tff(8194,plain,
% 1.26/1.43 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s86) | (~node26(s86)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s86) | (~node26(s86)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8195,plain,
% 1.26/1.43 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s86) | (~node26(s86)))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8196,plain,
% 1.26/1.43 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s86) | (~node26(s86))),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8195, 8194])).
% 1.26/1.43 tff(8197,plain,
% 1.26/1.43 (~node26(s86)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8196, 3949, 8193])).
% 1.26/1.43 tff(8198,plain,
% 1.26/1.43 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s85, c_t2) | (~node26(s85)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s85, c_t2) | (~node26(s85)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8199,plain,
% 1.26/1.43 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s85, c_t2) | (~node26(s85)))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8200,plain,
% 1.26/1.43 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s85, c_t2) | (~node26(s85))),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8199, 8198])).
% 1.26/1.43 tff(8201,plain,
% 1.26/1.43 (~node26(s85)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8200, 8110, 7210])).
% 1.26/1.43 tff(8202,plain,
% 1.26/1.43 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s84)) | (~m_main_v_state2(s84, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s84)) | (~m_main_v_state2(s84, c_c2)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8203,plain,
% 1.26/1.43 (((~m_main_v_state2(s84, c_c2)) | (~always25(s84))) <=> ((~always25(s84)) | (~m_main_v_state2(s84, c_c2)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8204,plain,
% 1.26/1.43 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s84, c_c2)) | (~always25(s84)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s84)) | (~m_main_v_state2(s84, c_c2))))),
% 1.26/1.43 inference(monotonicity,[status(thm)],[8203])).
% 1.26/1.43 tff(8205,plain,
% 1.26/1.43 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s84, c_c2)) | (~always25(s84)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s84)) | (~m_main_v_state2(s84, c_c2)))),
% 1.26/1.43 inference(transitivity,[status(thm)],[8204, 8202])).
% 1.26/1.43 tff(8206,plain,
% 1.26/1.43 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s84, c_c2)) | (~always25(s84)))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8207,plain,
% 1.26/1.43 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s84)) | (~m_main_v_state2(s84, c_c2))),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8206, 8205])).
% 1.26/1.43 tff(8208,plain,
% 1.26/1.43 (~always25(s84)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8207, 3908, 7139])).
% 1.26/1.43 tff(8209,plain,
% 1.26/1.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s83, s84)) | (~always25(s83)) | always25(s84))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s83, s84)) | (~always25(s83)) | always25(s84))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8210,plain,
% 1.26/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s83, s84)) | (~always25(s83)) | always25(s84))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8211,plain,
% 1.26/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s83, s84)) | (~always25(s83)) | always25(s84)),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8210, 8209])).
% 1.26/1.43 tff(8212,plain,
% 1.26/1.43 ((~always25(s83)) | always25(s84)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8211, 3934, 7065])).
% 1.26/1.43 tff(8213,plain,
% 1.26/1.43 (~always25(s83)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8212, 8208])).
% 1.26/1.43 tff(8214,plain,
% 1.26/1.43 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s83) | (~node26(s83)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s83) | (~node26(s83)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8215,plain,
% 1.26/1.43 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s83) | (~node26(s83)))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8216,plain,
% 1.26/1.43 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s83) | (~node26(s83))),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8215, 8214])).
% 1.26/1.43 tff(8217,plain,
% 1.26/1.43 (~node26(s83)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8216, 3949, 8213])).
% 1.26/1.43 tff(8218,plain,
% 1.26/1.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s82, s83)) | (~always25(s82)) | always25(s83))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s82, s83)) | (~always25(s82)) | always25(s83))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8219,plain,
% 1.26/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s82, s83)) | (~always25(s82)) | always25(s83))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8220,plain,
% 1.26/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s82, s83)) | (~always25(s82)) | always25(s83)),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8219, 8218])).
% 1.26/1.43 tff(8221,plain,
% 1.26/1.43 ((~always25(s82)) | always25(s83)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8220, 3934, 6990])).
% 1.26/1.43 tff(8222,plain,
% 1.26/1.43 (~always25(s82)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8221, 8213])).
% 1.26/1.43 tff(8223,plain,
% 1.26/1.43 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s82) | (~node26(s82)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s82) | (~node26(s82)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8224,plain,
% 1.26/1.43 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s82) | (~node26(s82)))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8225,plain,
% 1.26/1.43 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s82) | (~node26(s82))),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8224, 8223])).
% 1.26/1.43 tff(8226,plain,
% 1.26/1.43 (~node26(s82)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8225, 3949, 8222])).
% 1.26/1.43 tff(8227,plain,
% 1.26/1.43 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s81, c_t2) | (~node26(s81)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s81, c_t2) | (~node26(s81)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8228,plain,
% 1.26/1.43 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s81, c_t2) | (~node26(s81)))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8229,plain,
% 1.26/1.43 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s81, c_t2) | (~node26(s81))),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8228, 8227])).
% 1.26/1.43 tff(8230,plain,
% 1.26/1.43 (~node26(s81)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8229, 8110, 6915])).
% 1.26/1.43 tff(8231,plain,
% 1.26/1.43 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s80)) | (~m_main_v_state2(s80, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s80)) | (~m_main_v_state2(s80, c_c2)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8232,plain,
% 1.26/1.43 (((~m_main_v_state2(s80, c_c2)) | (~always25(s80))) <=> ((~always25(s80)) | (~m_main_v_state2(s80, c_c2)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8233,plain,
% 1.26/1.43 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s80, c_c2)) | (~always25(s80)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s80)) | (~m_main_v_state2(s80, c_c2))))),
% 1.26/1.43 inference(monotonicity,[status(thm)],[8232])).
% 1.26/1.43 tff(8234,plain,
% 1.26/1.43 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s80, c_c2)) | (~always25(s80)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s80)) | (~m_main_v_state2(s80, c_c2)))),
% 1.26/1.43 inference(transitivity,[status(thm)],[8233, 8231])).
% 1.26/1.43 tff(8235,plain,
% 1.26/1.43 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s80, c_c2)) | (~always25(s80)))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8236,plain,
% 1.26/1.43 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s80)) | (~m_main_v_state2(s80, c_c2))),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8235, 8234])).
% 1.26/1.43 tff(8237,plain,
% 1.26/1.43 (~always25(s80)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8236, 3908, 6779])).
% 1.26/1.43 tff(8238,plain,
% 1.26/1.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s79, s80)) | (~always25(s79)) | always25(s80))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s79, s80)) | (~always25(s79)) | always25(s80))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8239,plain,
% 1.26/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s79, s80)) | (~always25(s79)) | always25(s80))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8240,plain,
% 1.26/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s79, s80)) | (~always25(s79)) | always25(s80)),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8239, 8238])).
% 1.26/1.43 tff(8241,plain,
% 1.26/1.43 ((~always25(s79)) | always25(s80)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8240, 3934, 6770])).
% 1.26/1.43 tff(8242,plain,
% 1.26/1.43 (~always25(s79)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8241, 8237])).
% 1.26/1.43 tff(8243,plain,
% 1.26/1.43 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s79) | (~node26(s79)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s79) | (~node26(s79)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8244,plain,
% 1.26/1.43 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s79) | (~node26(s79)))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8245,plain,
% 1.26/1.43 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s79) | (~node26(s79))),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8244, 8243])).
% 1.26/1.43 tff(8246,plain,
% 1.26/1.43 (~node26(s79)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8245, 3949, 8242])).
% 1.26/1.43 tff(8247,plain,
% 1.26/1.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s78, s79)) | (~always25(s78)) | always25(s79))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s78, s79)) | (~always25(s78)) | always25(s79))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8248,plain,
% 1.26/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s78, s79)) | (~always25(s78)) | always25(s79))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8249,plain,
% 1.26/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s78, s79)) | (~always25(s78)) | always25(s79)),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8248, 8247])).
% 1.26/1.43 tff(8250,plain,
% 1.26/1.43 ((~always25(s78)) | always25(s79)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8249, 3934, 6692])).
% 1.26/1.43 tff(8251,plain,
% 1.26/1.43 (~always25(s78)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8250, 8242])).
% 1.26/1.43 tff(8252,plain,
% 1.26/1.43 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s78) | (~node26(s78)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s78) | (~node26(s78)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8253,plain,
% 1.26/1.43 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s78) | (~node26(s78)))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8254,plain,
% 1.26/1.43 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s78) | (~node26(s78))),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8253, 8252])).
% 1.26/1.43 tff(8255,plain,
% 1.26/1.43 (~node26(s78)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8254, 3949, 8251])).
% 1.26/1.43 tff(8256,plain,
% 1.26/1.43 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s77, c_t2) | (~node26(s77)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s77, c_t2) | (~node26(s77)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8257,plain,
% 1.26/1.43 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s77, c_t2) | (~node26(s77)))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8258,plain,
% 1.26/1.43 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s77, c_t2) | (~node26(s77))),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8257, 8256])).
% 1.26/1.43 tff(8259,plain,
% 1.26/1.43 (~node26(s77)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8258, 8110, 6582])).
% 1.26/1.43 tff(8260,plain,
% 1.26/1.43 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s76)) | (~m_main_v_state2(s76, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s76)) | (~m_main_v_state2(s76, c_c2)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8261,plain,
% 1.26/1.43 (((~m_main_v_state2(s76, c_c2)) | (~always25(s76))) <=> ((~always25(s76)) | (~m_main_v_state2(s76, c_c2)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8262,plain,
% 1.26/1.43 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s76, c_c2)) | (~always25(s76)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s76)) | (~m_main_v_state2(s76, c_c2))))),
% 1.26/1.43 inference(monotonicity,[status(thm)],[8261])).
% 1.26/1.43 tff(8263,plain,
% 1.26/1.43 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s76, c_c2)) | (~always25(s76)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s76)) | (~m_main_v_state2(s76, c_c2)))),
% 1.26/1.43 inference(transitivity,[status(thm)],[8262, 8260])).
% 1.26/1.43 tff(8264,plain,
% 1.26/1.43 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s76, c_c2)) | (~always25(s76)))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8265,plain,
% 1.26/1.43 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s76)) | (~m_main_v_state2(s76, c_c2))),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8264, 8263])).
% 1.26/1.43 tff(8266,plain,
% 1.26/1.43 (~always25(s76)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8265, 3908, 6511])).
% 1.26/1.43 tff(8267,plain,
% 1.26/1.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s75, s76)) | (~always25(s75)) | always25(s76))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s75, s76)) | (~always25(s75)) | always25(s76))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8268,plain,
% 1.26/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s75, s76)) | (~always25(s75)) | always25(s76))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8269,plain,
% 1.26/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s75, s76)) | (~always25(s75)) | always25(s76)),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8268, 8267])).
% 1.26/1.43 tff(8270,plain,
% 1.26/1.43 ((~always25(s75)) | always25(s76)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8269, 3934, 6437])).
% 1.26/1.43 tff(8271,plain,
% 1.26/1.43 (~always25(s75)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8270, 8266])).
% 1.26/1.43 tff(8272,plain,
% 1.26/1.43 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s75) | (~node26(s75)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s75) | (~node26(s75)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8273,plain,
% 1.26/1.43 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s75) | (~node26(s75)))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8274,plain,
% 1.26/1.43 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s75) | (~node26(s75))),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8273, 8272])).
% 1.26/1.43 tff(8275,plain,
% 1.26/1.43 (~node26(s75)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8274, 3949, 8271])).
% 1.26/1.43 tff(8276,plain,
% 1.26/1.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s74, s75)) | (~always25(s74)) | always25(s75))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s74, s75)) | (~always25(s74)) | always25(s75))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8277,plain,
% 1.26/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s74, s75)) | (~always25(s74)) | always25(s75))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8278,plain,
% 1.26/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s74, s75)) | (~always25(s74)) | always25(s75)),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8277, 8276])).
% 1.26/1.43 tff(8279,plain,
% 1.26/1.43 ((~always25(s74)) | always25(s75)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8278, 3934, 6362])).
% 1.26/1.43 tff(8280,plain,
% 1.26/1.43 (~always25(s74)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8279, 8271])).
% 1.26/1.43 tff(8281,plain,
% 1.26/1.43 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s74) | (~node26(s74)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s74) | (~node26(s74)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8282,plain,
% 1.26/1.43 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s74) | (~node26(s74)))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8283,plain,
% 1.26/1.43 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s74) | (~node26(s74))),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8282, 8281])).
% 1.26/1.43 tff(8284,plain,
% 1.26/1.43 (~node26(s74)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8283, 3949, 8280])).
% 1.26/1.43 tff(8285,plain,
% 1.26/1.43 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s73, c_t2) | (~node26(s73)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s73, c_t2) | (~node26(s73)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8286,plain,
% 1.26/1.43 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s73, c_t2) | (~node26(s73)))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8287,plain,
% 1.26/1.43 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s73, c_t2) | (~node26(s73))),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8286, 8285])).
% 1.26/1.43 tff(8288,plain,
% 1.26/1.43 (~node26(s73)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8287, 8110, 6287])).
% 1.26/1.43 tff(8289,plain,
% 1.26/1.43 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s72)) | (~m_main_v_state2(s72, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s72)) | (~m_main_v_state2(s72, c_c2)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8290,plain,
% 1.26/1.43 (((~m_main_v_state2(s72, c_c2)) | (~always25(s72))) <=> ((~always25(s72)) | (~m_main_v_state2(s72, c_c2)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8291,plain,
% 1.26/1.43 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s72, c_c2)) | (~always25(s72)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s72)) | (~m_main_v_state2(s72, c_c2))))),
% 1.26/1.43 inference(monotonicity,[status(thm)],[8290])).
% 1.26/1.43 tff(8292,plain,
% 1.26/1.43 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s72, c_c2)) | (~always25(s72)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s72)) | (~m_main_v_state2(s72, c_c2)))),
% 1.26/1.43 inference(transitivity,[status(thm)],[8291, 8289])).
% 1.26/1.43 tff(8293,plain,
% 1.26/1.43 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s72, c_c2)) | (~always25(s72)))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8294,plain,
% 1.26/1.43 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s72)) | (~m_main_v_state2(s72, c_c2))),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8293, 8292])).
% 1.26/1.43 tff(8295,plain,
% 1.26/1.43 (~always25(s72)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8294, 3908, 6151])).
% 1.26/1.43 tff(8296,plain,
% 1.26/1.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s71, s72)) | (~always25(s71)) | always25(s72))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s71, s72)) | (~always25(s71)) | always25(s72))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8297,plain,
% 1.26/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s71, s72)) | (~always25(s71)) | always25(s72))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8298,plain,
% 1.26/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s71, s72)) | (~always25(s71)) | always25(s72)),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8297, 8296])).
% 1.26/1.43 tff(8299,plain,
% 1.26/1.43 ((~always25(s71)) | always25(s72)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8298, 3934, 6142])).
% 1.26/1.43 tff(8300,plain,
% 1.26/1.43 (~always25(s71)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8299, 8295])).
% 1.26/1.43 tff(8301,plain,
% 1.26/1.43 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s71) | (~node26(s71)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s71) | (~node26(s71)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8302,plain,
% 1.26/1.43 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s71) | (~node26(s71)))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8303,plain,
% 1.26/1.43 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s71) | (~node26(s71))),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8302, 8301])).
% 1.26/1.43 tff(8304,plain,
% 1.26/1.43 (~node26(s71)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8303, 3949, 8300])).
% 1.26/1.43 tff(8305,plain,
% 1.26/1.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s70, s71)) | (~always25(s70)) | always25(s71))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s70, s71)) | (~always25(s70)) | always25(s71))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8306,plain,
% 1.26/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s70, s71)) | (~always25(s70)) | always25(s71))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8307,plain,
% 1.26/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s70, s71)) | (~always25(s70)) | always25(s71)),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8306, 8305])).
% 1.26/1.43 tff(8308,plain,
% 1.26/1.43 ((~always25(s70)) | always25(s71)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8307, 3934, 6064])).
% 1.26/1.43 tff(8309,plain,
% 1.26/1.43 (~always25(s70)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8308, 8300])).
% 1.26/1.43 tff(8310,plain,
% 1.26/1.43 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s70) | (~node26(s70)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s70) | (~node26(s70)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8311,plain,
% 1.26/1.43 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s70) | (~node26(s70)))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8312,plain,
% 1.26/1.43 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s70) | (~node26(s70))),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8311, 8310])).
% 1.26/1.43 tff(8313,plain,
% 1.26/1.43 (~node26(s70)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8312, 3949, 8309])).
% 1.26/1.43 tff(8314,plain,
% 1.26/1.43 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s69, c_t2) | (~node26(s69)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s69, c_t2) | (~node26(s69)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8315,plain,
% 1.26/1.43 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s69, c_t2) | (~node26(s69)))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8316,plain,
% 1.26/1.43 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s69, c_t2) | (~node26(s69))),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8315, 8314])).
% 1.26/1.43 tff(8317,plain,
% 1.26/1.43 (~node26(s69)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8316, 8110, 5954])).
% 1.26/1.43 tff(8318,plain,
% 1.26/1.43 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s68)) | (~m_main_v_state2(s68, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s68)) | (~m_main_v_state2(s68, c_c2)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8319,plain,
% 1.26/1.43 (((~m_main_v_state2(s68, c_c2)) | (~always25(s68))) <=> ((~always25(s68)) | (~m_main_v_state2(s68, c_c2)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8320,plain,
% 1.26/1.43 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s68, c_c2)) | (~always25(s68)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s68)) | (~m_main_v_state2(s68, c_c2))))),
% 1.26/1.43 inference(monotonicity,[status(thm)],[8319])).
% 1.26/1.43 tff(8321,plain,
% 1.26/1.43 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s68, c_c2)) | (~always25(s68)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s68)) | (~m_main_v_state2(s68, c_c2)))),
% 1.26/1.43 inference(transitivity,[status(thm)],[8320, 8318])).
% 1.26/1.43 tff(8322,plain,
% 1.26/1.43 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s68, c_c2)) | (~always25(s68)))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8323,plain,
% 1.26/1.43 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s68)) | (~m_main_v_state2(s68, c_c2))),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8322, 8321])).
% 1.26/1.43 tff(8324,plain,
% 1.26/1.43 (~always25(s68)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8323, 3908, 5883])).
% 1.26/1.43 tff(8325,plain,
% 1.26/1.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s67, s68)) | (~always25(s67)) | always25(s68))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s67, s68)) | (~always25(s67)) | always25(s68))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8326,plain,
% 1.26/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s67, s68)) | (~always25(s67)) | always25(s68))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8327,plain,
% 1.26/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s67, s68)) | (~always25(s67)) | always25(s68)),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8326, 8325])).
% 1.26/1.43 tff(8328,plain,
% 1.26/1.43 ((~always25(s67)) | always25(s68)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8327, 3934, 5809])).
% 1.26/1.43 tff(8329,plain,
% 1.26/1.43 (~always25(s67)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8328, 8324])).
% 1.26/1.43 tff(8330,plain,
% 1.26/1.43 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s67) | (~node26(s67)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s67) | (~node26(s67)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8331,plain,
% 1.26/1.43 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s67) | (~node26(s67)))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8332,plain,
% 1.26/1.43 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s67) | (~node26(s67))),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8331, 8330])).
% 1.26/1.43 tff(8333,plain,
% 1.26/1.43 (~node26(s67)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8332, 3949, 8329])).
% 1.26/1.43 tff(8334,plain,
% 1.26/1.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s66, s67)) | (~always25(s66)) | always25(s67))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s66, s67)) | (~always25(s66)) | always25(s67))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8335,plain,
% 1.26/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s66, s67)) | (~always25(s66)) | always25(s67))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8336,plain,
% 1.26/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s66, s67)) | (~always25(s66)) | always25(s67)),
% 1.26/1.43 inference(modus_ponens,[status(thm)],[8335, 8334])).
% 1.26/1.43 tff(8337,plain,
% 1.26/1.43 ((~always25(s66)) | always25(s67)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8336, 3934, 5734])).
% 1.26/1.43 tff(8338,plain,
% 1.26/1.43 (~always25(s66)),
% 1.26/1.43 inference(unit_resolution,[status(thm)],[8337, 8329])).
% 1.26/1.43 tff(8339,plain,
% 1.26/1.43 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s66) | (~node26(s66)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s66) | (~node26(s66)))),
% 1.26/1.43 inference(rewrite,[status(thm)],[])).
% 1.26/1.43 tff(8340,plain,
% 1.26/1.43 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s66) | (~node26(s66)))),
% 1.26/1.43 inference(quant_inst,[status(thm)],[])).
% 1.26/1.43 tff(8341,plain,
% 1.26/1.43 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s66) | (~node26(s66))),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8340, 8339])).
% 1.26/1.44 tff(8342,plain,
% 1.26/1.44 (~node26(s66)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8341, 3949, 8338])).
% 1.26/1.44 tff(8343,plain,
% 1.26/1.44 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s65, c_t2) | (~node26(s65)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s65, c_t2) | (~node26(s65)))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8344,plain,
% 1.26/1.44 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s65, c_t2) | (~node26(s65)))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8345,plain,
% 1.26/1.44 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s65, c_t2) | (~node26(s65))),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8344, 8343])).
% 1.26/1.44 tff(8346,plain,
% 1.26/1.44 (~node26(s65)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8345, 8110, 5659])).
% 1.26/1.44 tff(8347,plain,
% 1.26/1.44 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s64)) | (~m_main_v_state2(s64, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s64)) | (~m_main_v_state2(s64, c_c2)))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8348,plain,
% 1.26/1.44 (((~m_main_v_state2(s64, c_c2)) | (~always25(s64))) <=> ((~always25(s64)) | (~m_main_v_state2(s64, c_c2)))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8349,plain,
% 1.26/1.44 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s64, c_c2)) | (~always25(s64)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s64)) | (~m_main_v_state2(s64, c_c2))))),
% 1.26/1.44 inference(monotonicity,[status(thm)],[8348])).
% 1.26/1.44 tff(8350,plain,
% 1.26/1.44 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s64, c_c2)) | (~always25(s64)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s64)) | (~m_main_v_state2(s64, c_c2)))),
% 1.26/1.44 inference(transitivity,[status(thm)],[8349, 8347])).
% 1.26/1.44 tff(8351,plain,
% 1.26/1.44 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s64, c_c2)) | (~always25(s64)))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8352,plain,
% 1.26/1.44 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s64)) | (~m_main_v_state2(s64, c_c2))),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8351, 8350])).
% 1.26/1.44 tff(8353,plain,
% 1.26/1.44 (~always25(s64)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8352, 3908, 5523])).
% 1.26/1.44 tff(8354,plain,
% 1.26/1.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s63, s64)) | (~always25(s63)) | always25(s64))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s63, s64)) | (~always25(s63)) | always25(s64))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8355,plain,
% 1.26/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s63, s64)) | (~always25(s63)) | always25(s64))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8356,plain,
% 1.26/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s63, s64)) | (~always25(s63)) | always25(s64)),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8355, 8354])).
% 1.26/1.44 tff(8357,plain,
% 1.26/1.44 ((~always25(s63)) | always25(s64)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8356, 3934, 5514])).
% 1.26/1.44 tff(8358,plain,
% 1.26/1.44 (~always25(s63)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8357, 8353])).
% 1.26/1.44 tff(8359,plain,
% 1.26/1.44 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s63) | (~node26(s63)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s63) | (~node26(s63)))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8360,plain,
% 1.26/1.44 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s63) | (~node26(s63)))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8361,plain,
% 1.26/1.44 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s63) | (~node26(s63))),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8360, 8359])).
% 1.26/1.44 tff(8362,plain,
% 1.26/1.44 (~node26(s63)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8361, 3949, 8358])).
% 1.26/1.44 tff(8363,plain,
% 1.26/1.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s62, s63)) | (~always25(s62)) | always25(s63))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s62, s63)) | (~always25(s62)) | always25(s63))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8364,plain,
% 1.26/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s62, s63)) | (~always25(s62)) | always25(s63))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8365,plain,
% 1.26/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s62, s63)) | (~always25(s62)) | always25(s63)),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8364, 8363])).
% 1.26/1.44 tff(8366,plain,
% 1.26/1.44 ((~always25(s62)) | always25(s63)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8365, 3934, 5436])).
% 1.26/1.44 tff(8367,plain,
% 1.26/1.44 (~always25(s62)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8366, 8358])).
% 1.26/1.44 tff(8368,plain,
% 1.26/1.44 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s62) | (~node26(s62)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s62) | (~node26(s62)))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8369,plain,
% 1.26/1.44 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s62) | (~node26(s62)))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8370,plain,
% 1.26/1.44 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s62) | (~node26(s62))),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8369, 8368])).
% 1.26/1.44 tff(8371,plain,
% 1.26/1.44 (~node26(s62)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8370, 3949, 8367])).
% 1.26/1.44 tff(8372,plain,
% 1.26/1.44 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s61, c_t2) | (~node26(s61)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s61, c_t2) | (~node26(s61)))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8373,plain,
% 1.26/1.44 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s61, c_t2) | (~node26(s61)))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8374,plain,
% 1.26/1.44 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s61, c_t2) | (~node26(s61))),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8373, 8372])).
% 1.26/1.44 tff(8375,plain,
% 1.26/1.44 (~node26(s61)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8374, 8110, 5326])).
% 1.26/1.44 tff(8376,plain,
% 1.26/1.44 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s60)) | (~m_main_v_state2(s60, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s60)) | (~m_main_v_state2(s60, c_c2)))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8377,plain,
% 1.26/1.44 (((~m_main_v_state2(s60, c_c2)) | (~always25(s60))) <=> ((~always25(s60)) | (~m_main_v_state2(s60, c_c2)))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8378,plain,
% 1.26/1.44 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s60, c_c2)) | (~always25(s60)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s60)) | (~m_main_v_state2(s60, c_c2))))),
% 1.26/1.44 inference(monotonicity,[status(thm)],[8377])).
% 1.26/1.44 tff(8379,plain,
% 1.26/1.44 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s60, c_c2)) | (~always25(s60)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s60)) | (~m_main_v_state2(s60, c_c2)))),
% 1.26/1.44 inference(transitivity,[status(thm)],[8378, 8376])).
% 1.26/1.44 tff(8380,plain,
% 1.26/1.44 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s60, c_c2)) | (~always25(s60)))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8381,plain,
% 1.26/1.44 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s60)) | (~m_main_v_state2(s60, c_c2))),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8380, 8379])).
% 1.26/1.44 tff(8382,plain,
% 1.26/1.44 (~always25(s60)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8381, 3908, 5255])).
% 1.26/1.44 tff(8383,plain,
% 1.26/1.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s60)) | (~always25(s59)) | always25(s60))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s59, s60)) | (~always25(s59)) | always25(s60))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8384,plain,
% 1.26/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s59, s60)) | (~always25(s59)) | always25(s60))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8385,plain,
% 1.26/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s59, s60)) | (~always25(s59)) | always25(s60)),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8384, 8383])).
% 1.26/1.44 tff(8386,plain,
% 1.26/1.44 ((~always25(s59)) | always25(s60)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8385, 3934, 5181])).
% 1.26/1.44 tff(8387,plain,
% 1.26/1.44 (~always25(s59)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8386, 8382])).
% 1.26/1.44 tff(8388,plain,
% 1.26/1.44 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s59) | (~node26(s59)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s59) | (~node26(s59)))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8389,plain,
% 1.26/1.44 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s59) | (~node26(s59)))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8390,plain,
% 1.26/1.44 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s59) | (~node26(s59))),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8389, 8388])).
% 1.26/1.44 tff(8391,plain,
% 1.26/1.44 (~node26(s59)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8390, 3949, 8387])).
% 1.26/1.44 tff(8392,plain,
% 1.26/1.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s58, s59)) | (~always25(s58)) | always25(s59))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s58, s59)) | (~always25(s58)) | always25(s59))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8393,plain,
% 1.26/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s58, s59)) | (~always25(s58)) | always25(s59))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8394,plain,
% 1.26/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s58, s59)) | (~always25(s58)) | always25(s59)),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8393, 8392])).
% 1.26/1.44 tff(8395,plain,
% 1.26/1.44 ((~always25(s58)) | always25(s59)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8394, 3934, 5106])).
% 1.26/1.44 tff(8396,plain,
% 1.26/1.44 (~always25(s58)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8395, 8387])).
% 1.26/1.44 tff(8397,plain,
% 1.26/1.44 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s58) | (~node26(s58)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s58) | (~node26(s58)))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8398,plain,
% 1.26/1.44 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s58) | (~node26(s58)))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8399,plain,
% 1.26/1.44 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s58) | (~node26(s58))),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8398, 8397])).
% 1.26/1.44 tff(8400,plain,
% 1.26/1.44 (~node26(s58)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8399, 3949, 8396])).
% 1.26/1.44 tff(8401,plain,
% 1.26/1.44 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s57, c_t2) | (~node26(s57)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s57, c_t2) | (~node26(s57)))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8402,plain,
% 1.26/1.44 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s57, c_t2) | (~node26(s57)))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8403,plain,
% 1.26/1.44 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s57, c_t2) | (~node26(s57))),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8402, 8401])).
% 1.26/1.44 tff(8404,plain,
% 1.26/1.44 (~node26(s57)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8403, 8110, 5031])).
% 1.26/1.44 tff(8405,plain,
% 1.26/1.44 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s56)) | (~m_main_v_state2(s56, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s56)) | (~m_main_v_state2(s56, c_c2)))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8406,plain,
% 1.26/1.44 (((~m_main_v_state2(s56, c_c2)) | (~always25(s56))) <=> ((~always25(s56)) | (~m_main_v_state2(s56, c_c2)))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8407,plain,
% 1.26/1.44 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s56, c_c2)) | (~always25(s56)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s56)) | (~m_main_v_state2(s56, c_c2))))),
% 1.26/1.44 inference(monotonicity,[status(thm)],[8406])).
% 1.26/1.44 tff(8408,plain,
% 1.26/1.44 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s56, c_c2)) | (~always25(s56)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s56)) | (~m_main_v_state2(s56, c_c2)))),
% 1.26/1.44 inference(transitivity,[status(thm)],[8407, 8405])).
% 1.26/1.44 tff(8409,plain,
% 1.26/1.44 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s56, c_c2)) | (~always25(s56)))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8410,plain,
% 1.26/1.44 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s56)) | (~m_main_v_state2(s56, c_c2))),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8409, 8408])).
% 1.26/1.44 tff(8411,plain,
% 1.26/1.44 (~always25(s56)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8410, 3908, 4895])).
% 1.26/1.44 tff(8412,plain,
% 1.26/1.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s55, s56)) | (~always25(s55)) | always25(s56))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s55, s56)) | (~always25(s55)) | always25(s56))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8413,plain,
% 1.26/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s55, s56)) | (~always25(s55)) | always25(s56))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8414,plain,
% 1.26/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s55, s56)) | (~always25(s55)) | always25(s56)),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8413, 8412])).
% 1.26/1.44 tff(8415,plain,
% 1.26/1.44 ((~always25(s55)) | always25(s56)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8414, 3934, 4886])).
% 1.26/1.44 tff(8416,plain,
% 1.26/1.44 (~always25(s55)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8415, 8411])).
% 1.26/1.44 tff(8417,plain,
% 1.26/1.44 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s55) | (~node26(s55)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s55) | (~node26(s55)))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8418,plain,
% 1.26/1.44 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s55) | (~node26(s55)))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8419,plain,
% 1.26/1.44 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s55) | (~node26(s55))),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8418, 8417])).
% 1.26/1.44 tff(8420,plain,
% 1.26/1.44 (~node26(s55)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8419, 3949, 8416])).
% 1.26/1.44 tff(8421,plain,
% 1.26/1.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s54, s55)) | (~always25(s54)) | always25(s55))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s54, s55)) | (~always25(s54)) | always25(s55))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8422,plain,
% 1.26/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s54, s55)) | (~always25(s54)) | always25(s55))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8423,plain,
% 1.26/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s54, s55)) | (~always25(s54)) | always25(s55)),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8422, 8421])).
% 1.26/1.44 tff(8424,plain,
% 1.26/1.44 ((~always25(s54)) | always25(s55)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8423, 3934, 4808])).
% 1.26/1.44 tff(8425,plain,
% 1.26/1.44 (~always25(s54)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8424, 8416])).
% 1.26/1.44 tff(8426,plain,
% 1.26/1.44 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s54) | (~node26(s54)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s54) | (~node26(s54)))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8427,plain,
% 1.26/1.44 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s54) | (~node26(s54)))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8428,plain,
% 1.26/1.44 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s54) | (~node26(s54))),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8427, 8426])).
% 1.26/1.44 tff(8429,plain,
% 1.26/1.44 (~node26(s54)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8428, 3949, 8425])).
% 1.26/1.44 tff(8430,plain,
% 1.26/1.44 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s53, c_t2) | (~node26(s53)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s53, c_t2) | (~node26(s53)))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8431,plain,
% 1.26/1.44 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s53, c_t2) | (~node26(s53)))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8432,plain,
% 1.26/1.44 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s53, c_t2) | (~node26(s53))),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8431, 8430])).
% 1.26/1.44 tff(8433,plain,
% 1.26/1.44 (~node26(s53)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8432, 8110, 4698])).
% 1.26/1.44 tff(8434,plain,
% 1.26/1.44 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s52)) | (~m_main_v_state2(s52, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s52)) | (~m_main_v_state2(s52, c_c2)))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8435,plain,
% 1.26/1.44 (((~m_main_v_state2(s52, c_c2)) | (~always25(s52))) <=> ((~always25(s52)) | (~m_main_v_state2(s52, c_c2)))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8436,plain,
% 1.26/1.44 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s52, c_c2)) | (~always25(s52)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s52)) | (~m_main_v_state2(s52, c_c2))))),
% 1.26/1.44 inference(monotonicity,[status(thm)],[8435])).
% 1.26/1.44 tff(8437,plain,
% 1.26/1.44 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s52, c_c2)) | (~always25(s52)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s52)) | (~m_main_v_state2(s52, c_c2)))),
% 1.26/1.44 inference(transitivity,[status(thm)],[8436, 8434])).
% 1.26/1.44 tff(8438,plain,
% 1.26/1.44 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s52, c_c2)) | (~always25(s52)))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8439,plain,
% 1.26/1.44 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s52)) | (~m_main_v_state2(s52, c_c2))),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8438, 8437])).
% 1.26/1.44 tff(8440,plain,
% 1.26/1.44 (~always25(s52)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8439, 3908, 4627])).
% 1.26/1.44 tff(8441,plain,
% 1.26/1.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s51, s52)) | (~always25(s51)) | always25(s52))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s51, s52)) | (~always25(s51)) | always25(s52))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8442,plain,
% 1.26/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s51, s52)) | (~always25(s51)) | always25(s52))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8443,plain,
% 1.26/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s51, s52)) | (~always25(s51)) | always25(s52)),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8442, 8441])).
% 1.26/1.44 tff(8444,plain,
% 1.26/1.44 ((~always25(s51)) | always25(s52)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8443, 3934, 4553])).
% 1.26/1.44 tff(8445,plain,
% 1.26/1.44 (~always25(s51)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8444, 8440])).
% 1.26/1.44 tff(8446,plain,
% 1.26/1.44 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s51) | (~node26(s51)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s51) | (~node26(s51)))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8447,plain,
% 1.26/1.44 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s51) | (~node26(s51)))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8448,plain,
% 1.26/1.44 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s51) | (~node26(s51))),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8447, 8446])).
% 1.26/1.44 tff(8449,plain,
% 1.26/1.44 (~node26(s51)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8448, 3949, 8445])).
% 1.26/1.44 tff(8450,plain,
% 1.26/1.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s50, s51)) | (~always25(s50)) | always25(s51))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s50, s51)) | (~always25(s50)) | always25(s51))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8451,plain,
% 1.26/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s50, s51)) | (~always25(s50)) | always25(s51))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8452,plain,
% 1.26/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s50, s51)) | (~always25(s50)) | always25(s51)),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8451, 8450])).
% 1.26/1.44 tff(8453,plain,
% 1.26/1.44 ((~always25(s50)) | always25(s51)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8452, 3934, 4478])).
% 1.26/1.44 tff(8454,plain,
% 1.26/1.44 (~always25(s50)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8453, 8445])).
% 1.26/1.44 tff(8455,plain,
% 1.26/1.44 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s50) | (~node26(s50)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s50) | (~node26(s50)))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8456,plain,
% 1.26/1.44 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s50) | (~node26(s50)))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8457,plain,
% 1.26/1.44 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s50) | (~node26(s50))),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8456, 8455])).
% 1.26/1.44 tff(8458,plain,
% 1.26/1.44 (~node26(s50)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8457, 3949, 8454])).
% 1.26/1.44 tff(8459,plain,
% 1.26/1.44 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s49, c_t2) | (~node26(s49)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s49, c_t2) | (~node26(s49)))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8460,plain,
% 1.26/1.44 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s49, c_t2) | (~node26(s49)))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8461,plain,
% 1.26/1.44 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s49, c_t2) | (~node26(s49))),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8460, 8459])).
% 1.26/1.44 tff(8462,plain,
% 1.26/1.44 (~node26(s49)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8461, 8110, 4403])).
% 1.26/1.44 tff(8463,plain,
% 1.26/1.44 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s48)) | (~m_main_v_state2(s48, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s48)) | (~m_main_v_state2(s48, c_c2)))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8464,plain,
% 1.26/1.44 (((~m_main_v_state2(s48, c_c2)) | (~always25(s48))) <=> ((~always25(s48)) | (~m_main_v_state2(s48, c_c2)))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8465,plain,
% 1.26/1.44 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s48, c_c2)) | (~always25(s48)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s48)) | (~m_main_v_state2(s48, c_c2))))),
% 1.26/1.44 inference(monotonicity,[status(thm)],[8464])).
% 1.26/1.44 tff(8466,plain,
% 1.26/1.44 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s48, c_c2)) | (~always25(s48)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s48)) | (~m_main_v_state2(s48, c_c2)))),
% 1.26/1.44 inference(transitivity,[status(thm)],[8465, 8463])).
% 1.26/1.44 tff(8467,plain,
% 1.26/1.44 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s48, c_c2)) | (~always25(s48)))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8468,plain,
% 1.26/1.44 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s48)) | (~m_main_v_state2(s48, c_c2))),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8467, 8466])).
% 1.26/1.44 tff(8469,plain,
% 1.26/1.44 (~always25(s48)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8468, 3908, 4267])).
% 1.26/1.44 tff(8470,plain,
% 1.26/1.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s47, s48)) | (~always25(s47)) | always25(s48))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s47, s48)) | (~always25(s47)) | always25(s48))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8471,plain,
% 1.26/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s47, s48)) | (~always25(s47)) | always25(s48))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8472,plain,
% 1.26/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s47, s48)) | (~always25(s47)) | always25(s48)),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8471, 8470])).
% 1.26/1.44 tff(8473,plain,
% 1.26/1.44 ((~always25(s47)) | always25(s48)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8472, 3934, 4258])).
% 1.26/1.44 tff(8474,plain,
% 1.26/1.44 (~always25(s47)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8473, 8469])).
% 1.26/1.44 tff(8475,plain,
% 1.26/1.44 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s47) | (~node26(s47)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s47) | (~node26(s47)))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8476,plain,
% 1.26/1.44 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s47) | (~node26(s47)))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8477,plain,
% 1.26/1.44 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s47) | (~node26(s47))),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8476, 8475])).
% 1.26/1.44 tff(8478,plain,
% 1.26/1.44 (~node26(s47)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8477, 3949, 8474])).
% 1.26/1.44 tff(8479,plain,
% 1.26/1.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s46, s47)) | (~always25(s46)) | always25(s47))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s46, s47)) | (~always25(s46)) | always25(s47))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8480,plain,
% 1.26/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s46, s47)) | (~always25(s46)) | always25(s47))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8481,plain,
% 1.26/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s46, s47)) | (~always25(s46)) | always25(s47)),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8480, 8479])).
% 1.26/1.44 tff(8482,plain,
% 1.26/1.44 ((~always25(s46)) | always25(s47)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8481, 3934, 4180])).
% 1.26/1.44 tff(8483,plain,
% 1.26/1.44 (~always25(s46)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8482, 8474])).
% 1.26/1.44 tff(8484,plain,
% 1.26/1.44 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s46) | (~node26(s46)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s46) | (~node26(s46)))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8485,plain,
% 1.26/1.44 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s46) | (~node26(s46)))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8486,plain,
% 1.26/1.44 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s46) | (~node26(s46))),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8485, 8484])).
% 1.26/1.44 tff(8487,plain,
% 1.26/1.44 (~node26(s46)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8486, 3949, 8483])).
% 1.26/1.44 tff(8488,plain,
% 1.26/1.44 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s45, c_t2) | (~node26(s45)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s45, c_t2) | (~node26(s45)))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8489,plain,
% 1.26/1.44 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s45, c_t2) | (~node26(s45)))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8490,plain,
% 1.26/1.44 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s45, c_t2) | (~node26(s45))),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8489, 8488])).
% 1.26/1.44 tff(8491,plain,
% 1.26/1.44 (~node26(s45)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8490, 8110, 4070])).
% 1.26/1.44 tff(8492,plain,
% 1.26/1.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s43, s44)) | (~always25(s43)) | always25(s44))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s43, s44)) | (~always25(s43)) | always25(s44))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8493,plain,
% 1.26/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s43, s44)) | (~always25(s43)) | always25(s44))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8494,plain,
% 1.26/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s43, s44)) | (~always25(s43)) | always25(s44)),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8493, 8492])).
% 1.26/1.44 tff(8495,plain,
% 1.26/1.44 ((~always25(s43)) | always25(s44)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8494, 3934, 3892])).
% 1.26/1.44 tff(8496,plain,
% 1.26/1.44 (~always25(s43)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8495, 3915])).
% 1.26/1.44 tff(8497,plain,
% 1.26/1.44 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s43) | (~node26(s43)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s43) | (~node26(s43)))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8498,plain,
% 1.26/1.44 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s43) | (~node26(s43)))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8499,plain,
% 1.26/1.44 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s43) | (~node26(s43))),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8498, 8497])).
% 1.26/1.44 tff(8500,plain,
% 1.26/1.44 (~node26(s43)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8499, 3949, 8496])).
% 1.26/1.44 tff(8501,plain,
% 1.26/1.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s42, s43)) | (~always25(s42)) | always25(s43))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s42, s43)) | (~always25(s42)) | always25(s43))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8502,plain,
% 1.26/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s42, s43)) | (~always25(s42)) | always25(s43))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8503,plain,
% 1.26/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s42, s43)) | (~always25(s42)) | always25(s43)),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8502, 8501])).
% 1.26/1.44 tff(8504,plain,
% 1.26/1.44 ((~always25(s42)) | always25(s43)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8503, 3934, 3814])).
% 1.26/1.44 tff(8505,plain,
% 1.26/1.44 (~always25(s42)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8504, 8496])).
% 1.26/1.44 tff(8506,plain,
% 1.26/1.44 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s42) | (~node26(s42)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s42) | (~node26(s42)))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8507,plain,
% 1.26/1.44 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s42) | (~node26(s42)))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8508,plain,
% 1.26/1.44 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s42) | (~node26(s42))),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8507, 8506])).
% 1.26/1.44 tff(8509,plain,
% 1.26/1.44 (~node26(s42)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8508, 3949, 8505])).
% 1.26/1.44 tff(8510,plain,
% 1.26/1.44 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s41, c_t2) | (~node26(s41)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s41, c_t2) | (~node26(s41)))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8511,plain,
% 1.26/1.44 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s41, c_t2) | (~node26(s41)))),
% 1.26/1.44 inference(quant_inst,[status(thm)],[])).
% 1.26/1.44 tff(8512,plain,
% 1.26/1.44 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s41, c_t2) | (~node26(s41))),
% 1.26/1.44 inference(modus_ponens,[status(thm)],[8511, 8510])).
% 1.26/1.44 tff(8513,plain,
% 1.26/1.44 (~node26(s41)),
% 1.26/1.44 inference(unit_resolution,[status(thm)],[8512, 8110, 3704])).
% 1.26/1.44 tff(8514,plain,
% 1.26/1.44 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s40)) | (~m_main_v_state2(s40, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s40)) | (~m_main_v_state2(s40, c_c2)))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8515,plain,
% 1.26/1.44 (((~m_main_v_state2(s40, c_c2)) | (~always25(s40))) <=> ((~always25(s40)) | (~m_main_v_state2(s40, c_c2)))),
% 1.26/1.44 inference(rewrite,[status(thm)],[])).
% 1.26/1.44 tff(8516,plain,
% 1.26/1.44 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s40, c_c2)) | (~always25(s40)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s40)) | (~m_main_v_state2(s40, c_c2))))),
% 1.26/1.45 inference(monotonicity,[status(thm)],[8515])).
% 1.26/1.45 tff(8517,plain,
% 1.26/1.45 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s40, c_c2)) | (~always25(s40)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s40)) | (~m_main_v_state2(s40, c_c2)))),
% 1.26/1.45 inference(transitivity,[status(thm)],[8516, 8514])).
% 1.26/1.45 tff(8518,plain,
% 1.26/1.45 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s40, c_c2)) | (~always25(s40)))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8519,plain,
% 1.26/1.45 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s40)) | (~m_main_v_state2(s40, c_c2))),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8518, 8517])).
% 1.26/1.45 tff(8520,plain,
% 1.26/1.45 (~always25(s40)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8519, 3908, 3633])).
% 1.26/1.45 tff(8521,plain,
% 1.26/1.45 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s39, s40)) | (~always25(s39)) | always25(s40))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s39, s40)) | (~always25(s39)) | always25(s40))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8522,plain,
% 1.26/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s39, s40)) | (~always25(s39)) | always25(s40))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8523,plain,
% 1.26/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s39, s40)) | (~always25(s39)) | always25(s40)),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8522, 8521])).
% 1.26/1.45 tff(8524,plain,
% 1.26/1.45 ((~always25(s39)) | always25(s40)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8523, 3934, 3559])).
% 1.26/1.45 tff(8525,plain,
% 1.26/1.45 (~always25(s39)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8524, 8520])).
% 1.26/1.45 tff(8526,plain,
% 1.26/1.45 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s39) | (~node26(s39)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s39) | (~node26(s39)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8527,plain,
% 1.26/1.45 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s39) | (~node26(s39)))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8528,plain,
% 1.26/1.45 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s39) | (~node26(s39))),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8527, 8526])).
% 1.26/1.45 tff(8529,plain,
% 1.26/1.45 (~node26(s39)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8528, 3949, 8525])).
% 1.26/1.45 tff(8530,plain,
% 1.26/1.45 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s38, s39)) | (~always25(s38)) | always25(s39))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s38, s39)) | (~always25(s38)) | always25(s39))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8531,plain,
% 1.26/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s38, s39)) | (~always25(s38)) | always25(s39))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8532,plain,
% 1.26/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s38, s39)) | (~always25(s38)) | always25(s39)),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8531, 8530])).
% 1.26/1.45 tff(8533,plain,
% 1.26/1.45 ((~always25(s38)) | always25(s39)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8532, 3934, 3484])).
% 1.26/1.45 tff(8534,plain,
% 1.26/1.45 (~always25(s38)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8533, 8525])).
% 1.26/1.45 tff(8535,plain,
% 1.26/1.45 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s38) | (~node26(s38)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s38) | (~node26(s38)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8536,plain,
% 1.26/1.45 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s38) | (~node26(s38)))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8537,plain,
% 1.26/1.45 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s38) | (~node26(s38))),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8536, 8535])).
% 1.26/1.45 tff(8538,plain,
% 1.26/1.45 (~node26(s38)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8537, 3949, 8534])).
% 1.26/1.45 tff(8539,plain,
% 1.26/1.45 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s37, c_t2) | (~node26(s37)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s37, c_t2) | (~node26(s37)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8540,plain,
% 1.26/1.45 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s37, c_t2) | (~node26(s37)))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8541,plain,
% 1.26/1.45 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s37, c_t2) | (~node26(s37))),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8540, 8539])).
% 1.26/1.45 tff(8542,plain,
% 1.26/1.45 (~node26(s37)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8541, 8110, 3409])).
% 1.26/1.45 tff(8543,plain,
% 1.26/1.45 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s36)) | (~m_main_v_state2(s36, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s36)) | (~m_main_v_state2(s36, c_c2)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8544,plain,
% 1.26/1.45 (((~m_main_v_state2(s36, c_c2)) | (~always25(s36))) <=> ((~always25(s36)) | (~m_main_v_state2(s36, c_c2)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8545,plain,
% 1.26/1.45 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s36, c_c2)) | (~always25(s36)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s36)) | (~m_main_v_state2(s36, c_c2))))),
% 1.26/1.45 inference(monotonicity,[status(thm)],[8544])).
% 1.26/1.45 tff(8546,plain,
% 1.26/1.45 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s36, c_c2)) | (~always25(s36)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s36)) | (~m_main_v_state2(s36, c_c2)))),
% 1.26/1.45 inference(transitivity,[status(thm)],[8545, 8543])).
% 1.26/1.45 tff(8547,plain,
% 1.26/1.45 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s36, c_c2)) | (~always25(s36)))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8548,plain,
% 1.26/1.45 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s36)) | (~m_main_v_state2(s36, c_c2))),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8547, 8546])).
% 1.26/1.45 tff(8549,plain,
% 1.26/1.45 (~always25(s36)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8548, 3908, 3273])).
% 1.26/1.45 tff(8550,plain,
% 1.26/1.45 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s35, s36)) | (~always25(s35)) | always25(s36))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s35, s36)) | (~always25(s35)) | always25(s36))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8551,plain,
% 1.26/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s35, s36)) | (~always25(s35)) | always25(s36))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8552,plain,
% 1.26/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s35, s36)) | (~always25(s35)) | always25(s36)),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8551, 8550])).
% 1.26/1.45 tff(8553,plain,
% 1.26/1.45 ((~always25(s35)) | always25(s36)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8552, 3934, 3264])).
% 1.26/1.45 tff(8554,plain,
% 1.26/1.45 (~always25(s35)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8553, 8549])).
% 1.26/1.45 tff(8555,plain,
% 1.26/1.45 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s35) | (~node26(s35)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s35) | (~node26(s35)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8556,plain,
% 1.26/1.45 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s35) | (~node26(s35)))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8557,plain,
% 1.26/1.45 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s35) | (~node26(s35))),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8556, 8555])).
% 1.26/1.45 tff(8558,plain,
% 1.26/1.45 (~node26(s35)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8557, 3949, 8554])).
% 1.26/1.45 tff(8559,plain,
% 1.26/1.45 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s34, s35)) | (~always25(s34)) | always25(s35))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s34, s35)) | (~always25(s34)) | always25(s35))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8560,plain,
% 1.26/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s34, s35)) | (~always25(s34)) | always25(s35))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8561,plain,
% 1.26/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s34, s35)) | (~always25(s34)) | always25(s35)),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8560, 8559])).
% 1.26/1.45 tff(8562,plain,
% 1.26/1.45 ((~always25(s34)) | always25(s35)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8561, 3934, 3186])).
% 1.26/1.45 tff(8563,plain,
% 1.26/1.45 (~always25(s34)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8562, 8554])).
% 1.26/1.45 tff(8564,plain,
% 1.26/1.45 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s34) | (~node26(s34)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s34) | (~node26(s34)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8565,plain,
% 1.26/1.45 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s34) | (~node26(s34)))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8566,plain,
% 1.26/1.45 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s34) | (~node26(s34))),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8565, 8564])).
% 1.26/1.45 tff(8567,plain,
% 1.26/1.45 (~node26(s34)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8566, 3949, 8563])).
% 1.26/1.45 tff(8568,plain,
% 1.26/1.45 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s33, c_t2) | (~node26(s33)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s33, c_t2) | (~node26(s33)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8569,plain,
% 1.26/1.45 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s33, c_t2) | (~node26(s33)))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8570,plain,
% 1.26/1.45 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s33, c_t2) | (~node26(s33))),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8569, 8568])).
% 1.26/1.45 tff(8571,plain,
% 1.26/1.45 (~node26(s33)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8570, 8110, 3076])).
% 1.26/1.45 tff(8572,plain,
% 1.26/1.45 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s32)) | (~m_main_v_state2(s32, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s32)) | (~m_main_v_state2(s32, c_c2)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8573,plain,
% 1.26/1.45 (((~m_main_v_state2(s32, c_c2)) | (~always25(s32))) <=> ((~always25(s32)) | (~m_main_v_state2(s32, c_c2)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8574,plain,
% 1.26/1.45 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s32, c_c2)) | (~always25(s32)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s32)) | (~m_main_v_state2(s32, c_c2))))),
% 1.26/1.45 inference(monotonicity,[status(thm)],[8573])).
% 1.26/1.45 tff(8575,plain,
% 1.26/1.45 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s32, c_c2)) | (~always25(s32)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s32)) | (~m_main_v_state2(s32, c_c2)))),
% 1.26/1.45 inference(transitivity,[status(thm)],[8574, 8572])).
% 1.26/1.45 tff(8576,plain,
% 1.26/1.45 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s32, c_c2)) | (~always25(s32)))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8577,plain,
% 1.26/1.45 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s32)) | (~m_main_v_state2(s32, c_c2))),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8576, 8575])).
% 1.26/1.45 tff(8578,plain,
% 1.26/1.45 (~always25(s32)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8577, 3908, 3005])).
% 1.26/1.45 tff(8579,plain,
% 1.26/1.45 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s31, s32)) | (~always25(s31)) | always25(s32))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s31, s32)) | (~always25(s31)) | always25(s32))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8580,plain,
% 1.26/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s31, s32)) | (~always25(s31)) | always25(s32))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8581,plain,
% 1.26/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s31, s32)) | (~always25(s31)) | always25(s32)),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8580, 8579])).
% 1.26/1.45 tff(8582,plain,
% 1.26/1.45 ((~always25(s31)) | always25(s32)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8581, 3934, 2931])).
% 1.26/1.45 tff(8583,plain,
% 1.26/1.45 (~always25(s31)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8582, 8578])).
% 1.26/1.45 tff(8584,plain,
% 1.26/1.45 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s31) | (~node26(s31)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s31) | (~node26(s31)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8585,plain,
% 1.26/1.45 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s31) | (~node26(s31)))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8586,plain,
% 1.26/1.45 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s31) | (~node26(s31))),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8585, 8584])).
% 1.26/1.45 tff(8587,plain,
% 1.26/1.45 (~node26(s31)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8586, 3949, 8583])).
% 1.26/1.45 tff(8588,plain,
% 1.26/1.45 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s30, s31)) | (~always25(s30)) | always25(s31))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s30, s31)) | (~always25(s30)) | always25(s31))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8589,plain,
% 1.26/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s30, s31)) | (~always25(s30)) | always25(s31))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8590,plain,
% 1.26/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s30, s31)) | (~always25(s30)) | always25(s31)),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8589, 8588])).
% 1.26/1.45 tff(8591,plain,
% 1.26/1.45 ((~always25(s30)) | always25(s31)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8590, 3934, 2856])).
% 1.26/1.45 tff(8592,plain,
% 1.26/1.45 (~always25(s30)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8591, 8583])).
% 1.26/1.45 tff(8593,plain,
% 1.26/1.45 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s30) | (~node26(s30)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s30) | (~node26(s30)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8594,plain,
% 1.26/1.45 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s30) | (~node26(s30)))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8595,plain,
% 1.26/1.45 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s30) | (~node26(s30))),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8594, 8593])).
% 1.26/1.45 tff(8596,plain,
% 1.26/1.45 (~node26(s30)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8595, 3949, 8592])).
% 1.26/1.45 tff(8597,plain,
% 1.26/1.45 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s29, c_t2) | (~node26(s29)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s29, c_t2) | (~node26(s29)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8598,plain,
% 1.26/1.45 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s29, c_t2) | (~node26(s29)))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8599,plain,
% 1.26/1.45 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s29, c_t2) | (~node26(s29))),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8598, 8597])).
% 1.26/1.45 tff(8600,plain,
% 1.26/1.45 (~node26(s29)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8599, 8110, 2781])).
% 1.26/1.45 tff(8601,plain,
% 1.26/1.45 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s28)) | (~m_main_v_state2(s28, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s28)) | (~m_main_v_state2(s28, c_c2)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8602,plain,
% 1.26/1.45 (((~m_main_v_state2(s28, c_c2)) | (~always25(s28))) <=> ((~always25(s28)) | (~m_main_v_state2(s28, c_c2)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8603,plain,
% 1.26/1.45 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s28, c_c2)) | (~always25(s28)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s28)) | (~m_main_v_state2(s28, c_c2))))),
% 1.26/1.45 inference(monotonicity,[status(thm)],[8602])).
% 1.26/1.45 tff(8604,plain,
% 1.26/1.45 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s28, c_c2)) | (~always25(s28)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s28)) | (~m_main_v_state2(s28, c_c2)))),
% 1.26/1.45 inference(transitivity,[status(thm)],[8603, 8601])).
% 1.26/1.45 tff(8605,plain,
% 1.26/1.45 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s28, c_c2)) | (~always25(s28)))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8606,plain,
% 1.26/1.45 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s28)) | (~m_main_v_state2(s28, c_c2))),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8605, 8604])).
% 1.26/1.45 tff(8607,plain,
% 1.26/1.45 (~always25(s28)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8606, 3908, 2645])).
% 1.26/1.45 tff(8608,plain,
% 1.26/1.45 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s27, s28)) | (~always25(s27)) | always25(s28))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s27, s28)) | (~always25(s27)) | always25(s28))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8609,plain,
% 1.26/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s27, s28)) | (~always25(s27)) | always25(s28))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8610,plain,
% 1.26/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s27, s28)) | (~always25(s27)) | always25(s28)),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8609, 8608])).
% 1.26/1.45 tff(8611,plain,
% 1.26/1.45 ((~always25(s27)) | always25(s28)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8610, 3934, 2636])).
% 1.26/1.45 tff(8612,plain,
% 1.26/1.45 (~always25(s27)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8611, 8607])).
% 1.26/1.45 tff(8613,plain,
% 1.26/1.45 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s27) | (~node26(s27)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s27) | (~node26(s27)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8614,plain,
% 1.26/1.45 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s27) | (~node26(s27)))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8615,plain,
% 1.26/1.45 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s27) | (~node26(s27))),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8614, 8613])).
% 1.26/1.45 tff(8616,plain,
% 1.26/1.45 (~node26(s27)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8615, 3949, 8612])).
% 1.26/1.45 tff(8617,plain,
% 1.26/1.45 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s26, s27)) | (~always25(s26)) | always25(s27))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s26, s27)) | (~always25(s26)) | always25(s27))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8618,plain,
% 1.26/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s26, s27)) | (~always25(s26)) | always25(s27))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8619,plain,
% 1.26/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s26, s27)) | (~always25(s26)) | always25(s27)),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8618, 8617])).
% 1.26/1.45 tff(8620,plain,
% 1.26/1.45 ((~always25(s26)) | always25(s27)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8619, 3934, 2558])).
% 1.26/1.45 tff(8621,plain,
% 1.26/1.45 (~always25(s26)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8620, 8612])).
% 1.26/1.45 tff(8622,plain,
% 1.26/1.45 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s26) | (~node26(s26)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s26) | (~node26(s26)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8623,plain,
% 1.26/1.45 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s26) | (~node26(s26)))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8624,plain,
% 1.26/1.45 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s26) | (~node26(s26))),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8623, 8622])).
% 1.26/1.45 tff(8625,plain,
% 1.26/1.45 (~node26(s26)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8624, 3949, 8621])).
% 1.26/1.45 tff(8626,plain,
% 1.26/1.45 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s25, c_t2) | (~node26(s25)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s25, c_t2) | (~node26(s25)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8627,plain,
% 1.26/1.45 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s25, c_t2) | (~node26(s25)))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8628,plain,
% 1.26/1.45 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s25, c_t2) | (~node26(s25))),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8627, 8626])).
% 1.26/1.45 tff(8629,plain,
% 1.26/1.45 (~node26(s25)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8628, 8110, 2448])).
% 1.26/1.45 tff(8630,plain,
% 1.26/1.45 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s24)) | (~m_main_v_state2(s24, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s24)) | (~m_main_v_state2(s24, c_c2)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8631,plain,
% 1.26/1.45 (((~m_main_v_state2(s24, c_c2)) | (~always25(s24))) <=> ((~always25(s24)) | (~m_main_v_state2(s24, c_c2)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8632,plain,
% 1.26/1.45 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s24, c_c2)) | (~always25(s24)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s24)) | (~m_main_v_state2(s24, c_c2))))),
% 1.26/1.45 inference(monotonicity,[status(thm)],[8631])).
% 1.26/1.45 tff(8633,plain,
% 1.26/1.45 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s24, c_c2)) | (~always25(s24)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s24)) | (~m_main_v_state2(s24, c_c2)))),
% 1.26/1.45 inference(transitivity,[status(thm)],[8632, 8630])).
% 1.26/1.45 tff(8634,plain,
% 1.26/1.45 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s24, c_c2)) | (~always25(s24)))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8635,plain,
% 1.26/1.45 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s24)) | (~m_main_v_state2(s24, c_c2))),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8634, 8633])).
% 1.26/1.45 tff(8636,plain,
% 1.26/1.45 (~always25(s24)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8635, 3908, 2377])).
% 1.26/1.45 tff(8637,plain,
% 1.26/1.45 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s23, s24)) | (~always25(s23)) | always25(s24))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s23, s24)) | (~always25(s23)) | always25(s24))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8638,plain,
% 1.26/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s23, s24)) | (~always25(s23)) | always25(s24))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8639,plain,
% 1.26/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s23, s24)) | (~always25(s23)) | always25(s24)),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8638, 8637])).
% 1.26/1.45 tff(8640,plain,
% 1.26/1.45 ((~always25(s23)) | always25(s24)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8639, 3934, 2303])).
% 1.26/1.45 tff(8641,plain,
% 1.26/1.45 (~always25(s23)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8640, 8636])).
% 1.26/1.45 tff(8642,plain,
% 1.26/1.45 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s23) | (~node26(s23)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s23) | (~node26(s23)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8643,plain,
% 1.26/1.45 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s23) | (~node26(s23)))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8644,plain,
% 1.26/1.45 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s23) | (~node26(s23))),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8643, 8642])).
% 1.26/1.45 tff(8645,plain,
% 1.26/1.45 (~node26(s23)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8644, 3949, 8641])).
% 1.26/1.45 tff(8646,plain,
% 1.26/1.45 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s22, s23)) | (~always25(s22)) | always25(s23))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s22, s23)) | (~always25(s22)) | always25(s23))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8647,plain,
% 1.26/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s22, s23)) | (~always25(s22)) | always25(s23))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8648,plain,
% 1.26/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s22, s23)) | (~always25(s22)) | always25(s23)),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8647, 8646])).
% 1.26/1.45 tff(8649,plain,
% 1.26/1.45 ((~always25(s22)) | always25(s23)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8648, 3934, 2228])).
% 1.26/1.45 tff(8650,plain,
% 1.26/1.45 (~always25(s22)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8649, 8641])).
% 1.26/1.45 tff(8651,plain,
% 1.26/1.45 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s22) | (~node26(s22)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s22) | (~node26(s22)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8652,plain,
% 1.26/1.45 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s22) | (~node26(s22)))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8653,plain,
% 1.26/1.45 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s22) | (~node26(s22))),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8652, 8651])).
% 1.26/1.45 tff(8654,plain,
% 1.26/1.45 (~node26(s22)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8653, 3949, 8650])).
% 1.26/1.45 tff(8655,plain,
% 1.26/1.45 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s21, c_t2) | (~node26(s21)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s21, c_t2) | (~node26(s21)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8656,plain,
% 1.26/1.45 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s21, c_t2) | (~node26(s21)))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8657,plain,
% 1.26/1.45 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s21, c_t2) | (~node26(s21))),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8656, 8655])).
% 1.26/1.45 tff(8658,plain,
% 1.26/1.45 (~node26(s21)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8657, 8110, 2153])).
% 1.26/1.45 tff(8659,plain,
% 1.26/1.45 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s20)) | (~m_main_v_state2(s20, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s20)) | (~m_main_v_state2(s20, c_c2)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8660,plain,
% 1.26/1.45 (((~m_main_v_state2(s20, c_c2)) | (~always25(s20))) <=> ((~always25(s20)) | (~m_main_v_state2(s20, c_c2)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8661,plain,
% 1.26/1.45 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s20, c_c2)) | (~always25(s20)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s20)) | (~m_main_v_state2(s20, c_c2))))),
% 1.26/1.45 inference(monotonicity,[status(thm)],[8660])).
% 1.26/1.45 tff(8662,plain,
% 1.26/1.45 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s20, c_c2)) | (~always25(s20)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s20)) | (~m_main_v_state2(s20, c_c2)))),
% 1.26/1.45 inference(transitivity,[status(thm)],[8661, 8659])).
% 1.26/1.45 tff(8663,plain,
% 1.26/1.45 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s20, c_c2)) | (~always25(s20)))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8664,plain,
% 1.26/1.45 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s20)) | (~m_main_v_state2(s20, c_c2))),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8663, 8662])).
% 1.26/1.45 tff(8665,plain,
% 1.26/1.45 (~always25(s20)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8664, 3908, 2017])).
% 1.26/1.45 tff(8666,plain,
% 1.26/1.45 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s19, s20)) | (~always25(s19)) | always25(s20))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s19, s20)) | (~always25(s19)) | always25(s20))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8667,plain,
% 1.26/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s19, s20)) | (~always25(s19)) | always25(s20))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8668,plain,
% 1.26/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s19, s20)) | (~always25(s19)) | always25(s20)),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8667, 8666])).
% 1.26/1.45 tff(8669,plain,
% 1.26/1.45 ((~always25(s19)) | always25(s20)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8668, 3934, 2008])).
% 1.26/1.45 tff(8670,plain,
% 1.26/1.45 (~always25(s19)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8669, 8665])).
% 1.26/1.45 tff(8671,plain,
% 1.26/1.45 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s19) | (~node26(s19)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s19) | (~node26(s19)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8672,plain,
% 1.26/1.45 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s19) | (~node26(s19)))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8673,plain,
% 1.26/1.45 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s19) | (~node26(s19))),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8672, 8671])).
% 1.26/1.45 tff(8674,plain,
% 1.26/1.45 (~node26(s19)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8673, 3949, 8670])).
% 1.26/1.45 tff(8675,plain,
% 1.26/1.45 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s18, s19)) | (~always25(s18)) | always25(s19))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s18, s19)) | (~always25(s18)) | always25(s19))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8676,plain,
% 1.26/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s18, s19)) | (~always25(s18)) | always25(s19))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8677,plain,
% 1.26/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s18, s19)) | (~always25(s18)) | always25(s19)),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8676, 8675])).
% 1.26/1.45 tff(8678,plain,
% 1.26/1.45 ((~always25(s18)) | always25(s19)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8677, 3934, 1930])).
% 1.26/1.45 tff(8679,plain,
% 1.26/1.45 (~always25(s18)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8678, 8670])).
% 1.26/1.45 tff(8680,plain,
% 1.26/1.45 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s18) | (~node26(s18)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s18) | (~node26(s18)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8681,plain,
% 1.26/1.45 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s18) | (~node26(s18)))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8682,plain,
% 1.26/1.45 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s18) | (~node26(s18))),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8681, 8680])).
% 1.26/1.45 tff(8683,plain,
% 1.26/1.45 (~node26(s18)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8682, 3949, 8679])).
% 1.26/1.45 tff(8684,plain,
% 1.26/1.45 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s17, c_t2) | (~node26(s17)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s17, c_t2) | (~node26(s17)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8685,plain,
% 1.26/1.45 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s17, c_t2) | (~node26(s17)))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8686,plain,
% 1.26/1.45 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s17, c_t2) | (~node26(s17))),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8685, 8684])).
% 1.26/1.45 tff(8687,plain,
% 1.26/1.45 (~node26(s17)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8686, 8110, 1820])).
% 1.26/1.45 tff(8688,plain,
% 1.26/1.45 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s16)) | (~m_main_v_state2(s16, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s16)) | (~m_main_v_state2(s16, c_c2)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8689,plain,
% 1.26/1.45 (((~m_main_v_state2(s16, c_c2)) | (~always25(s16))) <=> ((~always25(s16)) | (~m_main_v_state2(s16, c_c2)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8690,plain,
% 1.26/1.45 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s16, c_c2)) | (~always25(s16)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s16)) | (~m_main_v_state2(s16, c_c2))))),
% 1.26/1.45 inference(monotonicity,[status(thm)],[8689])).
% 1.26/1.45 tff(8691,plain,
% 1.26/1.45 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s16, c_c2)) | (~always25(s16)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s16)) | (~m_main_v_state2(s16, c_c2)))),
% 1.26/1.45 inference(transitivity,[status(thm)],[8690, 8688])).
% 1.26/1.45 tff(8692,plain,
% 1.26/1.45 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s16, c_c2)) | (~always25(s16)))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8693,plain,
% 1.26/1.45 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s16)) | (~m_main_v_state2(s16, c_c2))),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8692, 8691])).
% 1.26/1.45 tff(8694,plain,
% 1.26/1.45 (~always25(s16)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8693, 3908, 1749])).
% 1.26/1.45 tff(8695,plain,
% 1.26/1.45 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s15, s16)) | (~always25(s15)) | always25(s16))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s15, s16)) | (~always25(s15)) | always25(s16))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8696,plain,
% 1.26/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s15, s16)) | (~always25(s15)) | always25(s16))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8697,plain,
% 1.26/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s15, s16)) | (~always25(s15)) | always25(s16)),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8696, 8695])).
% 1.26/1.45 tff(8698,plain,
% 1.26/1.45 ((~always25(s15)) | always25(s16)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8697, 3934, 1675])).
% 1.26/1.45 tff(8699,plain,
% 1.26/1.45 (~always25(s15)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8698, 8694])).
% 1.26/1.45 tff(8700,plain,
% 1.26/1.45 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s15) | (~node26(s15)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s15) | (~node26(s15)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8701,plain,
% 1.26/1.45 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s15) | (~node26(s15)))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8702,plain,
% 1.26/1.45 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s15) | (~node26(s15))),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8701, 8700])).
% 1.26/1.45 tff(8703,plain,
% 1.26/1.45 (~node26(s15)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8702, 3949, 8699])).
% 1.26/1.45 tff(8704,plain,
% 1.26/1.45 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s14, s15)) | (~always25(s14)) | always25(s15))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s14, s15)) | (~always25(s14)) | always25(s15))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8705,plain,
% 1.26/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s14, s15)) | (~always25(s14)) | always25(s15))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8706,plain,
% 1.26/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s14, s15)) | (~always25(s14)) | always25(s15)),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8705, 8704])).
% 1.26/1.45 tff(8707,plain,
% 1.26/1.45 ((~always25(s14)) | always25(s15)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8706, 3934, 1600])).
% 1.26/1.45 tff(8708,plain,
% 1.26/1.45 (~always25(s14)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8707, 8699])).
% 1.26/1.45 tff(8709,plain,
% 1.26/1.45 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s14) | (~node26(s14)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s14) | (~node26(s14)))),
% 1.26/1.45 inference(rewrite,[status(thm)],[])).
% 1.26/1.45 tff(8710,plain,
% 1.26/1.45 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s14) | (~node26(s14)))),
% 1.26/1.45 inference(quant_inst,[status(thm)],[])).
% 1.26/1.45 tff(8711,plain,
% 1.26/1.45 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s14) | (~node26(s14))),
% 1.26/1.45 inference(modus_ponens,[status(thm)],[8710, 8709])).
% 1.26/1.45 tff(8712,plain,
% 1.26/1.45 (~node26(s14)),
% 1.26/1.45 inference(unit_resolution,[status(thm)],[8711, 3949, 8708])).
% 1.26/1.45 tff(8713,plain,
% 1.26/1.45 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s13, c_t2) | (~node26(s13)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s13, c_t2) | (~node26(s13)))),
% 1.26/1.46 inference(rewrite,[status(thm)],[])).
% 1.26/1.46 tff(8714,plain,
% 1.26/1.46 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s13, c_t2) | (~node26(s13)))),
% 1.26/1.46 inference(quant_inst,[status(thm)],[])).
% 1.26/1.46 tff(8715,plain,
% 1.26/1.46 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s13, c_t2) | (~node26(s13))),
% 1.26/1.46 inference(modus_ponens,[status(thm)],[8714, 8713])).
% 1.26/1.46 tff(8716,plain,
% 1.26/1.46 (~node26(s13)),
% 1.26/1.46 inference(unit_resolution,[status(thm)],[8715, 8110, 1525])).
% 1.26/1.46 tff(8717,plain,
% 1.26/1.46 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s12)) | (~m_main_v_state2(s12, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s12)) | (~m_main_v_state2(s12, c_c2)))),
% 1.26/1.46 inference(rewrite,[status(thm)],[])).
% 1.26/1.46 tff(8718,plain,
% 1.26/1.46 (((~m_main_v_state2(s12, c_c2)) | (~always25(s12))) <=> ((~always25(s12)) | (~m_main_v_state2(s12, c_c2)))),
% 1.26/1.46 inference(rewrite,[status(thm)],[])).
% 1.26/1.46 tff(8719,plain,
% 1.26/1.46 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s12, c_c2)) | (~always25(s12)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s12)) | (~m_main_v_state2(s12, c_c2))))),
% 1.26/1.46 inference(monotonicity,[status(thm)],[8718])).
% 1.26/1.46 tff(8720,plain,
% 1.26/1.46 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s12, c_c2)) | (~always25(s12)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s12)) | (~m_main_v_state2(s12, c_c2)))),
% 1.26/1.46 inference(transitivity,[status(thm)],[8719, 8717])).
% 1.26/1.46 tff(8721,plain,
% 1.26/1.46 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s12, c_c2)) | (~always25(s12)))),
% 1.26/1.46 inference(quant_inst,[status(thm)],[])).
% 1.26/1.46 tff(8722,plain,
% 1.26/1.46 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s12)) | (~m_main_v_state2(s12, c_c2))),
% 1.26/1.46 inference(modus_ponens,[status(thm)],[8721, 8720])).
% 1.26/1.46 tff(8723,plain,
% 1.26/1.46 (~always25(s12)),
% 1.26/1.46 inference(unit_resolution,[status(thm)],[8722, 3908, 1389])).
% 1.26/1.46 tff(8724,plain,
% 1.26/1.46 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s11, s12)) | (~always25(s11)) | always25(s12))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s11, s12)) | (~always25(s11)) | always25(s12))),
% 1.26/1.46 inference(rewrite,[status(thm)],[])).
% 1.26/1.46 tff(8725,plain,
% 1.26/1.46 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s11, s12)) | (~always25(s11)) | always25(s12))),
% 1.26/1.46 inference(quant_inst,[status(thm)],[])).
% 1.26/1.46 tff(8726,plain,
% 1.26/1.46 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s11, s12)) | (~always25(s11)) | always25(s12)),
% 1.26/1.46 inference(modus_ponens,[status(thm)],[8725, 8724])).
% 1.26/1.46 tff(8727,plain,
% 1.26/1.46 ((~always25(s11)) | always25(s12)),
% 1.26/1.46 inference(unit_resolution,[status(thm)],[8726, 3934, 1380])).
% 1.26/1.46 tff(8728,plain,
% 1.26/1.46 (~always25(s11)),
% 1.26/1.46 inference(unit_resolution,[status(thm)],[8727, 8723])).
% 1.26/1.46 tff(8729,plain,
% 1.26/1.46 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s11) | (~node26(s11)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s11) | (~node26(s11)))),
% 1.26/1.46 inference(rewrite,[status(thm)],[])).
% 1.26/1.46 tff(8730,plain,
% 1.26/1.46 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s11) | (~node26(s11)))),
% 1.26/1.46 inference(quant_inst,[status(thm)],[])).
% 1.26/1.46 tff(8731,plain,
% 1.26/1.46 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s11) | (~node26(s11))),
% 1.26/1.46 inference(modus_ponens,[status(thm)],[8730, 8729])).
% 1.26/1.46 tff(8732,plain,
% 1.26/1.46 (~node26(s11)),
% 1.26/1.46 inference(unit_resolution,[status(thm)],[8731, 3949, 8728])).
% 1.26/1.46 tff(8733,plain,
% 1.26/1.46 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s10, s11)) | (~always25(s10)) | always25(s11))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s10, s11)) | (~always25(s10)) | always25(s11))),
% 1.26/1.46 inference(rewrite,[status(thm)],[])).
% 1.26/1.46 tff(8734,plain,
% 1.26/1.46 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s10, s11)) | (~always25(s10)) | always25(s11))),
% 1.26/1.46 inference(quant_inst,[status(thm)],[])).
% 1.26/1.46 tff(8735,plain,
% 1.26/1.46 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s10, s11)) | (~always25(s10)) | always25(s11)),
% 1.26/1.46 inference(modus_ponens,[status(thm)],[8734, 8733])).
% 1.26/1.46 tff(8736,plain,
% 1.26/1.46 ((~always25(s10)) | always25(s11)),
% 1.26/1.46 inference(unit_resolution,[status(thm)],[8735, 3934, 1302])).
% 1.26/1.46 tff(8737,plain,
% 1.26/1.46 (~always25(s10)),
% 1.26/1.46 inference(unit_resolution,[status(thm)],[8736, 8728])).
% 1.26/1.46 tff(8738,plain,
% 1.26/1.46 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s10) | (~node26(s10)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s10) | (~node26(s10)))),
% 1.26/1.46 inference(rewrite,[status(thm)],[])).
% 1.26/1.46 tff(8739,plain,
% 1.26/1.46 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s10) | (~node26(s10)))),
% 1.26/1.46 inference(quant_inst,[status(thm)],[])).
% 1.26/1.46 tff(8740,plain,
% 1.26/1.46 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s10) | (~node26(s10))),
% 1.26/1.46 inference(modus_ponens,[status(thm)],[8739, 8738])).
% 1.26/1.46 tff(8741,plain,
% 1.26/1.46 (~node26(s10)),
% 1.26/1.46 inference(unit_resolution,[status(thm)],[8740, 3949, 8737])).
% 1.26/1.46 tff(8742,plain,
% 1.26/1.46 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s9, c_t2) | (~node26(s9)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s9, c_t2) | (~node26(s9)))),
% 1.26/1.46 inference(rewrite,[status(thm)],[])).
% 1.26/1.46 tff(8743,plain,
% 1.26/1.46 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s9, c_t2) | (~node26(s9)))),
% 1.26/1.46 inference(quant_inst,[status(thm)],[])).
% 1.26/1.46 tff(8744,plain,
% 1.26/1.46 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s9, c_t2) | (~node26(s9))),
% 1.26/1.46 inference(modus_ponens,[status(thm)],[8743, 8742])).
% 1.26/1.46 tff(8745,plain,
% 1.26/1.46 (~node26(s9)),
% 1.26/1.46 inference(unit_resolution,[status(thm)],[8744, 8110, 1192])).
% 1.26/1.46 tff(8746,plain,
% 1.26/1.46 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s8)) | (~m_main_v_state2(s8, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s8)) | (~m_main_v_state2(s8, c_c2)))),
% 1.26/1.46 inference(rewrite,[status(thm)],[])).
% 1.26/1.46 tff(8747,plain,
% 1.26/1.46 (((~m_main_v_state2(s8, c_c2)) | (~always25(s8))) <=> ((~always25(s8)) | (~m_main_v_state2(s8, c_c2)))),
% 1.26/1.46 inference(rewrite,[status(thm)],[])).
% 1.26/1.46 tff(8748,plain,
% 1.26/1.46 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s8, c_c2)) | (~always25(s8)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s8)) | (~m_main_v_state2(s8, c_c2))))),
% 1.26/1.46 inference(monotonicity,[status(thm)],[8747])).
% 1.26/1.46 tff(8749,plain,
% 1.26/1.46 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s8, c_c2)) | (~always25(s8)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s8)) | (~m_main_v_state2(s8, c_c2)))),
% 1.26/1.46 inference(transitivity,[status(thm)],[8748, 8746])).
% 1.26/1.46 tff(8750,plain,
% 1.26/1.46 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s8, c_c2)) | (~always25(s8)))),
% 1.26/1.46 inference(quant_inst,[status(thm)],[])).
% 1.26/1.46 tff(8751,plain,
% 1.26/1.46 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s8)) | (~m_main_v_state2(s8, c_c2))),
% 1.26/1.46 inference(modus_ponens,[status(thm)],[8750, 8749])).
% 1.26/1.46 tff(8752,plain,
% 1.26/1.46 (~always25(s8)),
% 1.26/1.46 inference(unit_resolution,[status(thm)],[8751, 3908, 1121])).
% 1.26/1.46 tff(8753,plain,
% 1.26/1.46 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s7, s8)) | (~always25(s7)) | always25(s8))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s7, s8)) | (~always25(s7)) | always25(s8))),
% 1.26/1.46 inference(rewrite,[status(thm)],[])).
% 1.26/1.46 tff(8754,plain,
% 1.26/1.46 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s7, s8)) | (~always25(s7)) | always25(s8))),
% 1.26/1.46 inference(quant_inst,[status(thm)],[])).
% 1.26/1.46 tff(8755,plain,
% 1.26/1.46 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s7, s8)) | (~always25(s7)) | always25(s8)),
% 1.26/1.46 inference(modus_ponens,[status(thm)],[8754, 8753])).
% 1.26/1.46 tff(8756,plain,
% 1.26/1.46 ((~always25(s7)) | always25(s8)),
% 1.26/1.46 inference(unit_resolution,[status(thm)],[8755, 3934, 1047])).
% 1.26/1.46 tff(8757,plain,
% 1.26/1.46 (~always25(s7)),
% 1.26/1.46 inference(unit_resolution,[status(thm)],[8756, 8752])).
% 1.26/1.46 tff(8758,plain,
% 1.26/1.46 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s7) | (~node26(s7)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s7) | (~node26(s7)))),
% 1.26/1.46 inference(rewrite,[status(thm)],[])).
% 1.26/1.46 tff(8759,plain,
% 1.26/1.46 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s7) | (~node26(s7)))),
% 1.26/1.46 inference(quant_inst,[status(thm)],[])).
% 1.26/1.46 tff(8760,plain,
% 1.26/1.46 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s7) | (~node26(s7))),
% 1.26/1.46 inference(modus_ponens,[status(thm)],[8759, 8758])).
% 1.26/1.46 tff(8761,plain,
% 1.26/1.46 (~node26(s7)),
% 1.26/1.46 inference(unit_resolution,[status(thm)],[8760, 3949, 8757])).
% 1.26/1.46 tff(8762,plain,
% 1.26/1.46 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s6, s7)) | (~always25(s6)) | always25(s7))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s6, s7)) | (~always25(s6)) | always25(s7))),
% 1.26/1.46 inference(rewrite,[status(thm)],[])).
% 1.26/1.46 tff(8763,plain,
% 1.26/1.46 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s6, s7)) | (~always25(s6)) | always25(s7))),
% 1.26/1.46 inference(quant_inst,[status(thm)],[])).
% 1.26/1.46 tff(8764,plain,
% 1.26/1.46 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s6, s7)) | (~always25(s6)) | always25(s7)),
% 1.26/1.46 inference(modus_ponens,[status(thm)],[8763, 8762])).
% 1.26/1.46 tff(8765,plain,
% 1.26/1.46 ((~always25(s6)) | always25(s7)),
% 1.26/1.46 inference(unit_resolution,[status(thm)],[8764, 3934, 962])).
% 1.26/1.46 tff(8766,plain,
% 1.26/1.46 (~always25(s6)),
% 1.26/1.46 inference(unit_resolution,[status(thm)],[8765, 8757])).
% 1.26/1.46 tff(8767,plain,
% 1.26/1.46 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s6) | (~node26(s6)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s6) | (~node26(s6)))),
% 1.26/1.46 inference(rewrite,[status(thm)],[])).
% 1.26/1.46 tff(8768,plain,
% 1.26/1.46 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s6) | (~node26(s6)))),
% 1.26/1.46 inference(quant_inst,[status(thm)],[])).
% 1.26/1.46 tff(8769,plain,
% 1.26/1.46 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s6) | (~node26(s6))),
% 1.26/1.46 inference(modus_ponens,[status(thm)],[8768, 8767])).
% 1.26/1.46 tff(8770,plain,
% 1.26/1.46 (~node26(s6)),
% 1.26/1.46 inference(unit_resolution,[status(thm)],[8769, 3949, 8766])).
% 1.26/1.46 tff(8771,plain,
% 1.26/1.46 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s5, c_t2) | (~node26(s5)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s5, c_t2) | (~node26(s5)))),
% 1.26/1.46 inference(rewrite,[status(thm)],[])).
% 1.26/1.46 tff(8772,plain,
% 1.26/1.46 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s5, c_t2) | (~node26(s5)))),
% 1.26/1.46 inference(quant_inst,[status(thm)],[])).
% 1.26/1.46 tff(8773,plain,
% 1.26/1.46 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s5, c_t2) | (~node26(s5))),
% 1.26/1.46 inference(modus_ponens,[status(thm)],[8772, 8771])).
% 1.26/1.46 tff(8774,plain,
% 1.26/1.46 (~node26(s5)),
% 1.26/1.46 inference(unit_resolution,[status(thm)],[8773, 8110, 867])).
% 1.26/1.46 tff(8775,plain,
% 1.26/1.46 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s4)) | (~m_main_v_state2(s4, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s4)) | (~m_main_v_state2(s4, c_c2)))),
% 1.26/1.46 inference(rewrite,[status(thm)],[])).
% 1.26/1.46 tff(8776,plain,
% 1.26/1.46 (((~m_main_v_state2(s4, c_c2)) | (~always25(s4))) <=> ((~always25(s4)) | (~m_main_v_state2(s4, c_c2)))),
% 1.26/1.46 inference(rewrite,[status(thm)],[])).
% 1.26/1.46 tff(8777,plain,
% 1.26/1.46 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s4, c_c2)) | (~always25(s4)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~always25(s4)) | (~m_main_v_state2(s4, c_c2))))),
% 1.26/1.46 inference(monotonicity,[status(thm)],[8776])).
% 1.26/1.46 tff(8778,plain,
% 1.26/1.46 (((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s4, c_c2)) | (~always25(s4)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s4)) | (~m_main_v_state2(s4, c_c2)))),
% 1.26/1.46 inference(transitivity,[status(thm)],[8777, 8775])).
% 1.26/1.46 tff(8779,plain,
% 1.26/1.46 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | ((~m_main_v_state2(s4, c_c2)) | (~always25(s4)))),
% 1.26/1.46 inference(quant_inst,[status(thm)],[])).
% 1.26/1.46 tff(8780,plain,
% 1.26/1.46 ((~![X: $i] : ((~m_main_v_state2(X, c_c2)) | (~always25(X)))) | (~always25(s4)) | (~m_main_v_state2(s4, c_c2))),
% 1.26/1.46 inference(modus_ponens,[status(thm)],[8779, 8778])).
% 1.26/1.46 tff(8781,plain,
% 1.26/1.46 (~always25(s4)),
% 1.26/1.46 inference(unit_resolution,[status(thm)],[8780, 3908, 622])).
% 1.26/1.46 tff(8782,plain,
% 1.26/1.46 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s3, s4)) | (~always25(s3)) | always25(s4))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s3, s4)) | (~always25(s3)) | always25(s4))),
% 1.26/1.46 inference(rewrite,[status(thm)],[])).
% 1.26/1.46 tff(8783,plain,
% 1.26/1.46 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s3, s4)) | (~always25(s3)) | always25(s4))),
% 1.26/1.46 inference(quant_inst,[status(thm)],[])).
% 1.26/1.46 tff(8784,plain,
% 1.26/1.46 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s3, s4)) | (~always25(s3)) | always25(s4)),
% 1.26/1.46 inference(modus_ponens,[status(thm)],[8783, 8782])).
% 1.26/1.46 tff(8785,plain,
% 1.26/1.46 ((~always25(s3)) | always25(s4)),
% 1.26/1.46 inference(unit_resolution,[status(thm)],[8784, 3934, 603])).
% 1.26/1.46 tff(8786,plain,
% 1.26/1.46 (~always25(s3)),
% 1.26/1.46 inference(unit_resolution,[status(thm)],[8785, 8781])).
% 1.26/1.46 tff(8787,plain,
% 1.26/1.46 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s2, s3)) | (~always25(s2)) | always25(s3))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s2, s3)) | (~always25(s2)) | always25(s3))),
% 1.26/1.46 inference(rewrite,[status(thm)],[])).
% 1.26/1.46 tff(8788,plain,
% 1.26/1.46 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s2, s3)) | (~always25(s2)) | always25(s3))),
% 1.26/1.46 inference(quant_inst,[status(thm)],[])).
% 1.26/1.46 tff(8789,plain,
% 1.26/1.46 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s2, s3)) | (~always25(s2)) | always25(s3)),
% 1.26/1.46 inference(modus_ponens,[status(thm)],[8788, 8787])).
% 1.26/1.46 tff(8790,plain,
% 1.26/1.46 ((~always25(s2)) | always25(s3)),
% 1.26/1.46 inference(unit_resolution,[status(thm)],[8789, 3934, 484])).
% 1.26/1.46 tff(8791,plain,
% 1.26/1.46 (~always25(s2)),
% 1.26/1.46 inference(unit_resolution,[status(thm)],[8790, 8786])).
% 1.26/1.46 tff(8792,plain,
% 1.26/1.46 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s2) | (~node26(s2)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s2) | (~node26(s2)))),
% 1.26/1.46 inference(rewrite,[status(thm)],[])).
% 1.26/1.46 tff(8793,plain,
% 1.26/1.46 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s2) | (~node26(s2)))),
% 1.26/1.46 inference(quant_inst,[status(thm)],[])).
% 1.26/1.46 tff(8794,plain,
% 1.26/1.46 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s2) | (~node26(s2))),
% 1.26/1.46 inference(modus_ponens,[status(thm)],[8793, 8792])).
% 1.26/1.46 tff(8795,plain,
% 1.26/1.46 (~node26(s2)),
% 1.26/1.46 inference(unit_resolution,[status(thm)],[8794, 3949, 8791])).
% 1.26/1.46 tff(8796,plain,
% 1.26/1.46 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s1, s2)) | (~always25(s1)) | always25(s2))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s1, s2)) | (~always25(s1)) | always25(s2))),
% 1.26/1.46 inference(rewrite,[status(thm)],[])).
% 1.26/1.46 tff(8797,plain,
% 1.26/1.46 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s1, s2)) | (~always25(s1)) | always25(s2))),
% 1.26/1.46 inference(quant_inst,[status(thm)],[])).
% 1.26/1.46 tff(8798,plain,
% 1.26/1.46 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s1, s2)) | (~always25(s1)) | always25(s2)),
% 1.26/1.46 inference(modus_ponens,[status(thm)],[8797, 8796])).
% 1.26/1.46 tff(8799,plain,
% 1.26/1.46 ((~always25(s1)) | always25(s2)),
% 1.26/1.46 inference(unit_resolution,[status(thm)],[8798, 3934, 282])).
% 1.26/1.46 tff(8800,plain,
% 1.26/1.46 (~always25(s1)),
% 1.26/1.46 inference(unit_resolution,[status(thm)],[8799, 8791])).
% 1.26/1.46 tff(8801,plain,
% 1.26/1.46 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s1) | (~node26(s1)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s1) | (~node26(s1)))),
% 1.26/1.46 inference(rewrite,[status(thm)],[])).
% 1.26/1.46 tff(8802,plain,
% 1.26/1.46 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s1) | (~node26(s1)))),
% 1.26/1.46 inference(quant_inst,[status(thm)],[])).
% 1.26/1.46 tff(8803,plain,
% 1.26/1.46 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s1) | (~node26(s1))),
% 1.26/1.46 inference(modus_ponens,[status(thm)],[8802, 8801])).
% 1.26/1.46 tff(8804,plain,
% 1.26/1.46 (~node26(s1)),
% 1.26/1.46 inference(unit_resolution,[status(thm)],[8803, 3949, 8800])).
% 1.26/1.46 tff(8805,plain,
% 1.26/1.46 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s0, c_t2) | (~node26(s0)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s0, c_t2) | (~node26(s0)))),
% 1.26/1.46 inference(rewrite,[status(thm)],[])).
% 1.26/1.46 tff(8806,plain,
% 1.26/1.46 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | (m_main_v_state2(s0, c_t2) | (~node26(s0)))),
% 1.26/1.46 inference(quant_inst,[status(thm)],[])).
% 1.26/1.46 tff(8807,plain,
% 1.26/1.46 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node26(X)))) | m_main_v_state2(s0, c_t2) | (~node26(s0))),
% 1.26/1.46 inference(modus_ponens,[status(thm)],[8806, 8805])).
% 1.26/1.46 tff(8808,plain,
% 1.26/1.46 (~node26(s0)),
% 1.26/1.46 inference(unit_resolution,[status(thm)],[8807, 8110, 96])).
% 1.26/1.46 tff(8809,plain,
% 1.26/1.46 (until27(s0) <=> until27(s0)),
% 1.26/1.46 inference(rewrite,[status(thm)],[])).
% 1.26/1.46 tff(8810,axiom,(until27(s0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty26')).
% 1.26/1.46 tff(8811,plain,
% 1.26/1.46 (until27(s0)),
% 1.26/1.46 inference(modus_ponens,[status(thm)],[8810, 8809])).
% 1.26/1.46 tff(8812,plain,
% 1.26/1.46 (^[X: $i] : refl((node26(X) | (~until27(X)) | xuntil28(X)) <=> (node26(X) | (~until27(X)) | xuntil28(X)))),
% 1.26/1.46 inference(bind,[status(th)],[])).
% 1.26/1.46 tff(8813,plain,
% 1.26/1.46 (![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X)) <=> ![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))),
% 1.26/1.46 inference(quant_intro,[status(thm)],[8812])).
% 1.26/1.46 tff(8814,plain,
% 1.26/1.46 (![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X)) <=> ![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))),
% 1.26/1.46 inference(rewrite,[status(thm)],[])).
% 1.26/1.46 tff(8815,plain,
% 1.26/1.46 (^[X: $i] : rewrite(((node26(X) | xuntil28(X)) | (~until27(X))) <=> (node26(X) | (~until27(X)) | xuntil28(X)))),
% 1.26/1.46 inference(bind,[status(th)],[])).
% 1.26/1.46 tff(8816,plain,
% 1.26/1.46 (![X: $i] : ((node26(X) | xuntil28(X)) | (~until27(X))) <=> ![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))),
% 1.26/1.46 inference(quant_intro,[status(thm)],[8815])).
% 1.26/1.46 tff(8817,axiom,(![X: $i] : ((node26(X) | xuntil28(X)) | (~until27(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty19')).
% 1.26/1.46 tff(8818,plain,
% 1.26/1.46 (![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))),
% 1.26/1.46 inference(modus_ponens,[status(thm)],[8817, 8816])).
% 1.26/1.46 tff(8819,plain,
% 1.26/1.46 (![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))),
% 1.26/1.46 inference(modus_ponens,[status(thm)],[8818, 8814])).
% 1.26/1.46 tff(8820,plain,(
% 1.26/1.46 ![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))),
% 1.26/1.46 inference(skolemize,[status(sab)],[8819])).
% 1.26/1.46 tff(8821,plain,
% 1.26/1.46 (![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))),
% 1.26/1.46 inference(modus_ponens,[status(thm)],[8820, 8813])).
% 1.26/1.46 tff(8822,plain,
% 1.26/1.46 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s0) | node26(s0) | (~until27(s0)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s0) | node26(s0) | (~until27(s0)))),
% 1.26/1.46 inference(rewrite,[status(thm)],[])).
% 1.26/1.46 tff(8823,plain,
% 1.26/1.46 ((node26(s0) | (~until27(s0)) | xuntil28(s0)) <=> (xuntil28(s0) | node26(s0) | (~until27(s0)))),
% 1.26/1.46 inference(rewrite,[status(thm)],[])).
% 1.26/1.46 tff(8824,plain,
% 1.26/1.46 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s0) | (~until27(s0)) | xuntil28(s0))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s0) | node26(s0) | (~until27(s0))))),
% 1.26/1.46 inference(monotonicity,[status(thm)],[8823])).
% 1.26/1.46 tff(8825,plain,
% 1.26/1.46 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s0) | (~until27(s0)) | xuntil28(s0))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s0) | node26(s0) | (~until27(s0)))),
% 1.30/1.46 inference(transitivity,[status(thm)],[8824, 8822])).
% 1.30/1.46 tff(8826,plain,
% 1.30/1.46 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s0) | (~until27(s0)) | xuntil28(s0))),
% 1.30/1.46 inference(quant_inst,[status(thm)],[])).
% 1.30/1.46 tff(8827,plain,
% 1.30/1.46 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s0) | node26(s0) | (~until27(s0))),
% 1.30/1.46 inference(modus_ponens,[status(thm)],[8826, 8825])).
% 1.30/1.46 tff(8828,plain,
% 1.30/1.46 (xuntil28(s0) | node26(s0)),
% 1.30/1.46 inference(unit_resolution,[status(thm)],[8827, 8821, 8811])).
% 1.30/1.46 tff(8829,plain,
% 1.30/1.46 (xuntil28(s0)),
% 1.30/1.46 inference(unit_resolution,[status(thm)],[8828, 8808])).
% 1.30/1.46 tff(8830,plain,
% 1.30/1.46 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)) <=> ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)))),
% 1.30/1.46 inference(bind,[status(th)],[])).
% 1.30/1.46 tff(8831,plain,
% 1.30/1.46 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 1.30/1.46 inference(quant_intro,[status(thm)],[8830])).
% 1.30/1.46 tff(8832,plain,
% 1.30/1.46 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 1.30/1.46 inference(rewrite,[status(thm)],[])).
% 1.30/1.46 tff(8833,plain,
% 1.30/1.46 (^[Y: $i, X: $i] : rewrite(((until27(Y) | (~succ(X, Y))) | (~xuntil28(X))) <=> ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)))),
% 1.30/1.46 inference(bind,[status(th)],[])).
% 1.30/1.46 tff(8834,plain,
% 1.30/1.46 (![Y: $i, X: $i] : ((until27(Y) | (~succ(X, Y))) | (~xuntil28(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 1.30/1.46 inference(quant_intro,[status(thm)],[8833])).
% 1.30/1.46 tff(8835,axiom,(![Y: $i, X: $i] : ((until27(Y) | (~succ(X, Y))) | (~xuntil28(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty20')).
% 1.30/1.46 tff(8836,plain,
% 1.30/1.46 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 1.30/1.46 inference(modus_ponens,[status(thm)],[8835, 8834])).
% 1.30/1.46 tff(8837,plain,
% 1.30/1.46 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 1.30/1.46 inference(modus_ponens,[status(thm)],[8836, 8832])).
% 1.30/1.46 tff(8838,plain,(
% 1.30/1.46 ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 1.30/1.46 inference(skolemize,[status(sab)],[8837])).
% 1.30/1.46 tff(8839,plain,
% 1.30/1.46 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 1.30/1.46 inference(modus_ponens,[status(thm)],[8838, 8831])).
% 1.30/1.46 tff(8840,plain,
% 1.30/1.46 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s0, s1)) | (~xuntil28(s0)) | until27(s1))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s0, s1)) | (~xuntil28(s0)) | until27(s1))),
% 1.30/1.46 inference(rewrite,[status(thm)],[])).
% 1.30/1.46 tff(8841,plain,
% 1.30/1.46 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s0, s1)) | (~xuntil28(s0)) | until27(s1))),
% 1.30/1.46 inference(quant_inst,[status(thm)],[])).
% 1.30/1.46 tff(8842,plain,
% 1.30/1.46 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s0, s1)) | (~xuntil28(s0)) | until27(s1)),
% 1.30/1.46 inference(modus_ponens,[status(thm)],[8841, 8840])).
% 1.30/1.46 tff(8843,plain,
% 1.30/1.46 ((~xuntil28(s0)) | until27(s1)),
% 1.30/1.46 inference(unit_resolution,[status(thm)],[8842, 35, 8839])).
% 1.30/1.46 tff(8844,plain,
% 1.30/1.46 (until27(s1)),
% 1.30/1.46 inference(unit_resolution,[status(thm)],[8843, 8829])).
% 1.30/1.46 tff(8845,plain,
% 1.30/1.46 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s1) | node26(s1) | (~until27(s1)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s1) | node26(s1) | (~until27(s1)))),
% 1.30/1.46 inference(rewrite,[status(thm)],[])).
% 1.30/1.46 tff(8846,plain,
% 1.30/1.46 ((node26(s1) | (~until27(s1)) | xuntil28(s1)) <=> (xuntil28(s1) | node26(s1) | (~until27(s1)))),
% 1.30/1.46 inference(rewrite,[status(thm)],[])).
% 1.30/1.46 tff(8847,plain,
% 1.30/1.46 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s1) | (~until27(s1)) | xuntil28(s1))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s1) | node26(s1) | (~until27(s1))))),
% 1.30/1.46 inference(monotonicity,[status(thm)],[8846])).
% 1.30/1.46 tff(8848,plain,
% 1.30/1.46 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s1) | (~until27(s1)) | xuntil28(s1))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s1) | node26(s1) | (~until27(s1)))),
% 1.30/1.46 inference(transitivity,[status(thm)],[8847, 8845])).
% 1.30/1.46 tff(8849,plain,
% 1.30/1.46 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s1) | (~until27(s1)) | xuntil28(s1))),
% 1.30/1.46 inference(quant_inst,[status(thm)],[])).
% 1.30/1.46 tff(8850,plain,
% 1.30/1.46 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s1) | node26(s1) | (~until27(s1))),
% 1.30/1.46 inference(modus_ponens,[status(thm)],[8849, 8848])).
% 1.30/1.46 tff(8851,plain,
% 1.30/1.46 (xuntil28(s1) | node26(s1)),
% 1.30/1.46 inference(unit_resolution,[status(thm)],[8850, 8821, 8844])).
% 1.30/1.46 tff(8852,plain,
% 1.30/1.46 (xuntil28(s1)),
% 1.30/1.46 inference(unit_resolution,[status(thm)],[8851, 8804])).
% 1.30/1.46 tff(8853,plain,
% 1.30/1.46 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s1, s2)) | (~xuntil28(s1)) | until27(s2))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s1, s2)) | (~xuntil28(s1)) | until27(s2))),
% 1.30/1.46 inference(rewrite,[status(thm)],[])).
% 1.30/1.46 tff(8854,plain,
% 1.30/1.46 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s1, s2)) | (~xuntil28(s1)) | until27(s2))),
% 1.30/1.46 inference(quant_inst,[status(thm)],[])).
% 1.30/1.46 tff(8855,plain,
% 1.30/1.46 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s1, s2)) | (~xuntil28(s1)) | until27(s2)),
% 1.30/1.46 inference(modus_ponens,[status(thm)],[8854, 8853])).
% 1.30/1.46 tff(8856,plain,
% 1.30/1.46 ((~xuntil28(s1)) | until27(s2)),
% 1.30/1.46 inference(unit_resolution,[status(thm)],[8855, 278, 8839])).
% 1.30/1.46 tff(8857,plain,
% 1.30/1.46 (until27(s2)),
% 1.30/1.46 inference(unit_resolution,[status(thm)],[8856, 8852])).
% 1.30/1.46 tff(8858,plain,
% 1.30/1.46 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s2) | node26(s2) | (~until27(s2)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s2) | node26(s2) | (~until27(s2)))),
% 1.30/1.46 inference(rewrite,[status(thm)],[])).
% 1.30/1.46 tff(8859,plain,
% 1.30/1.46 ((node26(s2) | (~until27(s2)) | xuntil28(s2)) <=> (xuntil28(s2) | node26(s2) | (~until27(s2)))),
% 1.30/1.46 inference(rewrite,[status(thm)],[])).
% 1.30/1.46 tff(8860,plain,
% 1.30/1.46 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s2) | (~until27(s2)) | xuntil28(s2))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s2) | node26(s2) | (~until27(s2))))),
% 1.30/1.46 inference(monotonicity,[status(thm)],[8859])).
% 1.30/1.46 tff(8861,plain,
% 1.30/1.46 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s2) | (~until27(s2)) | xuntil28(s2))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s2) | node26(s2) | (~until27(s2)))),
% 1.30/1.46 inference(transitivity,[status(thm)],[8860, 8858])).
% 1.30/1.46 tff(8862,plain,
% 1.30/1.46 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s2) | (~until27(s2)) | xuntil28(s2))),
% 1.30/1.46 inference(quant_inst,[status(thm)],[])).
% 1.30/1.46 tff(8863,plain,
% 1.30/1.46 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s2) | node26(s2) | (~until27(s2))),
% 1.30/1.46 inference(modus_ponens,[status(thm)],[8862, 8861])).
% 1.30/1.46 tff(8864,plain,
% 1.30/1.46 (xuntil28(s2)),
% 1.30/1.46 inference(unit_resolution,[status(thm)],[8863, 8821, 8857, 8795])).
% 1.30/1.46 tff(8865,plain,
% 1.30/1.46 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s2, s3)) | (~xuntil28(s2)) | until27(s3))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s2, s3)) | (~xuntil28(s2)) | until27(s3))),
% 1.30/1.46 inference(rewrite,[status(thm)],[])).
% 1.30/1.46 tff(8866,plain,
% 1.30/1.46 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s2, s3)) | (~xuntil28(s2)) | until27(s3))),
% 1.30/1.46 inference(quant_inst,[status(thm)],[])).
% 1.30/1.46 tff(8867,plain,
% 1.30/1.46 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s2, s3)) | (~xuntil28(s2)) | until27(s3)),
% 1.30/1.46 inference(modus_ponens,[status(thm)],[8866, 8865])).
% 1.30/1.46 tff(8868,plain,
% 1.30/1.46 ((~xuntil28(s2)) | until27(s3)),
% 1.30/1.46 inference(unit_resolution,[status(thm)],[8867, 480, 8839])).
% 1.30/1.46 tff(8869,plain,
% 1.30/1.46 (until27(s3)),
% 1.30/1.46 inference(unit_resolution,[status(thm)],[8868, 8864])).
% 1.30/1.46 tff(8870,plain,
% 1.30/1.46 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s3) | (~node26(s3)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s3) | (~node26(s3)))),
% 1.30/1.46 inference(rewrite,[status(thm)],[])).
% 1.30/1.46 tff(8871,plain,
% 1.30/1.46 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s3) | (~node26(s3)))),
% 1.30/1.46 inference(quant_inst,[status(thm)],[])).
% 1.30/1.46 tff(8872,plain,
% 1.30/1.46 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s3) | (~node26(s3))),
% 1.30/1.46 inference(modus_ponens,[status(thm)],[8871, 8870])).
% 1.30/1.46 tff(8873,plain,
% 1.30/1.46 (~node26(s3)),
% 1.30/1.46 inference(unit_resolution,[status(thm)],[8872, 3949, 8786])).
% 1.30/1.46 tff(8874,plain,
% 1.30/1.46 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s3) | node26(s3) | (~until27(s3)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s3) | node26(s3) | (~until27(s3)))),
% 1.30/1.46 inference(rewrite,[status(thm)],[])).
% 1.30/1.46 tff(8875,plain,
% 1.30/1.46 ((node26(s3) | (~until27(s3)) | xuntil28(s3)) <=> (xuntil28(s3) | node26(s3) | (~until27(s3)))),
% 1.30/1.46 inference(rewrite,[status(thm)],[])).
% 1.30/1.46 tff(8876,plain,
% 1.30/1.46 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s3) | (~until27(s3)) | xuntil28(s3))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s3) | node26(s3) | (~until27(s3))))),
% 1.30/1.46 inference(monotonicity,[status(thm)],[8875])).
% 1.30/1.46 tff(8877,plain,
% 1.30/1.46 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s3) | (~until27(s3)) | xuntil28(s3))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s3) | node26(s3) | (~until27(s3)))),
% 1.30/1.46 inference(transitivity,[status(thm)],[8876, 8874])).
% 1.30/1.46 tff(8878,plain,
% 1.30/1.46 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s3) | (~until27(s3)) | xuntil28(s3))),
% 1.30/1.46 inference(quant_inst,[status(thm)],[])).
% 1.30/1.46 tff(8879,plain,
% 1.30/1.46 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s3) | node26(s3) | (~until27(s3))),
% 1.30/1.46 inference(modus_ponens,[status(thm)],[8878, 8877])).
% 1.30/1.46 tff(8880,plain,
% 1.30/1.46 (xuntil28(s3) | (~until27(s3))),
% 1.30/1.46 inference(unit_resolution,[status(thm)],[8879, 8821, 8873])).
% 1.30/1.46 tff(8881,plain,
% 1.30/1.46 (xuntil28(s3)),
% 1.30/1.46 inference(unit_resolution,[status(thm)],[8880, 8869])).
% 1.30/1.46 tff(8882,plain,
% 1.30/1.46 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s3, s4)) | (~xuntil28(s3)) | until27(s4))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s3, s4)) | (~xuntil28(s3)) | until27(s4))),
% 1.30/1.46 inference(rewrite,[status(thm)],[])).
% 1.30/1.46 tff(8883,plain,
% 1.30/1.46 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s3, s4)) | (~xuntil28(s3)) | until27(s4))),
% 1.30/1.46 inference(quant_inst,[status(thm)],[])).
% 1.30/1.46 tff(8884,plain,
% 1.30/1.46 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s3, s4)) | (~xuntil28(s3)) | until27(s4)),
% 1.30/1.46 inference(modus_ponens,[status(thm)],[8883, 8882])).
% 1.30/1.46 tff(8885,plain,
% 1.30/1.46 ((~xuntil28(s3)) | until27(s4)),
% 1.30/1.46 inference(unit_resolution,[status(thm)],[8884, 599, 8839])).
% 1.30/1.46 tff(8886,plain,
% 1.30/1.46 (until27(s4)),
% 1.30/1.46 inference(unit_resolution,[status(thm)],[8885, 8881])).
% 1.30/1.46 tff(8887,plain,
% 1.30/1.46 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s4) | (~node26(s4)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s4) | (~node26(s4)))),
% 1.30/1.46 inference(rewrite,[status(thm)],[])).
% 1.30/1.46 tff(8888,plain,
% 1.30/1.46 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s4) | (~node26(s4)))),
% 1.30/1.46 inference(quant_inst,[status(thm)],[])).
% 1.30/1.46 tff(8889,plain,
% 1.30/1.46 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s4) | (~node26(s4))),
% 1.30/1.46 inference(modus_ponens,[status(thm)],[8888, 8887])).
% 1.30/1.46 tff(8890,plain,
% 1.30/1.46 (~node26(s4)),
% 1.30/1.46 inference(unit_resolution,[status(thm)],[8889, 3949, 8781])).
% 1.30/1.46 tff(8891,plain,
% 1.30/1.46 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s4) | node26(s4) | (~until27(s4)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s4) | node26(s4) | (~until27(s4)))),
% 1.30/1.46 inference(rewrite,[status(thm)],[])).
% 1.30/1.46 tff(8892,plain,
% 1.30/1.46 ((node26(s4) | (~until27(s4)) | xuntil28(s4)) <=> (xuntil28(s4) | node26(s4) | (~until27(s4)))),
% 1.30/1.46 inference(rewrite,[status(thm)],[])).
% 1.30/1.46 tff(8893,plain,
% 1.30/1.46 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s4) | (~until27(s4)) | xuntil28(s4))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s4) | node26(s4) | (~until27(s4))))),
% 1.30/1.46 inference(monotonicity,[status(thm)],[8892])).
% 1.30/1.46 tff(8894,plain,
% 1.30/1.46 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s4) | (~until27(s4)) | xuntil28(s4))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s4) | node26(s4) | (~until27(s4)))),
% 1.30/1.46 inference(transitivity,[status(thm)],[8893, 8891])).
% 1.30/1.46 tff(8895,plain,
% 1.30/1.46 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s4) | (~until27(s4)) | xuntil28(s4))),
% 1.30/1.46 inference(quant_inst,[status(thm)],[])).
% 1.30/1.46 tff(8896,plain,
% 1.30/1.46 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s4) | node26(s4) | (~until27(s4))),
% 1.30/1.46 inference(modus_ponens,[status(thm)],[8895, 8894])).
% 1.30/1.46 tff(8897,plain,
% 1.30/1.46 (xuntil28(s4) | (~until27(s4))),
% 1.30/1.46 inference(unit_resolution,[status(thm)],[8896, 8821, 8890])).
% 1.30/1.46 tff(8898,plain,
% 1.30/1.46 (xuntil28(s4)),
% 1.30/1.46 inference(unit_resolution,[status(thm)],[8897, 8886])).
% 1.30/1.46 tff(8899,plain,
% 1.30/1.46 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s4, s5)) | (~xuntil28(s4)) | until27(s5))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s4, s5)) | (~xuntil28(s4)) | until27(s5))),
% 1.30/1.46 inference(rewrite,[status(thm)],[])).
% 1.30/1.46 tff(8900,plain,
% 1.30/1.46 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s4, s5)) | (~xuntil28(s4)) | until27(s5))),
% 1.30/1.46 inference(quant_inst,[status(thm)],[])).
% 1.30/1.46 tff(8901,plain,
% 1.30/1.46 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s4, s5)) | (~xuntil28(s4)) | until27(s5)),
% 1.30/1.46 inference(modus_ponens,[status(thm)],[8900, 8899])).
% 1.30/1.46 tff(8902,plain,
% 1.30/1.46 ((~xuntil28(s4)) | until27(s5)),
% 1.30/1.46 inference(unit_resolution,[status(thm)],[8901, 708, 8839])).
% 1.30/1.46 tff(8903,plain,
% 1.30/1.46 (until27(s5)),
% 1.30/1.46 inference(unit_resolution,[status(thm)],[8902, 8898])).
% 1.30/1.47 tff(8904,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s5) | node26(s5) | (~until27(s5)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s5) | node26(s5) | (~until27(s5)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(8905,plain,
% 1.30/1.47 ((node26(s5) | (~until27(s5)) | xuntil28(s5)) <=> (xuntil28(s5) | node26(s5) | (~until27(s5)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(8906,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s5) | (~until27(s5)) | xuntil28(s5))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s5) | node26(s5) | (~until27(s5))))),
% 1.30/1.47 inference(monotonicity,[status(thm)],[8905])).
% 1.30/1.47 tff(8907,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s5) | (~until27(s5)) | xuntil28(s5))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s5) | node26(s5) | (~until27(s5)))),
% 1.30/1.47 inference(transitivity,[status(thm)],[8906, 8904])).
% 1.30/1.47 tff(8908,plain,
% 1.30/1.47 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s5) | (~until27(s5)) | xuntil28(s5))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(8909,plain,
% 1.30/1.47 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s5) | node26(s5) | (~until27(s5))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[8908, 8907])).
% 1.30/1.47 tff(8910,plain,
% 1.30/1.47 (xuntil28(s5)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[8909, 8821, 8903, 8774])).
% 1.30/1.47 tff(8911,plain,
% 1.30/1.47 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s5, s6)) | (~xuntil28(s5)) | until27(s6))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s5, s6)) | (~xuntil28(s5)) | until27(s6))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(8912,plain,
% 1.30/1.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s5, s6)) | (~xuntil28(s5)) | until27(s6))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(8913,plain,
% 1.30/1.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s5, s6)) | (~xuntil28(s5)) | until27(s6)),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[8912, 8911])).
% 1.30/1.47 tff(8914,plain,
% 1.30/1.47 ((~xuntil28(s5)) | until27(s6)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[8913, 874, 8839])).
% 1.30/1.47 tff(8915,plain,
% 1.30/1.47 (until27(s6)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[8914, 8910])).
% 1.30/1.47 tff(8916,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s6) | node26(s6) | (~until27(s6)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s6) | node26(s6) | (~until27(s6)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(8917,plain,
% 1.30/1.47 ((node26(s6) | (~until27(s6)) | xuntil28(s6)) <=> (xuntil28(s6) | node26(s6) | (~until27(s6)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(8918,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s6) | (~until27(s6)) | xuntil28(s6))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s6) | node26(s6) | (~until27(s6))))),
% 1.30/1.47 inference(monotonicity,[status(thm)],[8917])).
% 1.30/1.47 tff(8919,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s6) | (~until27(s6)) | xuntil28(s6))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s6) | node26(s6) | (~until27(s6)))),
% 1.30/1.47 inference(transitivity,[status(thm)],[8918, 8916])).
% 1.30/1.47 tff(8920,plain,
% 1.30/1.47 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s6) | (~until27(s6)) | xuntil28(s6))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(8921,plain,
% 1.30/1.47 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s6) | node26(s6) | (~until27(s6))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[8920, 8919])).
% 1.30/1.47 tff(8922,plain,
% 1.30/1.47 (xuntil28(s6) | node26(s6)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[8921, 8821, 8915])).
% 1.30/1.47 tff(8923,plain,
% 1.30/1.47 (xuntil28(s6)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[8922, 8770])).
% 1.30/1.47 tff(8924,plain,
% 1.30/1.47 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s6, s7)) | (~xuntil28(s6)) | until27(s7))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s6, s7)) | (~xuntil28(s6)) | until27(s7))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(8925,plain,
% 1.30/1.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s6, s7)) | (~xuntil28(s6)) | until27(s7))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(8926,plain,
% 1.30/1.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s6, s7)) | (~xuntil28(s6)) | until27(s7)),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[8925, 8924])).
% 1.30/1.47 tff(8927,plain,
% 1.30/1.47 ((~xuntil28(s6)) | until27(s7)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[8926, 958, 8839])).
% 1.30/1.47 tff(8928,plain,
% 1.30/1.47 (until27(s7)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[8927, 8923])).
% 1.30/1.47 tff(8929,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s7) | node26(s7) | (~until27(s7)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s7) | node26(s7) | (~until27(s7)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(8930,plain,
% 1.30/1.47 ((node26(s7) | (~until27(s7)) | xuntil28(s7)) <=> (xuntil28(s7) | node26(s7) | (~until27(s7)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(8931,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s7) | (~until27(s7)) | xuntil28(s7))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s7) | node26(s7) | (~until27(s7))))),
% 1.30/1.47 inference(monotonicity,[status(thm)],[8930])).
% 1.30/1.47 tff(8932,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s7) | (~until27(s7)) | xuntil28(s7))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s7) | node26(s7) | (~until27(s7)))),
% 1.30/1.47 inference(transitivity,[status(thm)],[8931, 8929])).
% 1.30/1.47 tff(8933,plain,
% 1.30/1.47 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s7) | (~until27(s7)) | xuntil28(s7))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(8934,plain,
% 1.30/1.47 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s7) | node26(s7) | (~until27(s7))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[8933, 8932])).
% 1.30/1.47 tff(8935,plain,
% 1.30/1.47 (xuntil28(s7)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[8934, 8821, 8928, 8761])).
% 1.30/1.47 tff(8936,plain,
% 1.30/1.47 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s7, s8)) | (~xuntil28(s7)) | until27(s8))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s7, s8)) | (~xuntil28(s7)) | until27(s8))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(8937,plain,
% 1.30/1.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s7, s8)) | (~xuntil28(s7)) | until27(s8))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(8938,plain,
% 1.30/1.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s7, s8)) | (~xuntil28(s7)) | until27(s8)),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[8937, 8936])).
% 1.30/1.47 tff(8939,plain,
% 1.30/1.47 ((~xuntil28(s7)) | until27(s8)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[8938, 1043, 8839])).
% 1.30/1.47 tff(8940,plain,
% 1.30/1.47 (until27(s8)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[8939, 8935])).
% 1.30/1.47 tff(8941,plain,
% 1.30/1.47 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s8) | (~node26(s8)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s8) | (~node26(s8)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(8942,plain,
% 1.30/1.47 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s8) | (~node26(s8)))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(8943,plain,
% 1.30/1.47 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s8) | (~node26(s8))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[8942, 8941])).
% 1.30/1.47 tff(8944,plain,
% 1.30/1.47 (~node26(s8)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[8943, 3949, 8752])).
% 1.30/1.47 tff(8945,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s8) | node26(s8) | (~until27(s8)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s8) | node26(s8) | (~until27(s8)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(8946,plain,
% 1.30/1.47 ((node26(s8) | (~until27(s8)) | xuntil28(s8)) <=> (xuntil28(s8) | node26(s8) | (~until27(s8)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(8947,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s8) | (~until27(s8)) | xuntil28(s8))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s8) | node26(s8) | (~until27(s8))))),
% 1.30/1.47 inference(monotonicity,[status(thm)],[8946])).
% 1.30/1.47 tff(8948,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s8) | (~until27(s8)) | xuntil28(s8))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s8) | node26(s8) | (~until27(s8)))),
% 1.30/1.47 inference(transitivity,[status(thm)],[8947, 8945])).
% 1.30/1.47 tff(8949,plain,
% 1.30/1.47 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s8) | (~until27(s8)) | xuntil28(s8))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(8950,plain,
% 1.30/1.47 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s8) | node26(s8) | (~until27(s8))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[8949, 8948])).
% 1.30/1.47 tff(8951,plain,
% 1.30/1.47 (xuntil28(s8) | (~until27(s8))),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[8950, 8821, 8944])).
% 1.30/1.47 tff(8952,plain,
% 1.30/1.47 (xuntil28(s8)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[8951, 8940])).
% 1.30/1.47 tff(8953,plain,
% 1.30/1.47 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s8, s9)) | (~xuntil28(s8)) | until27(s9))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s8, s9)) | (~xuntil28(s8)) | until27(s9))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(8954,plain,
% 1.30/1.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s8, s9)) | (~xuntil28(s8)) | until27(s9))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(8955,plain,
% 1.30/1.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s8, s9)) | (~xuntil28(s8)) | until27(s9)),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[8954, 8953])).
% 1.30/1.47 tff(8956,plain,
% 1.30/1.47 ((~xuntil28(s8)) | until27(s9)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[8955, 1132, 8839])).
% 1.30/1.47 tff(8957,plain,
% 1.30/1.47 (until27(s9)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[8956, 8952])).
% 1.30/1.47 tff(8958,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s9) | node26(s9) | (~until27(s9)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s9) | node26(s9) | (~until27(s9)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(8959,plain,
% 1.30/1.47 ((node26(s9) | (~until27(s9)) | xuntil28(s9)) <=> (xuntil28(s9) | node26(s9) | (~until27(s9)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(8960,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s9) | (~until27(s9)) | xuntil28(s9))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s9) | node26(s9) | (~until27(s9))))),
% 1.30/1.47 inference(monotonicity,[status(thm)],[8959])).
% 1.30/1.47 tff(8961,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s9) | (~until27(s9)) | xuntil28(s9))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s9) | node26(s9) | (~until27(s9)))),
% 1.30/1.47 inference(transitivity,[status(thm)],[8960, 8958])).
% 1.30/1.47 tff(8962,plain,
% 1.30/1.47 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s9) | (~until27(s9)) | xuntil28(s9))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(8963,plain,
% 1.30/1.47 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s9) | node26(s9) | (~until27(s9))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[8962, 8961])).
% 1.30/1.47 tff(8964,plain,
% 1.30/1.47 (xuntil28(s9)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[8963, 8821, 8957, 8745])).
% 1.30/1.47 tff(8965,plain,
% 1.30/1.47 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s9, s10)) | (~xuntil28(s9)) | until27(s10))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s9, s10)) | (~xuntil28(s9)) | until27(s10))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(8966,plain,
% 1.30/1.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s9, s10)) | (~xuntil28(s9)) | until27(s10))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(8967,plain,
% 1.30/1.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s9, s10)) | (~xuntil28(s9)) | until27(s10)),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[8966, 8965])).
% 1.30/1.47 tff(8968,plain,
% 1.30/1.47 ((~xuntil28(s9)) | until27(s10)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[8967, 1199, 8839])).
% 1.30/1.47 tff(8969,plain,
% 1.30/1.47 (until27(s10)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[8968, 8964])).
% 1.30/1.47 tff(8970,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s10) | node26(s10) | (~until27(s10)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s10) | node26(s10) | (~until27(s10)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(8971,plain,
% 1.30/1.47 ((node26(s10) | (~until27(s10)) | xuntil28(s10)) <=> (xuntil28(s10) | node26(s10) | (~until27(s10)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(8972,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s10) | (~until27(s10)) | xuntil28(s10))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s10) | node26(s10) | (~until27(s10))))),
% 1.30/1.47 inference(monotonicity,[status(thm)],[8971])).
% 1.30/1.47 tff(8973,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s10) | (~until27(s10)) | xuntil28(s10))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s10) | node26(s10) | (~until27(s10)))),
% 1.30/1.47 inference(transitivity,[status(thm)],[8972, 8970])).
% 1.30/1.47 tff(8974,plain,
% 1.30/1.47 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s10) | (~until27(s10)) | xuntil28(s10))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(8975,plain,
% 1.30/1.47 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s10) | node26(s10) | (~until27(s10))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[8974, 8973])).
% 1.30/1.47 tff(8976,plain,
% 1.30/1.47 (xuntil28(s10) | node26(s10)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[8975, 8821, 8969])).
% 1.30/1.47 tff(8977,plain,
% 1.30/1.47 (xuntil28(s10)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[8976, 8741])).
% 1.30/1.47 tff(8978,plain,
% 1.30/1.47 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s10, s11)) | (~xuntil28(s10)) | until27(s11))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s10, s11)) | (~xuntil28(s10)) | until27(s11))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(8979,plain,
% 1.30/1.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s10, s11)) | (~xuntil28(s10)) | until27(s11))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(8980,plain,
% 1.30/1.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s10, s11)) | (~xuntil28(s10)) | until27(s11)),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[8979, 8978])).
% 1.30/1.47 tff(8981,plain,
% 1.30/1.47 ((~xuntil28(s10)) | until27(s11)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[8980, 1298, 8839])).
% 1.30/1.47 tff(8982,plain,
% 1.30/1.47 (until27(s11)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[8981, 8977])).
% 1.30/1.47 tff(8983,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s11) | node26(s11) | (~until27(s11)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s11) | node26(s11) | (~until27(s11)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(8984,plain,
% 1.30/1.47 ((node26(s11) | (~until27(s11)) | xuntil28(s11)) <=> (xuntil28(s11) | node26(s11) | (~until27(s11)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(8985,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s11) | (~until27(s11)) | xuntil28(s11))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s11) | node26(s11) | (~until27(s11))))),
% 1.30/1.47 inference(monotonicity,[status(thm)],[8984])).
% 1.30/1.47 tff(8986,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s11) | (~until27(s11)) | xuntil28(s11))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s11) | node26(s11) | (~until27(s11)))),
% 1.30/1.47 inference(transitivity,[status(thm)],[8985, 8983])).
% 1.30/1.47 tff(8987,plain,
% 1.30/1.47 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s11) | (~until27(s11)) | xuntil28(s11))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(8988,plain,
% 1.30/1.47 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s11) | node26(s11) | (~until27(s11))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[8987, 8986])).
% 1.30/1.47 tff(8989,plain,
% 1.30/1.47 (xuntil28(s11)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[8988, 8821, 8982, 8732])).
% 1.30/1.47 tff(8990,plain,
% 1.30/1.47 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s11, s12)) | (~xuntil28(s11)) | until27(s12))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s11, s12)) | (~xuntil28(s11)) | until27(s12))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(8991,plain,
% 1.30/1.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s11, s12)) | (~xuntil28(s11)) | until27(s12))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(8992,plain,
% 1.30/1.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s11, s12)) | (~xuntil28(s11)) | until27(s12)),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[8991, 8990])).
% 1.30/1.47 tff(8993,plain,
% 1.30/1.47 ((~xuntil28(s11)) | until27(s12)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[8992, 1376, 8839])).
% 1.30/1.47 tff(8994,plain,
% 1.30/1.47 (until27(s12)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[8993, 8989])).
% 1.30/1.47 tff(8995,plain,
% 1.30/1.47 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s12) | (~node26(s12)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s12) | (~node26(s12)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(8996,plain,
% 1.30/1.47 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s12) | (~node26(s12)))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(8997,plain,
% 1.30/1.47 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s12) | (~node26(s12))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[8996, 8995])).
% 1.30/1.47 tff(8998,plain,
% 1.30/1.47 (~node26(s12)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[8997, 3949, 8723])).
% 1.30/1.47 tff(8999,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s12) | node26(s12) | (~until27(s12)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s12) | node26(s12) | (~until27(s12)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(9000,plain,
% 1.30/1.47 ((node26(s12) | (~until27(s12)) | xuntil28(s12)) <=> (xuntil28(s12) | node26(s12) | (~until27(s12)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(9001,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s12) | (~until27(s12)) | xuntil28(s12))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s12) | node26(s12) | (~until27(s12))))),
% 1.30/1.47 inference(monotonicity,[status(thm)],[9000])).
% 1.30/1.47 tff(9002,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s12) | (~until27(s12)) | xuntil28(s12))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s12) | node26(s12) | (~until27(s12)))),
% 1.30/1.47 inference(transitivity,[status(thm)],[9001, 8999])).
% 1.30/1.47 tff(9003,plain,
% 1.30/1.47 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s12) | (~until27(s12)) | xuntil28(s12))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(9004,plain,
% 1.30/1.47 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s12) | node26(s12) | (~until27(s12))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[9003, 9002])).
% 1.30/1.47 tff(9005,plain,
% 1.30/1.47 (xuntil28(s12) | (~until27(s12))),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[9004, 8821, 8998])).
% 1.30/1.47 tff(9006,plain,
% 1.30/1.47 (xuntil28(s12)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[9005, 8994])).
% 1.30/1.47 tff(9007,plain,
% 1.30/1.47 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s12, s13)) | (~xuntil28(s12)) | until27(s13))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s12, s13)) | (~xuntil28(s12)) | until27(s13))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(9008,plain,
% 1.30/1.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s12, s13)) | (~xuntil28(s12)) | until27(s13))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(9009,plain,
% 1.30/1.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s12, s13)) | (~xuntil28(s12)) | until27(s13)),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[9008, 9007])).
% 1.30/1.47 tff(9010,plain,
% 1.30/1.47 ((~xuntil28(s12)) | until27(s13)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[9009, 1437, 8839])).
% 1.30/1.47 tff(9011,plain,
% 1.30/1.47 (until27(s13)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[9010, 9006])).
% 1.30/1.47 tff(9012,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s13) | node26(s13) | (~until27(s13)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s13) | node26(s13) | (~until27(s13)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(9013,plain,
% 1.30/1.47 ((node26(s13) | (~until27(s13)) | xuntil28(s13)) <=> (xuntil28(s13) | node26(s13) | (~until27(s13)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(9014,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s13) | (~until27(s13)) | xuntil28(s13))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s13) | node26(s13) | (~until27(s13))))),
% 1.30/1.47 inference(monotonicity,[status(thm)],[9013])).
% 1.30/1.47 tff(9015,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s13) | (~until27(s13)) | xuntil28(s13))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s13) | node26(s13) | (~until27(s13)))),
% 1.30/1.47 inference(transitivity,[status(thm)],[9014, 9012])).
% 1.30/1.47 tff(9016,plain,
% 1.30/1.47 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s13) | (~until27(s13)) | xuntil28(s13))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(9017,plain,
% 1.30/1.47 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s13) | node26(s13) | (~until27(s13))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[9016, 9015])).
% 1.30/1.47 tff(9018,plain,
% 1.30/1.47 (xuntil28(s13)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[9017, 8821, 9011, 8716])).
% 1.30/1.47 tff(9019,plain,
% 1.30/1.47 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s13, s14)) | (~xuntil28(s13)) | until27(s14))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s13, s14)) | (~xuntil28(s13)) | until27(s14))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(9020,plain,
% 1.30/1.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s13, s14)) | (~xuntil28(s13)) | until27(s14))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(9021,plain,
% 1.30/1.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s13, s14)) | (~xuntil28(s13)) | until27(s14)),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[9020, 9019])).
% 1.30/1.47 tff(9022,plain,
% 1.30/1.47 ((~xuntil28(s13)) | until27(s14)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[9021, 1532, 8839])).
% 1.30/1.47 tff(9023,plain,
% 1.30/1.47 (until27(s14)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[9022, 9018])).
% 1.30/1.47 tff(9024,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s14) | node26(s14) | (~until27(s14)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s14) | node26(s14) | (~until27(s14)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(9025,plain,
% 1.30/1.47 ((node26(s14) | (~until27(s14)) | xuntil28(s14)) <=> (xuntil28(s14) | node26(s14) | (~until27(s14)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(9026,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s14) | (~until27(s14)) | xuntil28(s14))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s14) | node26(s14) | (~until27(s14))))),
% 1.30/1.47 inference(monotonicity,[status(thm)],[9025])).
% 1.30/1.47 tff(9027,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s14) | (~until27(s14)) | xuntil28(s14))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s14) | node26(s14) | (~until27(s14)))),
% 1.30/1.47 inference(transitivity,[status(thm)],[9026, 9024])).
% 1.30/1.47 tff(9028,plain,
% 1.30/1.47 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s14) | (~until27(s14)) | xuntil28(s14))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(9029,plain,
% 1.30/1.47 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s14) | node26(s14) | (~until27(s14))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[9028, 9027])).
% 1.30/1.47 tff(9030,plain,
% 1.30/1.47 (xuntil28(s14) | node26(s14)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[9029, 8821, 9023])).
% 1.30/1.47 tff(9031,plain,
% 1.30/1.47 (xuntil28(s14)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[9030, 8712])).
% 1.30/1.47 tff(9032,plain,
% 1.30/1.47 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s14, s15)) | (~xuntil28(s14)) | until27(s15))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s14, s15)) | (~xuntil28(s14)) | until27(s15))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(9033,plain,
% 1.30/1.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s14, s15)) | (~xuntil28(s14)) | until27(s15))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(9034,plain,
% 1.30/1.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s14, s15)) | (~xuntil28(s14)) | until27(s15)),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[9033, 9032])).
% 1.30/1.47 tff(9035,plain,
% 1.30/1.47 ((~xuntil28(s14)) | until27(s15)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[9034, 1596, 8839])).
% 1.30/1.47 tff(9036,plain,
% 1.30/1.47 (until27(s15)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[9035, 9031])).
% 1.30/1.47 tff(9037,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s15) | node26(s15) | (~until27(s15)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s15) | node26(s15) | (~until27(s15)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(9038,plain,
% 1.30/1.47 ((node26(s15) | (~until27(s15)) | xuntil28(s15)) <=> (xuntil28(s15) | node26(s15) | (~until27(s15)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(9039,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s15) | (~until27(s15)) | xuntil28(s15))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s15) | node26(s15) | (~until27(s15))))),
% 1.30/1.47 inference(monotonicity,[status(thm)],[9038])).
% 1.30/1.47 tff(9040,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s15) | (~until27(s15)) | xuntil28(s15))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s15) | node26(s15) | (~until27(s15)))),
% 1.30/1.47 inference(transitivity,[status(thm)],[9039, 9037])).
% 1.30/1.47 tff(9041,plain,
% 1.30/1.47 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s15) | (~until27(s15)) | xuntil28(s15))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(9042,plain,
% 1.30/1.47 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s15) | node26(s15) | (~until27(s15))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[9041, 9040])).
% 1.30/1.47 tff(9043,plain,
% 1.30/1.47 (xuntil28(s15)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[9042, 8821, 9036, 8703])).
% 1.30/1.47 tff(9044,plain,
% 1.30/1.47 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s15, s16)) | (~xuntil28(s15)) | until27(s16))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s15, s16)) | (~xuntil28(s15)) | until27(s16))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(9045,plain,
% 1.30/1.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s15, s16)) | (~xuntil28(s15)) | until27(s16))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(9046,plain,
% 1.30/1.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s15, s16)) | (~xuntil28(s15)) | until27(s16)),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[9045, 9044])).
% 1.30/1.47 tff(9047,plain,
% 1.30/1.47 ((~xuntil28(s15)) | until27(s16)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[9046, 1671, 8839])).
% 1.30/1.47 tff(9048,plain,
% 1.30/1.47 (until27(s16)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[9047, 9043])).
% 1.30/1.47 tff(9049,plain,
% 1.30/1.47 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s16) | (~node26(s16)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s16) | (~node26(s16)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(9050,plain,
% 1.30/1.47 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s16) | (~node26(s16)))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(9051,plain,
% 1.30/1.47 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s16) | (~node26(s16))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[9050, 9049])).
% 1.30/1.47 tff(9052,plain,
% 1.30/1.47 (~node26(s16)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[9051, 3949, 8694])).
% 1.30/1.47 tff(9053,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s16) | node26(s16) | (~until27(s16)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s16) | node26(s16) | (~until27(s16)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(9054,plain,
% 1.30/1.47 ((node26(s16) | (~until27(s16)) | xuntil28(s16)) <=> (xuntil28(s16) | node26(s16) | (~until27(s16)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(9055,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s16) | (~until27(s16)) | xuntil28(s16))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s16) | node26(s16) | (~until27(s16))))),
% 1.30/1.47 inference(monotonicity,[status(thm)],[9054])).
% 1.30/1.47 tff(9056,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s16) | (~until27(s16)) | xuntil28(s16))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s16) | node26(s16) | (~until27(s16)))),
% 1.30/1.47 inference(transitivity,[status(thm)],[9055, 9053])).
% 1.30/1.47 tff(9057,plain,
% 1.30/1.47 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s16) | (~until27(s16)) | xuntil28(s16))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(9058,plain,
% 1.30/1.47 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s16) | node26(s16) | (~until27(s16))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[9057, 9056])).
% 1.30/1.47 tff(9059,plain,
% 1.30/1.47 (xuntil28(s16) | (~until27(s16))),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[9058, 8821, 9052])).
% 1.30/1.47 tff(9060,plain,
% 1.30/1.47 (xuntil28(s16)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[9059, 9048])).
% 1.30/1.47 tff(9061,plain,
% 1.30/1.47 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s16, s17)) | (~xuntil28(s16)) | until27(s17))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s16, s17)) | (~xuntil28(s16)) | until27(s17))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(9062,plain,
% 1.30/1.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s16, s17)) | (~xuntil28(s16)) | until27(s17))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(9063,plain,
% 1.30/1.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s16, s17)) | (~xuntil28(s16)) | until27(s17)),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[9062, 9061])).
% 1.30/1.47 tff(9064,plain,
% 1.30/1.47 ((~xuntil28(s16)) | until27(s17)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[9063, 1760, 8839])).
% 1.30/1.47 tff(9065,plain,
% 1.30/1.47 (until27(s17)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[9064, 9060])).
% 1.30/1.47 tff(9066,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s17) | node26(s17) | (~until27(s17)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s17) | node26(s17) | (~until27(s17)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(9067,plain,
% 1.30/1.47 ((node26(s17) | (~until27(s17)) | xuntil28(s17)) <=> (xuntil28(s17) | node26(s17) | (~until27(s17)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(9068,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s17) | (~until27(s17)) | xuntil28(s17))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s17) | node26(s17) | (~until27(s17))))),
% 1.30/1.47 inference(monotonicity,[status(thm)],[9067])).
% 1.30/1.47 tff(9069,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s17) | (~until27(s17)) | xuntil28(s17))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s17) | node26(s17) | (~until27(s17)))),
% 1.30/1.47 inference(transitivity,[status(thm)],[9068, 9066])).
% 1.30/1.47 tff(9070,plain,
% 1.30/1.47 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s17) | (~until27(s17)) | xuntil28(s17))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(9071,plain,
% 1.30/1.47 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s17) | node26(s17) | (~until27(s17))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[9070, 9069])).
% 1.30/1.47 tff(9072,plain,
% 1.30/1.47 (xuntil28(s17)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[9071, 8821, 9065, 8687])).
% 1.30/1.47 tff(9073,plain,
% 1.30/1.47 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s17, s18)) | (~xuntil28(s17)) | until27(s18))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s17, s18)) | (~xuntil28(s17)) | until27(s18))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(9074,plain,
% 1.30/1.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s17, s18)) | (~xuntil28(s17)) | until27(s18))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(9075,plain,
% 1.30/1.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s17, s18)) | (~xuntil28(s17)) | until27(s18)),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[9074, 9073])).
% 1.30/1.47 tff(9076,plain,
% 1.30/1.47 ((~xuntil28(s17)) | until27(s18)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[9075, 1827, 8839])).
% 1.30/1.47 tff(9077,plain,
% 1.30/1.47 (until27(s18)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[9076, 9072])).
% 1.30/1.47 tff(9078,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s18) | node26(s18) | (~until27(s18)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s18) | node26(s18) | (~until27(s18)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(9079,plain,
% 1.30/1.47 ((node26(s18) | (~until27(s18)) | xuntil28(s18)) <=> (xuntil28(s18) | node26(s18) | (~until27(s18)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(9080,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s18) | (~until27(s18)) | xuntil28(s18))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s18) | node26(s18) | (~until27(s18))))),
% 1.30/1.47 inference(monotonicity,[status(thm)],[9079])).
% 1.30/1.47 tff(9081,plain,
% 1.30/1.47 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s18) | (~until27(s18)) | xuntil28(s18))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s18) | node26(s18) | (~until27(s18)))),
% 1.30/1.48 inference(transitivity,[status(thm)],[9080, 9078])).
% 1.30/1.48 tff(9082,plain,
% 1.30/1.48 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s18) | (~until27(s18)) | xuntil28(s18))),
% 1.30/1.48 inference(quant_inst,[status(thm)],[])).
% 1.30/1.48 tff(9083,plain,
% 1.30/1.48 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s18) | node26(s18) | (~until27(s18))),
% 1.30/1.48 inference(modus_ponens,[status(thm)],[9082, 9081])).
% 1.30/1.48 tff(9084,plain,
% 1.30/1.48 (xuntil28(s18) | node26(s18)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9083, 8821, 9077])).
% 1.30/1.48 tff(9085,plain,
% 1.30/1.48 (xuntil28(s18)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9084, 8683])).
% 1.30/1.48 tff(9086,plain,
% 1.30/1.48 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s18, s19)) | (~xuntil28(s18)) | until27(s19))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s18, s19)) | (~xuntil28(s18)) | until27(s19))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9087,plain,
% 1.30/1.48 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s18, s19)) | (~xuntil28(s18)) | until27(s19))),
% 1.30/1.48 inference(quant_inst,[status(thm)],[])).
% 1.30/1.48 tff(9088,plain,
% 1.30/1.48 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s18, s19)) | (~xuntil28(s18)) | until27(s19)),
% 1.30/1.48 inference(modus_ponens,[status(thm)],[9087, 9086])).
% 1.30/1.48 tff(9089,plain,
% 1.30/1.48 ((~xuntil28(s18)) | until27(s19)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9088, 1926, 8839])).
% 1.30/1.48 tff(9090,plain,
% 1.30/1.48 (until27(s19)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9089, 9085])).
% 1.30/1.48 tff(9091,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s19) | node26(s19) | (~until27(s19)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s19) | node26(s19) | (~until27(s19)))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9092,plain,
% 1.30/1.48 ((node26(s19) | (~until27(s19)) | xuntil28(s19)) <=> (xuntil28(s19) | node26(s19) | (~until27(s19)))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9093,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s19) | (~until27(s19)) | xuntil28(s19))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s19) | node26(s19) | (~until27(s19))))),
% 1.30/1.48 inference(monotonicity,[status(thm)],[9092])).
% 1.30/1.48 tff(9094,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s19) | (~until27(s19)) | xuntil28(s19))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s19) | node26(s19) | (~until27(s19)))),
% 1.30/1.48 inference(transitivity,[status(thm)],[9093, 9091])).
% 1.30/1.48 tff(9095,plain,
% 1.30/1.48 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s19) | (~until27(s19)) | xuntil28(s19))),
% 1.30/1.48 inference(quant_inst,[status(thm)],[])).
% 1.30/1.48 tff(9096,plain,
% 1.30/1.48 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s19) | node26(s19) | (~until27(s19))),
% 1.30/1.48 inference(modus_ponens,[status(thm)],[9095, 9094])).
% 1.30/1.48 tff(9097,plain,
% 1.30/1.48 (xuntil28(s19)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9096, 8821, 9090, 8674])).
% 1.30/1.48 tff(9098,plain,
% 1.30/1.48 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s19, s20)) | (~xuntil28(s19)) | until27(s20))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s19, s20)) | (~xuntil28(s19)) | until27(s20))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9099,plain,
% 1.30/1.48 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s19, s20)) | (~xuntil28(s19)) | until27(s20))),
% 1.30/1.48 inference(quant_inst,[status(thm)],[])).
% 1.30/1.48 tff(9100,plain,
% 1.30/1.48 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s19, s20)) | (~xuntil28(s19)) | until27(s20)),
% 1.30/1.48 inference(modus_ponens,[status(thm)],[9099, 9098])).
% 1.30/1.48 tff(9101,plain,
% 1.30/1.48 ((~xuntil28(s19)) | until27(s20)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9100, 2004, 8839])).
% 1.30/1.48 tff(9102,plain,
% 1.30/1.48 (until27(s20)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9101, 9097])).
% 1.30/1.48 tff(9103,plain,
% 1.30/1.48 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s20) | (~node26(s20)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s20) | (~node26(s20)))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9104,plain,
% 1.30/1.48 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s20) | (~node26(s20)))),
% 1.30/1.48 inference(quant_inst,[status(thm)],[])).
% 1.30/1.48 tff(9105,plain,
% 1.30/1.48 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s20) | (~node26(s20))),
% 1.30/1.48 inference(modus_ponens,[status(thm)],[9104, 9103])).
% 1.30/1.48 tff(9106,plain,
% 1.30/1.48 (~node26(s20)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9105, 3949, 8665])).
% 1.30/1.48 tff(9107,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s20) | node26(s20) | (~until27(s20)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s20) | node26(s20) | (~until27(s20)))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9108,plain,
% 1.30/1.48 ((node26(s20) | (~until27(s20)) | xuntil28(s20)) <=> (xuntil28(s20) | node26(s20) | (~until27(s20)))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9109,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s20) | (~until27(s20)) | xuntil28(s20))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s20) | node26(s20) | (~until27(s20))))),
% 1.30/1.48 inference(monotonicity,[status(thm)],[9108])).
% 1.30/1.48 tff(9110,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s20) | (~until27(s20)) | xuntil28(s20))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s20) | node26(s20) | (~until27(s20)))),
% 1.30/1.48 inference(transitivity,[status(thm)],[9109, 9107])).
% 1.30/1.48 tff(9111,plain,
% 1.30/1.48 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s20) | (~until27(s20)) | xuntil28(s20))),
% 1.30/1.48 inference(quant_inst,[status(thm)],[])).
% 1.30/1.48 tff(9112,plain,
% 1.30/1.48 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s20) | node26(s20) | (~until27(s20))),
% 1.30/1.48 inference(modus_ponens,[status(thm)],[9111, 9110])).
% 1.30/1.48 tff(9113,plain,
% 1.30/1.48 (xuntil28(s20) | (~until27(s20))),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9112, 8821, 9106])).
% 1.30/1.48 tff(9114,plain,
% 1.30/1.48 (xuntil28(s20)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9113, 9102])).
% 1.30/1.48 tff(9115,plain,
% 1.30/1.48 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s20, s21)) | (~xuntil28(s20)) | until27(s21))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s20, s21)) | (~xuntil28(s20)) | until27(s21))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9116,plain,
% 1.30/1.48 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s20, s21)) | (~xuntil28(s20)) | until27(s21))),
% 1.30/1.48 inference(quant_inst,[status(thm)],[])).
% 1.30/1.48 tff(9117,plain,
% 1.30/1.48 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s20, s21)) | (~xuntil28(s20)) | until27(s21)),
% 1.30/1.48 inference(modus_ponens,[status(thm)],[9116, 9115])).
% 1.30/1.48 tff(9118,plain,
% 1.30/1.48 ((~xuntil28(s20)) | until27(s21)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9117, 2065, 8839])).
% 1.30/1.48 tff(9119,plain,
% 1.30/1.48 (until27(s21)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9118, 9114])).
% 1.30/1.48 tff(9120,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s21) | node26(s21) | (~until27(s21)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s21) | node26(s21) | (~until27(s21)))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9121,plain,
% 1.30/1.48 ((node26(s21) | (~until27(s21)) | xuntil28(s21)) <=> (xuntil28(s21) | node26(s21) | (~until27(s21)))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9122,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s21) | (~until27(s21)) | xuntil28(s21))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s21) | node26(s21) | (~until27(s21))))),
% 1.30/1.48 inference(monotonicity,[status(thm)],[9121])).
% 1.30/1.48 tff(9123,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s21) | (~until27(s21)) | xuntil28(s21))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s21) | node26(s21) | (~until27(s21)))),
% 1.30/1.48 inference(transitivity,[status(thm)],[9122, 9120])).
% 1.30/1.48 tff(9124,plain,
% 1.30/1.48 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s21) | (~until27(s21)) | xuntil28(s21))),
% 1.30/1.48 inference(quant_inst,[status(thm)],[])).
% 1.30/1.48 tff(9125,plain,
% 1.30/1.48 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s21) | node26(s21) | (~until27(s21))),
% 1.30/1.48 inference(modus_ponens,[status(thm)],[9124, 9123])).
% 1.30/1.48 tff(9126,plain,
% 1.30/1.48 (xuntil28(s21)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9125, 8821, 9119, 8658])).
% 1.30/1.48 tff(9127,plain,
% 1.30/1.48 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s21, s22)) | (~xuntil28(s21)) | until27(s22))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s21, s22)) | (~xuntil28(s21)) | until27(s22))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9128,plain,
% 1.30/1.48 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s21, s22)) | (~xuntil28(s21)) | until27(s22))),
% 1.30/1.48 inference(quant_inst,[status(thm)],[])).
% 1.30/1.48 tff(9129,plain,
% 1.30/1.48 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s21, s22)) | (~xuntil28(s21)) | until27(s22)),
% 1.30/1.48 inference(modus_ponens,[status(thm)],[9128, 9127])).
% 1.30/1.48 tff(9130,plain,
% 1.30/1.48 ((~xuntil28(s21)) | until27(s22)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9129, 2160, 8839])).
% 1.30/1.48 tff(9131,plain,
% 1.30/1.48 (until27(s22)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9130, 9126])).
% 1.30/1.48 tff(9132,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s22) | node26(s22) | (~until27(s22)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s22) | node26(s22) | (~until27(s22)))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9133,plain,
% 1.30/1.48 ((node26(s22) | (~until27(s22)) | xuntil28(s22)) <=> (xuntil28(s22) | node26(s22) | (~until27(s22)))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9134,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s22) | (~until27(s22)) | xuntil28(s22))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s22) | node26(s22) | (~until27(s22))))),
% 1.30/1.48 inference(monotonicity,[status(thm)],[9133])).
% 1.30/1.48 tff(9135,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s22) | (~until27(s22)) | xuntil28(s22))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s22) | node26(s22) | (~until27(s22)))),
% 1.30/1.48 inference(transitivity,[status(thm)],[9134, 9132])).
% 1.30/1.48 tff(9136,plain,
% 1.30/1.48 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s22) | (~until27(s22)) | xuntil28(s22))),
% 1.30/1.48 inference(quant_inst,[status(thm)],[])).
% 1.30/1.48 tff(9137,plain,
% 1.30/1.48 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s22) | node26(s22) | (~until27(s22))),
% 1.30/1.48 inference(modus_ponens,[status(thm)],[9136, 9135])).
% 1.30/1.48 tff(9138,plain,
% 1.30/1.48 (xuntil28(s22) | node26(s22)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9137, 8821, 9131])).
% 1.30/1.48 tff(9139,plain,
% 1.30/1.48 (xuntil28(s22)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9138, 8654])).
% 1.30/1.48 tff(9140,plain,
% 1.30/1.48 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s22, s23)) | (~xuntil28(s22)) | until27(s23))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s22, s23)) | (~xuntil28(s22)) | until27(s23))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9141,plain,
% 1.30/1.48 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s22, s23)) | (~xuntil28(s22)) | until27(s23))),
% 1.30/1.48 inference(quant_inst,[status(thm)],[])).
% 1.30/1.48 tff(9142,plain,
% 1.30/1.48 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s22, s23)) | (~xuntil28(s22)) | until27(s23)),
% 1.30/1.48 inference(modus_ponens,[status(thm)],[9141, 9140])).
% 1.30/1.48 tff(9143,plain,
% 1.30/1.48 ((~xuntil28(s22)) | until27(s23)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9142, 2224, 8839])).
% 1.30/1.48 tff(9144,plain,
% 1.30/1.48 (until27(s23)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9143, 9139])).
% 1.30/1.48 tff(9145,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s23) | node26(s23) | (~until27(s23)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s23) | node26(s23) | (~until27(s23)))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9146,plain,
% 1.30/1.48 ((node26(s23) | (~until27(s23)) | xuntil28(s23)) <=> (xuntil28(s23) | node26(s23) | (~until27(s23)))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9147,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s23) | (~until27(s23)) | xuntil28(s23))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s23) | node26(s23) | (~until27(s23))))),
% 1.30/1.48 inference(monotonicity,[status(thm)],[9146])).
% 1.30/1.48 tff(9148,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s23) | (~until27(s23)) | xuntil28(s23))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s23) | node26(s23) | (~until27(s23)))),
% 1.30/1.48 inference(transitivity,[status(thm)],[9147, 9145])).
% 1.30/1.48 tff(9149,plain,
% 1.30/1.48 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s23) | (~until27(s23)) | xuntil28(s23))),
% 1.30/1.48 inference(quant_inst,[status(thm)],[])).
% 1.30/1.48 tff(9150,plain,
% 1.30/1.48 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s23) | node26(s23) | (~until27(s23))),
% 1.30/1.48 inference(modus_ponens,[status(thm)],[9149, 9148])).
% 1.30/1.48 tff(9151,plain,
% 1.30/1.48 (xuntil28(s23)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9150, 8821, 9144, 8645])).
% 1.30/1.48 tff(9152,plain,
% 1.30/1.48 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s23, s24)) | (~xuntil28(s23)) | until27(s24))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s23, s24)) | (~xuntil28(s23)) | until27(s24))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9153,plain,
% 1.30/1.48 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s23, s24)) | (~xuntil28(s23)) | until27(s24))),
% 1.30/1.48 inference(quant_inst,[status(thm)],[])).
% 1.30/1.48 tff(9154,plain,
% 1.30/1.48 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s23, s24)) | (~xuntil28(s23)) | until27(s24)),
% 1.30/1.48 inference(modus_ponens,[status(thm)],[9153, 9152])).
% 1.30/1.48 tff(9155,plain,
% 1.30/1.48 ((~xuntil28(s23)) | until27(s24)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9154, 2299, 8839])).
% 1.30/1.48 tff(9156,plain,
% 1.30/1.48 (until27(s24)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9155, 9151])).
% 1.30/1.48 tff(9157,plain,
% 1.30/1.48 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s24) | (~node26(s24)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s24) | (~node26(s24)))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9158,plain,
% 1.30/1.48 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s24) | (~node26(s24)))),
% 1.30/1.48 inference(quant_inst,[status(thm)],[])).
% 1.30/1.48 tff(9159,plain,
% 1.30/1.48 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s24) | (~node26(s24))),
% 1.30/1.48 inference(modus_ponens,[status(thm)],[9158, 9157])).
% 1.30/1.48 tff(9160,plain,
% 1.30/1.48 (~node26(s24)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9159, 3949, 8636])).
% 1.30/1.48 tff(9161,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s24) | node26(s24) | (~until27(s24)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s24) | node26(s24) | (~until27(s24)))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9162,plain,
% 1.30/1.48 ((node26(s24) | (~until27(s24)) | xuntil28(s24)) <=> (xuntil28(s24) | node26(s24) | (~until27(s24)))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9163,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s24) | (~until27(s24)) | xuntil28(s24))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s24) | node26(s24) | (~until27(s24))))),
% 1.30/1.48 inference(monotonicity,[status(thm)],[9162])).
% 1.30/1.48 tff(9164,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s24) | (~until27(s24)) | xuntil28(s24))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s24) | node26(s24) | (~until27(s24)))),
% 1.30/1.48 inference(transitivity,[status(thm)],[9163, 9161])).
% 1.30/1.48 tff(9165,plain,
% 1.30/1.48 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s24) | (~until27(s24)) | xuntil28(s24))),
% 1.30/1.48 inference(quant_inst,[status(thm)],[])).
% 1.30/1.48 tff(9166,plain,
% 1.30/1.48 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s24) | node26(s24) | (~until27(s24))),
% 1.30/1.48 inference(modus_ponens,[status(thm)],[9165, 9164])).
% 1.30/1.48 tff(9167,plain,
% 1.30/1.48 (xuntil28(s24) | (~until27(s24))),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9166, 8821, 9160])).
% 1.30/1.48 tff(9168,plain,
% 1.30/1.48 (xuntil28(s24)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9167, 9156])).
% 1.30/1.48 tff(9169,plain,
% 1.30/1.48 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s24, s25)) | (~xuntil28(s24)) | until27(s25))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s24, s25)) | (~xuntil28(s24)) | until27(s25))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9170,plain,
% 1.30/1.48 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s24, s25)) | (~xuntil28(s24)) | until27(s25))),
% 1.30/1.48 inference(quant_inst,[status(thm)],[])).
% 1.30/1.48 tff(9171,plain,
% 1.30/1.48 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s24, s25)) | (~xuntil28(s24)) | until27(s25)),
% 1.30/1.48 inference(modus_ponens,[status(thm)],[9170, 9169])).
% 1.30/1.48 tff(9172,plain,
% 1.30/1.48 ((~xuntil28(s24)) | until27(s25)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9171, 2388, 8839])).
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% 1.30/1.48 (until27(s25)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9172, 9168])).
% 1.30/1.48 tff(9174,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s25) | node26(s25) | (~until27(s25)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s25) | node26(s25) | (~until27(s25)))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9175,plain,
% 1.30/1.48 ((node26(s25) | (~until27(s25)) | xuntil28(s25)) <=> (xuntil28(s25) | node26(s25) | (~until27(s25)))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9176,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s25) | (~until27(s25)) | xuntil28(s25))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s25) | node26(s25) | (~until27(s25))))),
% 1.30/1.48 inference(monotonicity,[status(thm)],[9175])).
% 1.30/1.48 tff(9177,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s25) | (~until27(s25)) | xuntil28(s25))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s25) | node26(s25) | (~until27(s25)))),
% 1.30/1.48 inference(transitivity,[status(thm)],[9176, 9174])).
% 1.30/1.48 tff(9178,plain,
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% 1.30/1.48 inference(quant_inst,[status(thm)],[])).
% 1.30/1.48 tff(9179,plain,
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% 1.30/1.48 inference(modus_ponens,[status(thm)],[9178, 9177])).
% 1.30/1.48 tff(9180,plain,
% 1.30/1.48 (xuntil28(s25)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9179, 8821, 9173, 8629])).
% 1.30/1.48 tff(9181,plain,
% 1.30/1.48 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s25, s26)) | (~xuntil28(s25)) | until27(s26))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s25, s26)) | (~xuntil28(s25)) | until27(s26))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9182,plain,
% 1.30/1.48 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s25, s26)) | (~xuntil28(s25)) | until27(s26))),
% 1.30/1.48 inference(quant_inst,[status(thm)],[])).
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% 1.30/1.48 inference(modus_ponens,[status(thm)],[9182, 9181])).
% 1.30/1.48 tff(9184,plain,
% 1.30/1.48 ((~xuntil28(s25)) | until27(s26)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9183, 2455, 8839])).
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% 1.30/1.48 (until27(s26)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9184, 9180])).
% 1.30/1.48 tff(9186,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s26) | node26(s26) | (~until27(s26)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s26) | node26(s26) | (~until27(s26)))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9187,plain,
% 1.30/1.48 ((node26(s26) | (~until27(s26)) | xuntil28(s26)) <=> (xuntil28(s26) | node26(s26) | (~until27(s26)))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9188,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s26) | (~until27(s26)) | xuntil28(s26))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s26) | node26(s26) | (~until27(s26))))),
% 1.30/1.48 inference(monotonicity,[status(thm)],[9187])).
% 1.30/1.48 tff(9189,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s26) | (~until27(s26)) | xuntil28(s26))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s26) | node26(s26) | (~until27(s26)))),
% 1.30/1.48 inference(transitivity,[status(thm)],[9188, 9186])).
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% 1.30/1.48 inference(quant_inst,[status(thm)],[])).
% 1.30/1.48 tff(9191,plain,
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% 1.30/1.48 inference(modus_ponens,[status(thm)],[9190, 9189])).
% 1.30/1.48 tff(9192,plain,
% 1.30/1.48 (xuntil28(s26) | node26(s26)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9191, 8821, 9185])).
% 1.30/1.48 tff(9193,plain,
% 1.30/1.48 (xuntil28(s26)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9192, 8625])).
% 1.30/1.48 tff(9194,plain,
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% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9195,plain,
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% 1.30/1.48 inference(quant_inst,[status(thm)],[])).
% 1.30/1.48 tff(9196,plain,
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% 1.30/1.48 inference(modus_ponens,[status(thm)],[9195, 9194])).
% 1.30/1.48 tff(9197,plain,
% 1.30/1.48 ((~xuntil28(s26)) | until27(s27)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9196, 2554, 8839])).
% 1.30/1.48 tff(9198,plain,
% 1.30/1.48 (until27(s27)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9197, 9193])).
% 1.30/1.48 tff(9199,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s27) | node26(s27) | (~until27(s27)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s27) | node26(s27) | (~until27(s27)))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9200,plain,
% 1.30/1.48 ((node26(s27) | (~until27(s27)) | xuntil28(s27)) <=> (xuntil28(s27) | node26(s27) | (~until27(s27)))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9201,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s27) | (~until27(s27)) | xuntil28(s27))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s27) | node26(s27) | (~until27(s27))))),
% 1.30/1.48 inference(monotonicity,[status(thm)],[9200])).
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% 1.30/1.48 inference(transitivity,[status(thm)],[9201, 9199])).
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% 1.30/1.48 inference(quant_inst,[status(thm)],[])).
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% 1.30/1.48 inference(modus_ponens,[status(thm)],[9203, 9202])).
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% 1.30/1.48 (xuntil28(s27)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9204, 8821, 9198, 8616])).
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% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9207,plain,
% 1.30/1.48 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s27, s28)) | (~xuntil28(s27)) | until27(s28))),
% 1.30/1.48 inference(quant_inst,[status(thm)],[])).
% 1.30/1.48 tff(9208,plain,
% 1.30/1.48 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s27, s28)) | (~xuntil28(s27)) | until27(s28)),
% 1.30/1.48 inference(modus_ponens,[status(thm)],[9207, 9206])).
% 1.30/1.48 tff(9209,plain,
% 1.30/1.48 ((~xuntil28(s27)) | until27(s28)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9208, 2632, 8839])).
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% 1.30/1.48 (until27(s28)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9209, 9205])).
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% 1.30/1.48 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s28) | (~node26(s28)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s28) | (~node26(s28)))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
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% 1.30/1.48 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s28) | (~node26(s28)))),
% 1.30/1.48 inference(quant_inst,[status(thm)],[])).
% 1.30/1.48 tff(9213,plain,
% 1.30/1.48 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s28) | (~node26(s28))),
% 1.30/1.48 inference(modus_ponens,[status(thm)],[9212, 9211])).
% 1.30/1.48 tff(9214,plain,
% 1.30/1.48 (~node26(s28)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9213, 3949, 8607])).
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% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s28) | node26(s28) | (~until27(s28)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s28) | node26(s28) | (~until27(s28)))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9216,plain,
% 1.30/1.48 ((node26(s28) | (~until27(s28)) | xuntil28(s28)) <=> (xuntil28(s28) | node26(s28) | (~until27(s28)))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9217,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s28) | (~until27(s28)) | xuntil28(s28))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s28) | node26(s28) | (~until27(s28))))),
% 1.30/1.48 inference(monotonicity,[status(thm)],[9216])).
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% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s28) | (~until27(s28)) | xuntil28(s28))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s28) | node26(s28) | (~until27(s28)))),
% 1.30/1.48 inference(transitivity,[status(thm)],[9217, 9215])).
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% 1.30/1.48 inference(quant_inst,[status(thm)],[])).
% 1.30/1.48 tff(9220,plain,
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% 1.30/1.48 inference(modus_ponens,[status(thm)],[9219, 9218])).
% 1.30/1.48 tff(9221,plain,
% 1.30/1.48 (xuntil28(s28) | (~until27(s28))),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9220, 8821, 9214])).
% 1.30/1.48 tff(9222,plain,
% 1.30/1.48 (xuntil28(s28)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9221, 9210])).
% 1.30/1.48 tff(9223,plain,
% 1.30/1.48 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s28, s29)) | (~xuntil28(s28)) | until27(s29))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s28, s29)) | (~xuntil28(s28)) | until27(s29))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9224,plain,
% 1.30/1.48 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s28, s29)) | (~xuntil28(s28)) | until27(s29))),
% 1.30/1.48 inference(quant_inst,[status(thm)],[])).
% 1.30/1.48 tff(9225,plain,
% 1.30/1.48 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s28, s29)) | (~xuntil28(s28)) | until27(s29)),
% 1.30/1.48 inference(modus_ponens,[status(thm)],[9224, 9223])).
% 1.30/1.48 tff(9226,plain,
% 1.30/1.48 ((~xuntil28(s28)) | until27(s29)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9225, 2693, 8839])).
% 1.30/1.48 tff(9227,plain,
% 1.30/1.48 (until27(s29)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9226, 9222])).
% 1.30/1.48 tff(9228,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s29) | node26(s29) | (~until27(s29)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s29) | node26(s29) | (~until27(s29)))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9229,plain,
% 1.30/1.48 ((node26(s29) | (~until27(s29)) | xuntil28(s29)) <=> (xuntil28(s29) | node26(s29) | (~until27(s29)))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9230,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s29) | (~until27(s29)) | xuntil28(s29))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s29) | node26(s29) | (~until27(s29))))),
% 1.30/1.48 inference(monotonicity,[status(thm)],[9229])).
% 1.30/1.48 tff(9231,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s29) | (~until27(s29)) | xuntil28(s29))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s29) | node26(s29) | (~until27(s29)))),
% 1.30/1.48 inference(transitivity,[status(thm)],[9230, 9228])).
% 1.30/1.48 tff(9232,plain,
% 1.30/1.48 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s29) | (~until27(s29)) | xuntil28(s29))),
% 1.30/1.48 inference(quant_inst,[status(thm)],[])).
% 1.30/1.48 tff(9233,plain,
% 1.30/1.48 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s29) | node26(s29) | (~until27(s29))),
% 1.30/1.48 inference(modus_ponens,[status(thm)],[9232, 9231])).
% 1.30/1.48 tff(9234,plain,
% 1.30/1.48 (xuntil28(s29)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9233, 8821, 9227, 8600])).
% 1.30/1.48 tff(9235,plain,
% 1.30/1.48 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s29, s30)) | (~xuntil28(s29)) | until27(s30))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s29, s30)) | (~xuntil28(s29)) | until27(s30))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9236,plain,
% 1.30/1.48 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s29, s30)) | (~xuntil28(s29)) | until27(s30))),
% 1.30/1.48 inference(quant_inst,[status(thm)],[])).
% 1.30/1.48 tff(9237,plain,
% 1.30/1.48 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s29, s30)) | (~xuntil28(s29)) | until27(s30)),
% 1.30/1.48 inference(modus_ponens,[status(thm)],[9236, 9235])).
% 1.30/1.48 tff(9238,plain,
% 1.30/1.48 ((~xuntil28(s29)) | until27(s30)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9237, 2788, 8839])).
% 1.30/1.48 tff(9239,plain,
% 1.30/1.48 (until27(s30)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9238, 9234])).
% 1.30/1.48 tff(9240,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s30) | node26(s30) | (~until27(s30)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s30) | node26(s30) | (~until27(s30)))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9241,plain,
% 1.30/1.48 ((node26(s30) | (~until27(s30)) | xuntil28(s30)) <=> (xuntil28(s30) | node26(s30) | (~until27(s30)))),
% 1.30/1.48 inference(rewrite,[status(thm)],[])).
% 1.30/1.48 tff(9242,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s30) | (~until27(s30)) | xuntil28(s30))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s30) | node26(s30) | (~until27(s30))))),
% 1.30/1.48 inference(monotonicity,[status(thm)],[9241])).
% 1.30/1.48 tff(9243,plain,
% 1.30/1.48 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s30) | (~until27(s30)) | xuntil28(s30))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s30) | node26(s30) | (~until27(s30)))),
% 1.30/1.48 inference(transitivity,[status(thm)],[9242, 9240])).
% 1.30/1.48 tff(9244,plain,
% 1.30/1.48 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s30) | (~until27(s30)) | xuntil28(s30))),
% 1.30/1.48 inference(quant_inst,[status(thm)],[])).
% 1.30/1.48 tff(9245,plain,
% 1.30/1.48 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s30) | node26(s30) | (~until27(s30))),
% 1.30/1.48 inference(modus_ponens,[status(thm)],[9244, 9243])).
% 1.30/1.48 tff(9246,plain,
% 1.30/1.48 (xuntil28(s30) | node26(s30)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9245, 8821, 9239])).
% 1.30/1.48 tff(9247,plain,
% 1.30/1.48 (xuntil28(s30)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[9246, 8596])).
% 1.30/1.48 tff(9248,plain,
% 1.30/1.48 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s30, s31)) | (~xuntil28(s30)) | until27(s31))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s30, s31)) | (~xuntil28(s30)) | until27(s31))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9249,plain,
% 1.30/1.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s30, s31)) | (~xuntil28(s30)) | until27(s31))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9250,plain,
% 1.30/1.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s30, s31)) | (~xuntil28(s30)) | until27(s31)),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9249, 9248])).
% 1.30/1.49 tff(9251,plain,
% 1.30/1.49 ((~xuntil28(s30)) | until27(s31)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9250, 2852, 8839])).
% 1.30/1.49 tff(9252,plain,
% 1.30/1.49 (until27(s31)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9251, 9247])).
% 1.30/1.49 tff(9253,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s31) | node26(s31) | (~until27(s31)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s31) | node26(s31) | (~until27(s31)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9254,plain,
% 1.30/1.49 ((node26(s31) | (~until27(s31)) | xuntil28(s31)) <=> (xuntil28(s31) | node26(s31) | (~until27(s31)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9255,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s31) | (~until27(s31)) | xuntil28(s31))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s31) | node26(s31) | (~until27(s31))))),
% 1.30/1.49 inference(monotonicity,[status(thm)],[9254])).
% 1.30/1.49 tff(9256,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s31) | (~until27(s31)) | xuntil28(s31))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s31) | node26(s31) | (~until27(s31)))),
% 1.30/1.49 inference(transitivity,[status(thm)],[9255, 9253])).
% 1.30/1.49 tff(9257,plain,
% 1.30/1.49 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s31) | (~until27(s31)) | xuntil28(s31))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9258,plain,
% 1.30/1.49 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s31) | node26(s31) | (~until27(s31))),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9257, 9256])).
% 1.30/1.49 tff(9259,plain,
% 1.30/1.49 (xuntil28(s31)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9258, 8821, 9252, 8587])).
% 1.30/1.49 tff(9260,plain,
% 1.30/1.49 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s31, s32)) | (~xuntil28(s31)) | until27(s32))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s31, s32)) | (~xuntil28(s31)) | until27(s32))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9261,plain,
% 1.30/1.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s31, s32)) | (~xuntil28(s31)) | until27(s32))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9262,plain,
% 1.30/1.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s31, s32)) | (~xuntil28(s31)) | until27(s32)),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9261, 9260])).
% 1.30/1.49 tff(9263,plain,
% 1.30/1.49 ((~xuntil28(s31)) | until27(s32)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9262, 2927, 8839])).
% 1.30/1.49 tff(9264,plain,
% 1.30/1.49 (until27(s32)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9263, 9259])).
% 1.30/1.49 tff(9265,plain,
% 1.30/1.49 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s32) | (~node26(s32)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s32) | (~node26(s32)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9266,plain,
% 1.30/1.49 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s32) | (~node26(s32)))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9267,plain,
% 1.30/1.49 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s32) | (~node26(s32))),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9266, 9265])).
% 1.30/1.49 tff(9268,plain,
% 1.30/1.49 (~node26(s32)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9267, 3949, 8578])).
% 1.30/1.49 tff(9269,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s32) | node26(s32) | (~until27(s32)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s32) | node26(s32) | (~until27(s32)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9270,plain,
% 1.30/1.49 ((node26(s32) | (~until27(s32)) | xuntil28(s32)) <=> (xuntil28(s32) | node26(s32) | (~until27(s32)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9271,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s32) | (~until27(s32)) | xuntil28(s32))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s32) | node26(s32) | (~until27(s32))))),
% 1.30/1.49 inference(monotonicity,[status(thm)],[9270])).
% 1.30/1.49 tff(9272,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s32) | (~until27(s32)) | xuntil28(s32))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s32) | node26(s32) | (~until27(s32)))),
% 1.30/1.49 inference(transitivity,[status(thm)],[9271, 9269])).
% 1.30/1.49 tff(9273,plain,
% 1.30/1.49 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s32) | (~until27(s32)) | xuntil28(s32))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9274,plain,
% 1.30/1.49 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s32) | node26(s32) | (~until27(s32))),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9273, 9272])).
% 1.30/1.49 tff(9275,plain,
% 1.30/1.49 (xuntil28(s32) | (~until27(s32))),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9274, 8821, 9268])).
% 1.30/1.49 tff(9276,plain,
% 1.30/1.49 (xuntil28(s32)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9275, 9264])).
% 1.30/1.49 tff(9277,plain,
% 1.30/1.49 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s32, s33)) | (~xuntil28(s32)) | until27(s33))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s32, s33)) | (~xuntil28(s32)) | until27(s33))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9278,plain,
% 1.30/1.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s32, s33)) | (~xuntil28(s32)) | until27(s33))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9279,plain,
% 1.30/1.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s32, s33)) | (~xuntil28(s32)) | until27(s33)),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9278, 9277])).
% 1.30/1.49 tff(9280,plain,
% 1.30/1.49 ((~xuntil28(s32)) | until27(s33)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9279, 3016, 8839])).
% 1.30/1.49 tff(9281,plain,
% 1.30/1.49 (until27(s33)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9280, 9276])).
% 1.30/1.49 tff(9282,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s33) | node26(s33) | (~until27(s33)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s33) | node26(s33) | (~until27(s33)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9283,plain,
% 1.30/1.49 ((node26(s33) | (~until27(s33)) | xuntil28(s33)) <=> (xuntil28(s33) | node26(s33) | (~until27(s33)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9284,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s33) | (~until27(s33)) | xuntil28(s33))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s33) | node26(s33) | (~until27(s33))))),
% 1.30/1.49 inference(monotonicity,[status(thm)],[9283])).
% 1.30/1.49 tff(9285,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s33) | (~until27(s33)) | xuntil28(s33))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s33) | node26(s33) | (~until27(s33)))),
% 1.30/1.49 inference(transitivity,[status(thm)],[9284, 9282])).
% 1.30/1.49 tff(9286,plain,
% 1.30/1.49 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s33) | (~until27(s33)) | xuntil28(s33))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9287,plain,
% 1.30/1.49 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s33) | node26(s33) | (~until27(s33))),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9286, 9285])).
% 1.30/1.49 tff(9288,plain,
% 1.30/1.49 (xuntil28(s33)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9287, 8821, 9281, 8571])).
% 1.30/1.49 tff(9289,plain,
% 1.30/1.49 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s33, s34)) | (~xuntil28(s33)) | until27(s34))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s33, s34)) | (~xuntil28(s33)) | until27(s34))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9290,plain,
% 1.30/1.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s33, s34)) | (~xuntil28(s33)) | until27(s34))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9291,plain,
% 1.30/1.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s33, s34)) | (~xuntil28(s33)) | until27(s34)),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9290, 9289])).
% 1.30/1.49 tff(9292,plain,
% 1.30/1.49 ((~xuntil28(s33)) | until27(s34)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9291, 3083, 8839])).
% 1.30/1.49 tff(9293,plain,
% 1.30/1.49 (until27(s34)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9292, 9288])).
% 1.30/1.49 tff(9294,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s34) | node26(s34) | (~until27(s34)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s34) | node26(s34) | (~until27(s34)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9295,plain,
% 1.30/1.49 ((node26(s34) | (~until27(s34)) | xuntil28(s34)) <=> (xuntil28(s34) | node26(s34) | (~until27(s34)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9296,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s34) | (~until27(s34)) | xuntil28(s34))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s34) | node26(s34) | (~until27(s34))))),
% 1.30/1.49 inference(monotonicity,[status(thm)],[9295])).
% 1.30/1.49 tff(9297,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s34) | (~until27(s34)) | xuntil28(s34))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s34) | node26(s34) | (~until27(s34)))),
% 1.30/1.49 inference(transitivity,[status(thm)],[9296, 9294])).
% 1.30/1.49 tff(9298,plain,
% 1.30/1.49 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s34) | (~until27(s34)) | xuntil28(s34))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9299,plain,
% 1.30/1.49 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s34) | node26(s34) | (~until27(s34))),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9298, 9297])).
% 1.30/1.49 tff(9300,plain,
% 1.30/1.49 (xuntil28(s34) | node26(s34)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9299, 8821, 9293])).
% 1.30/1.49 tff(9301,plain,
% 1.30/1.49 (xuntil28(s34)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9300, 8567])).
% 1.30/1.49 tff(9302,plain,
% 1.30/1.49 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s34, s35)) | (~xuntil28(s34)) | until27(s35))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s34, s35)) | (~xuntil28(s34)) | until27(s35))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9303,plain,
% 1.30/1.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s34, s35)) | (~xuntil28(s34)) | until27(s35))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9304,plain,
% 1.30/1.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s34, s35)) | (~xuntil28(s34)) | until27(s35)),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9303, 9302])).
% 1.30/1.49 tff(9305,plain,
% 1.30/1.49 ((~xuntil28(s34)) | until27(s35)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9304, 3182, 8839])).
% 1.30/1.49 tff(9306,plain,
% 1.30/1.49 (until27(s35)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9305, 9301])).
% 1.30/1.49 tff(9307,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s35) | node26(s35) | (~until27(s35)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s35) | node26(s35) | (~until27(s35)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9308,plain,
% 1.30/1.49 ((node26(s35) | (~until27(s35)) | xuntil28(s35)) <=> (xuntil28(s35) | node26(s35) | (~until27(s35)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9309,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s35) | (~until27(s35)) | xuntil28(s35))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s35) | node26(s35) | (~until27(s35))))),
% 1.30/1.49 inference(monotonicity,[status(thm)],[9308])).
% 1.30/1.49 tff(9310,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s35) | (~until27(s35)) | xuntil28(s35))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s35) | node26(s35) | (~until27(s35)))),
% 1.30/1.49 inference(transitivity,[status(thm)],[9309, 9307])).
% 1.30/1.49 tff(9311,plain,
% 1.30/1.49 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s35) | (~until27(s35)) | xuntil28(s35))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9312,plain,
% 1.30/1.49 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s35) | node26(s35) | (~until27(s35))),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9311, 9310])).
% 1.30/1.49 tff(9313,plain,
% 1.30/1.49 (xuntil28(s35)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9312, 8821, 9306, 8558])).
% 1.30/1.49 tff(9314,plain,
% 1.30/1.49 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s35, s36)) | (~xuntil28(s35)) | until27(s36))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s35, s36)) | (~xuntil28(s35)) | until27(s36))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9315,plain,
% 1.30/1.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s35, s36)) | (~xuntil28(s35)) | until27(s36))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9316,plain,
% 1.30/1.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s35, s36)) | (~xuntil28(s35)) | until27(s36)),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9315, 9314])).
% 1.30/1.49 tff(9317,plain,
% 1.30/1.49 ((~xuntil28(s35)) | until27(s36)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9316, 3260, 8839])).
% 1.30/1.49 tff(9318,plain,
% 1.30/1.49 (until27(s36)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9317, 9313])).
% 1.30/1.49 tff(9319,plain,
% 1.30/1.49 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s36) | (~node26(s36)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s36) | (~node26(s36)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9320,plain,
% 1.30/1.49 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s36) | (~node26(s36)))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9321,plain,
% 1.30/1.49 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s36) | (~node26(s36))),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9320, 9319])).
% 1.30/1.49 tff(9322,plain,
% 1.30/1.49 (~node26(s36)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9321, 3949, 8549])).
% 1.30/1.49 tff(9323,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s36) | node26(s36) | (~until27(s36)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s36) | node26(s36) | (~until27(s36)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9324,plain,
% 1.30/1.49 ((node26(s36) | (~until27(s36)) | xuntil28(s36)) <=> (xuntil28(s36) | node26(s36) | (~until27(s36)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9325,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s36) | (~until27(s36)) | xuntil28(s36))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s36) | node26(s36) | (~until27(s36))))),
% 1.30/1.49 inference(monotonicity,[status(thm)],[9324])).
% 1.30/1.49 tff(9326,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s36) | (~until27(s36)) | xuntil28(s36))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s36) | node26(s36) | (~until27(s36)))),
% 1.30/1.49 inference(transitivity,[status(thm)],[9325, 9323])).
% 1.30/1.49 tff(9327,plain,
% 1.30/1.49 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s36) | (~until27(s36)) | xuntil28(s36))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9328,plain,
% 1.30/1.49 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s36) | node26(s36) | (~until27(s36))),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9327, 9326])).
% 1.30/1.49 tff(9329,plain,
% 1.30/1.49 (xuntil28(s36) | (~until27(s36))),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9328, 8821, 9322])).
% 1.30/1.49 tff(9330,plain,
% 1.30/1.49 (xuntil28(s36)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9329, 9318])).
% 1.30/1.49 tff(9331,plain,
% 1.30/1.49 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s36, s37)) | (~xuntil28(s36)) | until27(s37))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s36, s37)) | (~xuntil28(s36)) | until27(s37))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9332,plain,
% 1.30/1.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s36, s37)) | (~xuntil28(s36)) | until27(s37))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9333,plain,
% 1.30/1.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s36, s37)) | (~xuntil28(s36)) | until27(s37)),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9332, 9331])).
% 1.30/1.49 tff(9334,plain,
% 1.30/1.49 ((~xuntil28(s36)) | until27(s37)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9333, 3321, 8839])).
% 1.30/1.49 tff(9335,plain,
% 1.30/1.49 (until27(s37)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9334, 9330])).
% 1.30/1.49 tff(9336,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s37) | node26(s37) | (~until27(s37)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s37) | node26(s37) | (~until27(s37)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9337,plain,
% 1.30/1.49 ((node26(s37) | (~until27(s37)) | xuntil28(s37)) <=> (xuntil28(s37) | node26(s37) | (~until27(s37)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9338,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s37) | (~until27(s37)) | xuntil28(s37))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s37) | node26(s37) | (~until27(s37))))),
% 1.30/1.49 inference(monotonicity,[status(thm)],[9337])).
% 1.30/1.49 tff(9339,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s37) | (~until27(s37)) | xuntil28(s37))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s37) | node26(s37) | (~until27(s37)))),
% 1.30/1.49 inference(transitivity,[status(thm)],[9338, 9336])).
% 1.30/1.49 tff(9340,plain,
% 1.30/1.49 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s37) | (~until27(s37)) | xuntil28(s37))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9341,plain,
% 1.30/1.49 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s37) | node26(s37) | (~until27(s37))),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9340, 9339])).
% 1.30/1.49 tff(9342,plain,
% 1.30/1.49 (xuntil28(s37)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9341, 8821, 9335, 8542])).
% 1.30/1.49 tff(9343,plain,
% 1.30/1.49 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s37, s38)) | (~xuntil28(s37)) | until27(s38))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s37, s38)) | (~xuntil28(s37)) | until27(s38))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9344,plain,
% 1.30/1.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s37, s38)) | (~xuntil28(s37)) | until27(s38))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9345,plain,
% 1.30/1.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s37, s38)) | (~xuntil28(s37)) | until27(s38)),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9344, 9343])).
% 1.30/1.49 tff(9346,plain,
% 1.30/1.49 ((~xuntil28(s37)) | until27(s38)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9345, 3416, 8839])).
% 1.30/1.49 tff(9347,plain,
% 1.30/1.49 (until27(s38)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9346, 9342])).
% 1.30/1.49 tff(9348,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s38) | node26(s38) | (~until27(s38)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s38) | node26(s38) | (~until27(s38)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9349,plain,
% 1.30/1.49 ((node26(s38) | (~until27(s38)) | xuntil28(s38)) <=> (xuntil28(s38) | node26(s38) | (~until27(s38)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9350,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s38) | (~until27(s38)) | xuntil28(s38))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s38) | node26(s38) | (~until27(s38))))),
% 1.30/1.49 inference(monotonicity,[status(thm)],[9349])).
% 1.30/1.49 tff(9351,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s38) | (~until27(s38)) | xuntil28(s38))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s38) | node26(s38) | (~until27(s38)))),
% 1.30/1.49 inference(transitivity,[status(thm)],[9350, 9348])).
% 1.30/1.49 tff(9352,plain,
% 1.30/1.49 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s38) | (~until27(s38)) | xuntil28(s38))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9353,plain,
% 1.30/1.49 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s38) | node26(s38) | (~until27(s38))),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9352, 9351])).
% 1.30/1.49 tff(9354,plain,
% 1.30/1.49 (xuntil28(s38) | node26(s38)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9353, 8821, 9347])).
% 1.30/1.49 tff(9355,plain,
% 1.30/1.49 (xuntil28(s38)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9354, 8538])).
% 1.30/1.49 tff(9356,plain,
% 1.30/1.49 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s38, s39)) | (~xuntil28(s38)) | until27(s39))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s38, s39)) | (~xuntil28(s38)) | until27(s39))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9357,plain,
% 1.30/1.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s38, s39)) | (~xuntil28(s38)) | until27(s39))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9358,plain,
% 1.30/1.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s38, s39)) | (~xuntil28(s38)) | until27(s39)),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9357, 9356])).
% 1.30/1.49 tff(9359,plain,
% 1.30/1.49 ((~xuntil28(s38)) | until27(s39)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9358, 3480, 8839])).
% 1.30/1.49 tff(9360,plain,
% 1.30/1.49 (until27(s39)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9359, 9355])).
% 1.30/1.49 tff(9361,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s39) | node26(s39) | (~until27(s39)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s39) | node26(s39) | (~until27(s39)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9362,plain,
% 1.30/1.49 ((node26(s39) | (~until27(s39)) | xuntil28(s39)) <=> (xuntil28(s39) | node26(s39) | (~until27(s39)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9363,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s39) | (~until27(s39)) | xuntil28(s39))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s39) | node26(s39) | (~until27(s39))))),
% 1.30/1.49 inference(monotonicity,[status(thm)],[9362])).
% 1.30/1.49 tff(9364,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s39) | (~until27(s39)) | xuntil28(s39))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s39) | node26(s39) | (~until27(s39)))),
% 1.30/1.49 inference(transitivity,[status(thm)],[9363, 9361])).
% 1.30/1.49 tff(9365,plain,
% 1.30/1.49 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s39) | (~until27(s39)) | xuntil28(s39))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9366,plain,
% 1.30/1.49 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s39) | node26(s39) | (~until27(s39))),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9365, 9364])).
% 1.30/1.49 tff(9367,plain,
% 1.30/1.49 (xuntil28(s39)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9366, 8821, 9360, 8529])).
% 1.30/1.49 tff(9368,plain,
% 1.30/1.49 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s39, s40)) | (~xuntil28(s39)) | until27(s40))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s39, s40)) | (~xuntil28(s39)) | until27(s40))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9369,plain,
% 1.30/1.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s39, s40)) | (~xuntil28(s39)) | until27(s40))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9370,plain,
% 1.30/1.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s39, s40)) | (~xuntil28(s39)) | until27(s40)),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9369, 9368])).
% 1.30/1.49 tff(9371,plain,
% 1.30/1.49 ((~xuntil28(s39)) | until27(s40)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9370, 3555, 8839])).
% 1.30/1.49 tff(9372,plain,
% 1.30/1.49 (until27(s40)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9371, 9367])).
% 1.30/1.49 tff(9373,plain,
% 1.30/1.49 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s40) | (~node26(s40)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s40) | (~node26(s40)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9374,plain,
% 1.30/1.49 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s40) | (~node26(s40)))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9375,plain,
% 1.30/1.49 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s40) | (~node26(s40))),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9374, 9373])).
% 1.30/1.49 tff(9376,plain,
% 1.30/1.49 (~node26(s40)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9375, 3949, 8520])).
% 1.30/1.49 tff(9377,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s40) | node26(s40) | (~until27(s40)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s40) | node26(s40) | (~until27(s40)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9378,plain,
% 1.30/1.49 ((node26(s40) | (~until27(s40)) | xuntil28(s40)) <=> (xuntil28(s40) | node26(s40) | (~until27(s40)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9379,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s40) | (~until27(s40)) | xuntil28(s40))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s40) | node26(s40) | (~until27(s40))))),
% 1.30/1.49 inference(monotonicity,[status(thm)],[9378])).
% 1.30/1.49 tff(9380,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s40) | (~until27(s40)) | xuntil28(s40))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s40) | node26(s40) | (~until27(s40)))),
% 1.30/1.49 inference(transitivity,[status(thm)],[9379, 9377])).
% 1.30/1.49 tff(9381,plain,
% 1.30/1.49 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s40) | (~until27(s40)) | xuntil28(s40))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9382,plain,
% 1.30/1.49 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s40) | node26(s40) | (~until27(s40))),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9381, 9380])).
% 1.30/1.49 tff(9383,plain,
% 1.30/1.49 (xuntil28(s40) | (~until27(s40))),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9382, 8821, 9376])).
% 1.30/1.49 tff(9384,plain,
% 1.30/1.49 (xuntil28(s40)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9383, 9372])).
% 1.30/1.49 tff(9385,plain,
% 1.30/1.49 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s40, s41)) | (~xuntil28(s40)) | until27(s41))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s40, s41)) | (~xuntil28(s40)) | until27(s41))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9386,plain,
% 1.30/1.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s40, s41)) | (~xuntil28(s40)) | until27(s41))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9387,plain,
% 1.30/1.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s40, s41)) | (~xuntil28(s40)) | until27(s41)),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9386, 9385])).
% 1.30/1.49 tff(9388,plain,
% 1.30/1.49 ((~xuntil28(s40)) | until27(s41)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9387, 3644, 8839])).
% 1.30/1.49 tff(9389,plain,
% 1.30/1.49 (until27(s41)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9388, 9384])).
% 1.30/1.49 tff(9390,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s41) | node26(s41) | (~until27(s41)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s41) | node26(s41) | (~until27(s41)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9391,plain,
% 1.30/1.49 ((node26(s41) | (~until27(s41)) | xuntil28(s41)) <=> (xuntil28(s41) | node26(s41) | (~until27(s41)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9392,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s41) | (~until27(s41)) | xuntil28(s41))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s41) | node26(s41) | (~until27(s41))))),
% 1.30/1.49 inference(monotonicity,[status(thm)],[9391])).
% 1.30/1.49 tff(9393,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s41) | (~until27(s41)) | xuntil28(s41))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s41) | node26(s41) | (~until27(s41)))),
% 1.30/1.49 inference(transitivity,[status(thm)],[9392, 9390])).
% 1.30/1.49 tff(9394,plain,
% 1.30/1.49 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s41) | (~until27(s41)) | xuntil28(s41))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9395,plain,
% 1.30/1.49 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s41) | node26(s41) | (~until27(s41))),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9394, 9393])).
% 1.30/1.49 tff(9396,plain,
% 1.30/1.49 (xuntil28(s41)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9395, 8821, 9389, 8513])).
% 1.30/1.49 tff(9397,plain,
% 1.30/1.49 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s41, s42)) | (~xuntil28(s41)) | until27(s42))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s41, s42)) | (~xuntil28(s41)) | until27(s42))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9398,plain,
% 1.30/1.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s41, s42)) | (~xuntil28(s41)) | until27(s42))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9399,plain,
% 1.30/1.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s41, s42)) | (~xuntil28(s41)) | until27(s42)),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9398, 9397])).
% 1.30/1.49 tff(9400,plain,
% 1.30/1.49 ((~xuntil28(s41)) | until27(s42)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9399, 3711, 8839])).
% 1.30/1.49 tff(9401,plain,
% 1.30/1.49 (until27(s42)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9400, 9396])).
% 1.30/1.49 tff(9402,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s42) | node26(s42) | (~until27(s42)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s42) | node26(s42) | (~until27(s42)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9403,plain,
% 1.30/1.49 ((node26(s42) | (~until27(s42)) | xuntil28(s42)) <=> (xuntil28(s42) | node26(s42) | (~until27(s42)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9404,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s42) | (~until27(s42)) | xuntil28(s42))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s42) | node26(s42) | (~until27(s42))))),
% 1.30/1.49 inference(monotonicity,[status(thm)],[9403])).
% 1.30/1.49 tff(9405,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s42) | (~until27(s42)) | xuntil28(s42))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s42) | node26(s42) | (~until27(s42)))),
% 1.30/1.49 inference(transitivity,[status(thm)],[9404, 9402])).
% 1.30/1.49 tff(9406,plain,
% 1.30/1.49 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s42) | (~until27(s42)) | xuntil28(s42))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9407,plain,
% 1.30/1.49 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s42) | node26(s42) | (~until27(s42))),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9406, 9405])).
% 1.30/1.49 tff(9408,plain,
% 1.30/1.49 (xuntil28(s42) | node26(s42)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9407, 8821, 9401])).
% 1.30/1.49 tff(9409,plain,
% 1.30/1.49 (xuntil28(s42)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9408, 8509])).
% 1.30/1.49 tff(9410,plain,
% 1.30/1.49 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s42, s43)) | (~xuntil28(s42)) | until27(s43))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s42, s43)) | (~xuntil28(s42)) | until27(s43))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9411,plain,
% 1.30/1.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s42, s43)) | (~xuntil28(s42)) | until27(s43))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9412,plain,
% 1.30/1.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s42, s43)) | (~xuntil28(s42)) | until27(s43)),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9411, 9410])).
% 1.30/1.49 tff(9413,plain,
% 1.30/1.49 ((~xuntil28(s42)) | until27(s43)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9412, 3810, 8839])).
% 1.30/1.49 tff(9414,plain,
% 1.30/1.49 (until27(s43)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9413, 9409])).
% 1.30/1.49 tff(9415,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s43) | node26(s43) | (~until27(s43)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s43) | node26(s43) | (~until27(s43)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9416,plain,
% 1.30/1.49 ((node26(s43) | (~until27(s43)) | xuntil28(s43)) <=> (xuntil28(s43) | node26(s43) | (~until27(s43)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9417,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s43) | (~until27(s43)) | xuntil28(s43))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s43) | node26(s43) | (~until27(s43))))),
% 1.30/1.49 inference(monotonicity,[status(thm)],[9416])).
% 1.30/1.49 tff(9418,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s43) | (~until27(s43)) | xuntil28(s43))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s43) | node26(s43) | (~until27(s43)))),
% 1.30/1.49 inference(transitivity,[status(thm)],[9417, 9415])).
% 1.30/1.49 tff(9419,plain,
% 1.30/1.49 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s43) | (~until27(s43)) | xuntil28(s43))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9420,plain,
% 1.30/1.49 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s43) | node26(s43) | (~until27(s43))),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9419, 9418])).
% 1.30/1.49 tff(9421,plain,
% 1.30/1.49 (xuntil28(s43)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9420, 8821, 9414, 8500])).
% 1.30/1.49 tff(9422,plain,
% 1.30/1.49 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s43, s44)) | (~xuntil28(s43)) | until27(s44))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s43, s44)) | (~xuntil28(s43)) | until27(s44))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9423,plain,
% 1.30/1.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s43, s44)) | (~xuntil28(s43)) | until27(s44))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9424,plain,
% 1.30/1.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s43, s44)) | (~xuntil28(s43)) | until27(s44)),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9423, 9422])).
% 1.30/1.49 tff(9425,plain,
% 1.30/1.49 ((~xuntil28(s43)) | until27(s44)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9424, 3888, 8839])).
% 1.30/1.49 tff(9426,plain,
% 1.30/1.49 (until27(s44)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9425, 9421])).
% 1.30/1.49 tff(9427,plain,
% 1.30/1.49 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s44) | (~node26(s44)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s44) | (~node26(s44)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9428,plain,
% 1.30/1.49 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s44) | (~node26(s44)))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9429,plain,
% 1.30/1.49 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s44) | (~node26(s44))),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9428, 9427])).
% 1.30/1.49 tff(9430,plain,
% 1.30/1.49 (~node26(s44)),
% 1.30/1.49 inference(unit_resolution,[status(thm)],[9429, 3949, 3915])).
% 1.30/1.49 tff(9431,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s44) | node26(s44) | (~until27(s44)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s44) | node26(s44) | (~until27(s44)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9432,plain,
% 1.30/1.49 ((node26(s44) | (~until27(s44)) | xuntil28(s44)) <=> (xuntil28(s44) | node26(s44) | (~until27(s44)))),
% 1.30/1.49 inference(rewrite,[status(thm)],[])).
% 1.30/1.49 tff(9433,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s44) | (~until27(s44)) | xuntil28(s44))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s44) | node26(s44) | (~until27(s44))))),
% 1.30/1.49 inference(monotonicity,[status(thm)],[9432])).
% 1.30/1.49 tff(9434,plain,
% 1.30/1.49 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s44) | (~until27(s44)) | xuntil28(s44))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s44) | node26(s44) | (~until27(s44)))),
% 1.30/1.49 inference(transitivity,[status(thm)],[9433, 9431])).
% 1.30/1.49 tff(9435,plain,
% 1.30/1.49 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s44) | (~until27(s44)) | xuntil28(s44))),
% 1.30/1.49 inference(quant_inst,[status(thm)],[])).
% 1.30/1.49 tff(9436,plain,
% 1.30/1.49 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s44) | node26(s44) | (~until27(s44))),
% 1.30/1.49 inference(modus_ponens,[status(thm)],[9435, 9434])).
% 1.30/1.49 tff(9437,plain,
% 1.30/1.49 (xuntil28(s44) | (~until27(s44))),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9436, 8821, 9430])).
% 1.30/1.50 tff(9438,plain,
% 1.30/1.50 (xuntil28(s44)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9437, 9426])).
% 1.30/1.50 tff(9439,plain,
% 1.30/1.50 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s44, s45)) | (~xuntil28(s44)) | until27(s45))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s44, s45)) | (~xuntil28(s44)) | until27(s45))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9440,plain,
% 1.30/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s44, s45)) | (~xuntil28(s44)) | until27(s45))),
% 1.30/1.50 inference(quant_inst,[status(thm)],[])).
% 1.30/1.50 tff(9441,plain,
% 1.30/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s44, s45)) | (~xuntil28(s44)) | until27(s45)),
% 1.30/1.50 inference(modus_ponens,[status(thm)],[9440, 9439])).
% 1.30/1.50 tff(9442,plain,
% 1.30/1.50 ((~xuntil28(s44)) | until27(s45)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9441, 4010, 8839])).
% 1.30/1.50 tff(9443,plain,
% 1.30/1.50 (until27(s45)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9442, 9438])).
% 1.30/1.50 tff(9444,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s45) | node26(s45) | (~until27(s45)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s45) | node26(s45) | (~until27(s45)))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9445,plain,
% 1.30/1.50 ((node26(s45) | (~until27(s45)) | xuntil28(s45)) <=> (xuntil28(s45) | node26(s45) | (~until27(s45)))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9446,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s45) | (~until27(s45)) | xuntil28(s45))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s45) | node26(s45) | (~until27(s45))))),
% 1.30/1.50 inference(monotonicity,[status(thm)],[9445])).
% 1.30/1.50 tff(9447,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s45) | (~until27(s45)) | xuntil28(s45))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s45) | node26(s45) | (~until27(s45)))),
% 1.30/1.50 inference(transitivity,[status(thm)],[9446, 9444])).
% 1.30/1.50 tff(9448,plain,
% 1.30/1.50 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s45) | (~until27(s45)) | xuntil28(s45))),
% 1.30/1.50 inference(quant_inst,[status(thm)],[])).
% 1.30/1.50 tff(9449,plain,
% 1.30/1.50 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s45) | node26(s45) | (~until27(s45))),
% 1.30/1.50 inference(modus_ponens,[status(thm)],[9448, 9447])).
% 1.30/1.50 tff(9450,plain,
% 1.30/1.50 (xuntil28(s45)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9449, 8821, 9443, 8491])).
% 1.30/1.50 tff(9451,plain,
% 1.30/1.50 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s45, s46)) | (~xuntil28(s45)) | until27(s46))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s45, s46)) | (~xuntil28(s45)) | until27(s46))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9452,plain,
% 1.30/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s45, s46)) | (~xuntil28(s45)) | until27(s46))),
% 1.30/1.50 inference(quant_inst,[status(thm)],[])).
% 1.30/1.50 tff(9453,plain,
% 1.30/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s45, s46)) | (~xuntil28(s45)) | until27(s46)),
% 1.30/1.50 inference(modus_ponens,[status(thm)],[9452, 9451])).
% 1.30/1.50 tff(9454,plain,
% 1.30/1.50 ((~xuntil28(s45)) | until27(s46)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9453, 4077, 8839])).
% 1.30/1.50 tff(9455,plain,
% 1.30/1.50 (until27(s46)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9454, 9450])).
% 1.30/1.50 tff(9456,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s46) | node26(s46) | (~until27(s46)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s46) | node26(s46) | (~until27(s46)))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9457,plain,
% 1.30/1.50 ((node26(s46) | (~until27(s46)) | xuntil28(s46)) <=> (xuntil28(s46) | node26(s46) | (~until27(s46)))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9458,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s46) | (~until27(s46)) | xuntil28(s46))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s46) | node26(s46) | (~until27(s46))))),
% 1.30/1.50 inference(monotonicity,[status(thm)],[9457])).
% 1.30/1.50 tff(9459,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s46) | (~until27(s46)) | xuntil28(s46))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s46) | node26(s46) | (~until27(s46)))),
% 1.30/1.50 inference(transitivity,[status(thm)],[9458, 9456])).
% 1.30/1.50 tff(9460,plain,
% 1.30/1.50 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s46) | (~until27(s46)) | xuntil28(s46))),
% 1.30/1.50 inference(quant_inst,[status(thm)],[])).
% 1.30/1.50 tff(9461,plain,
% 1.30/1.50 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s46) | node26(s46) | (~until27(s46))),
% 1.30/1.50 inference(modus_ponens,[status(thm)],[9460, 9459])).
% 1.30/1.50 tff(9462,plain,
% 1.30/1.50 (xuntil28(s46) | node26(s46)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9461, 8821, 9455])).
% 1.30/1.50 tff(9463,plain,
% 1.30/1.50 (xuntil28(s46)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9462, 8487])).
% 1.30/1.50 tff(9464,plain,
% 1.30/1.50 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s46, s47)) | (~xuntil28(s46)) | until27(s47))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s46, s47)) | (~xuntil28(s46)) | until27(s47))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9465,plain,
% 1.30/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s46, s47)) | (~xuntil28(s46)) | until27(s47))),
% 1.30/1.50 inference(quant_inst,[status(thm)],[])).
% 1.30/1.50 tff(9466,plain,
% 1.30/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s46, s47)) | (~xuntil28(s46)) | until27(s47)),
% 1.30/1.50 inference(modus_ponens,[status(thm)],[9465, 9464])).
% 1.30/1.50 tff(9467,plain,
% 1.30/1.50 ((~xuntil28(s46)) | until27(s47)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9466, 4176, 8839])).
% 1.30/1.50 tff(9468,plain,
% 1.30/1.50 (until27(s47)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9467, 9463])).
% 1.30/1.50 tff(9469,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s47) | node26(s47) | (~until27(s47)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s47) | node26(s47) | (~until27(s47)))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9470,plain,
% 1.30/1.50 ((node26(s47) | (~until27(s47)) | xuntil28(s47)) <=> (xuntil28(s47) | node26(s47) | (~until27(s47)))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9471,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s47) | (~until27(s47)) | xuntil28(s47))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s47) | node26(s47) | (~until27(s47))))),
% 1.30/1.50 inference(monotonicity,[status(thm)],[9470])).
% 1.30/1.50 tff(9472,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s47) | (~until27(s47)) | xuntil28(s47))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s47) | node26(s47) | (~until27(s47)))),
% 1.30/1.50 inference(transitivity,[status(thm)],[9471, 9469])).
% 1.30/1.50 tff(9473,plain,
% 1.30/1.50 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s47) | (~until27(s47)) | xuntil28(s47))),
% 1.30/1.50 inference(quant_inst,[status(thm)],[])).
% 1.30/1.50 tff(9474,plain,
% 1.30/1.50 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s47) | node26(s47) | (~until27(s47))),
% 1.30/1.50 inference(modus_ponens,[status(thm)],[9473, 9472])).
% 1.30/1.50 tff(9475,plain,
% 1.30/1.50 (xuntil28(s47)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9474, 8821, 9468, 8478])).
% 1.30/1.50 tff(9476,plain,
% 1.30/1.50 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s47, s48)) | (~xuntil28(s47)) | until27(s48))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s47, s48)) | (~xuntil28(s47)) | until27(s48))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9477,plain,
% 1.30/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s47, s48)) | (~xuntil28(s47)) | until27(s48))),
% 1.30/1.50 inference(quant_inst,[status(thm)],[])).
% 1.30/1.50 tff(9478,plain,
% 1.30/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s47, s48)) | (~xuntil28(s47)) | until27(s48)),
% 1.30/1.50 inference(modus_ponens,[status(thm)],[9477, 9476])).
% 1.30/1.50 tff(9479,plain,
% 1.30/1.50 ((~xuntil28(s47)) | until27(s48)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9478, 4254, 8839])).
% 1.30/1.50 tff(9480,plain,
% 1.30/1.50 (until27(s48)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9479, 9475])).
% 1.30/1.50 tff(9481,plain,
% 1.30/1.50 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s48) | (~node26(s48)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s48) | (~node26(s48)))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9482,plain,
% 1.30/1.50 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s48) | (~node26(s48)))),
% 1.30/1.50 inference(quant_inst,[status(thm)],[])).
% 1.30/1.50 tff(9483,plain,
% 1.30/1.50 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s48) | (~node26(s48))),
% 1.30/1.50 inference(modus_ponens,[status(thm)],[9482, 9481])).
% 1.30/1.50 tff(9484,plain,
% 1.30/1.50 (~node26(s48)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9483, 3949, 8469])).
% 1.30/1.50 tff(9485,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s48) | node26(s48) | (~until27(s48)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s48) | node26(s48) | (~until27(s48)))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9486,plain,
% 1.30/1.50 ((node26(s48) | (~until27(s48)) | xuntil28(s48)) <=> (xuntil28(s48) | node26(s48) | (~until27(s48)))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9487,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s48) | (~until27(s48)) | xuntil28(s48))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s48) | node26(s48) | (~until27(s48))))),
% 1.30/1.50 inference(monotonicity,[status(thm)],[9486])).
% 1.30/1.50 tff(9488,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s48) | (~until27(s48)) | xuntil28(s48))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s48) | node26(s48) | (~until27(s48)))),
% 1.30/1.50 inference(transitivity,[status(thm)],[9487, 9485])).
% 1.30/1.50 tff(9489,plain,
% 1.30/1.50 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s48) | (~until27(s48)) | xuntil28(s48))),
% 1.30/1.50 inference(quant_inst,[status(thm)],[])).
% 1.30/1.50 tff(9490,plain,
% 1.30/1.50 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s48) | node26(s48) | (~until27(s48))),
% 1.30/1.50 inference(modus_ponens,[status(thm)],[9489, 9488])).
% 1.30/1.50 tff(9491,plain,
% 1.30/1.50 (xuntil28(s48) | (~until27(s48))),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9490, 8821, 9484])).
% 1.30/1.50 tff(9492,plain,
% 1.30/1.50 (xuntil28(s48)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9491, 9480])).
% 1.30/1.50 tff(9493,plain,
% 1.30/1.50 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s48, s49)) | (~xuntil28(s48)) | until27(s49))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s48, s49)) | (~xuntil28(s48)) | until27(s49))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9494,plain,
% 1.30/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s48, s49)) | (~xuntil28(s48)) | until27(s49))),
% 1.30/1.50 inference(quant_inst,[status(thm)],[])).
% 1.30/1.50 tff(9495,plain,
% 1.30/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s48, s49)) | (~xuntil28(s48)) | until27(s49)),
% 1.30/1.50 inference(modus_ponens,[status(thm)],[9494, 9493])).
% 1.30/1.50 tff(9496,plain,
% 1.30/1.50 ((~xuntil28(s48)) | until27(s49)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9495, 4315, 8839])).
% 1.30/1.50 tff(9497,plain,
% 1.30/1.50 (until27(s49)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9496, 9492])).
% 1.30/1.50 tff(9498,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s49) | node26(s49) | (~until27(s49)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s49) | node26(s49) | (~until27(s49)))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9499,plain,
% 1.30/1.50 ((node26(s49) | (~until27(s49)) | xuntil28(s49)) <=> (xuntil28(s49) | node26(s49) | (~until27(s49)))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9500,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s49) | (~until27(s49)) | xuntil28(s49))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s49) | node26(s49) | (~until27(s49))))),
% 1.30/1.50 inference(monotonicity,[status(thm)],[9499])).
% 1.30/1.50 tff(9501,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s49) | (~until27(s49)) | xuntil28(s49))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s49) | node26(s49) | (~until27(s49)))),
% 1.30/1.50 inference(transitivity,[status(thm)],[9500, 9498])).
% 1.30/1.50 tff(9502,plain,
% 1.30/1.50 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s49) | (~until27(s49)) | xuntil28(s49))),
% 1.30/1.50 inference(quant_inst,[status(thm)],[])).
% 1.30/1.50 tff(9503,plain,
% 1.30/1.50 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s49) | node26(s49) | (~until27(s49))),
% 1.30/1.50 inference(modus_ponens,[status(thm)],[9502, 9501])).
% 1.30/1.50 tff(9504,plain,
% 1.30/1.50 (xuntil28(s49)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9503, 8821, 9497, 8462])).
% 1.30/1.50 tff(9505,plain,
% 1.30/1.50 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s49, s50)) | (~xuntil28(s49)) | until27(s50))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s49, s50)) | (~xuntil28(s49)) | until27(s50))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9506,plain,
% 1.30/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s49, s50)) | (~xuntil28(s49)) | until27(s50))),
% 1.30/1.50 inference(quant_inst,[status(thm)],[])).
% 1.30/1.50 tff(9507,plain,
% 1.30/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s49, s50)) | (~xuntil28(s49)) | until27(s50)),
% 1.30/1.50 inference(modus_ponens,[status(thm)],[9506, 9505])).
% 1.30/1.50 tff(9508,plain,
% 1.30/1.50 ((~xuntil28(s49)) | until27(s50)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9507, 4410, 8839])).
% 1.30/1.50 tff(9509,plain,
% 1.30/1.50 (until27(s50)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9508, 9504])).
% 1.30/1.50 tff(9510,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s50) | node26(s50) | (~until27(s50)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s50) | node26(s50) | (~until27(s50)))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9511,plain,
% 1.30/1.50 ((node26(s50) | (~until27(s50)) | xuntil28(s50)) <=> (xuntil28(s50) | node26(s50) | (~until27(s50)))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9512,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s50) | (~until27(s50)) | xuntil28(s50))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s50) | node26(s50) | (~until27(s50))))),
% 1.30/1.50 inference(monotonicity,[status(thm)],[9511])).
% 1.30/1.50 tff(9513,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s50) | (~until27(s50)) | xuntil28(s50))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s50) | node26(s50) | (~until27(s50)))),
% 1.30/1.50 inference(transitivity,[status(thm)],[9512, 9510])).
% 1.30/1.50 tff(9514,plain,
% 1.30/1.50 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s50) | (~until27(s50)) | xuntil28(s50))),
% 1.30/1.50 inference(quant_inst,[status(thm)],[])).
% 1.30/1.50 tff(9515,plain,
% 1.30/1.50 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s50) | node26(s50) | (~until27(s50))),
% 1.30/1.50 inference(modus_ponens,[status(thm)],[9514, 9513])).
% 1.30/1.50 tff(9516,plain,
% 1.30/1.50 (xuntil28(s50) | node26(s50)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9515, 8821, 9509])).
% 1.30/1.50 tff(9517,plain,
% 1.30/1.50 (xuntil28(s50)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9516, 8458])).
% 1.30/1.50 tff(9518,plain,
% 1.30/1.50 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s50, s51)) | (~xuntil28(s50)) | until27(s51))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s50, s51)) | (~xuntil28(s50)) | until27(s51))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9519,plain,
% 1.30/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s50, s51)) | (~xuntil28(s50)) | until27(s51))),
% 1.30/1.50 inference(quant_inst,[status(thm)],[])).
% 1.30/1.50 tff(9520,plain,
% 1.30/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s50, s51)) | (~xuntil28(s50)) | until27(s51)),
% 1.30/1.50 inference(modus_ponens,[status(thm)],[9519, 9518])).
% 1.30/1.50 tff(9521,plain,
% 1.30/1.50 ((~xuntil28(s50)) | until27(s51)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9520, 4474, 8839])).
% 1.30/1.50 tff(9522,plain,
% 1.30/1.50 (until27(s51)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9521, 9517])).
% 1.30/1.50 tff(9523,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s51) | node26(s51) | (~until27(s51)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s51) | node26(s51) | (~until27(s51)))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9524,plain,
% 1.30/1.50 ((node26(s51) | (~until27(s51)) | xuntil28(s51)) <=> (xuntil28(s51) | node26(s51) | (~until27(s51)))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9525,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s51) | (~until27(s51)) | xuntil28(s51))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s51) | node26(s51) | (~until27(s51))))),
% 1.30/1.50 inference(monotonicity,[status(thm)],[9524])).
% 1.30/1.50 tff(9526,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s51) | (~until27(s51)) | xuntil28(s51))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s51) | node26(s51) | (~until27(s51)))),
% 1.30/1.50 inference(transitivity,[status(thm)],[9525, 9523])).
% 1.30/1.50 tff(9527,plain,
% 1.30/1.50 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s51) | (~until27(s51)) | xuntil28(s51))),
% 1.30/1.50 inference(quant_inst,[status(thm)],[])).
% 1.30/1.50 tff(9528,plain,
% 1.30/1.50 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s51) | node26(s51) | (~until27(s51))),
% 1.30/1.50 inference(modus_ponens,[status(thm)],[9527, 9526])).
% 1.30/1.50 tff(9529,plain,
% 1.30/1.50 (xuntil28(s51)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9528, 8821, 9522, 8449])).
% 1.30/1.50 tff(9530,plain,
% 1.30/1.50 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s51, s52)) | (~xuntil28(s51)) | until27(s52))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s51, s52)) | (~xuntil28(s51)) | until27(s52))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9531,plain,
% 1.30/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s51, s52)) | (~xuntil28(s51)) | until27(s52))),
% 1.30/1.50 inference(quant_inst,[status(thm)],[])).
% 1.30/1.50 tff(9532,plain,
% 1.30/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s51, s52)) | (~xuntil28(s51)) | until27(s52)),
% 1.30/1.50 inference(modus_ponens,[status(thm)],[9531, 9530])).
% 1.30/1.50 tff(9533,plain,
% 1.30/1.50 ((~xuntil28(s51)) | until27(s52)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9532, 4549, 8839])).
% 1.30/1.50 tff(9534,plain,
% 1.30/1.50 (until27(s52)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9533, 9529])).
% 1.30/1.50 tff(9535,plain,
% 1.30/1.50 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s52) | (~node26(s52)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s52) | (~node26(s52)))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9536,plain,
% 1.30/1.50 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s52) | (~node26(s52)))),
% 1.30/1.50 inference(quant_inst,[status(thm)],[])).
% 1.30/1.50 tff(9537,plain,
% 1.30/1.50 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s52) | (~node26(s52))),
% 1.30/1.50 inference(modus_ponens,[status(thm)],[9536, 9535])).
% 1.30/1.50 tff(9538,plain,
% 1.30/1.50 (~node26(s52)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9537, 3949, 8440])).
% 1.30/1.50 tff(9539,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s52) | node26(s52) | (~until27(s52)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s52) | node26(s52) | (~until27(s52)))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9540,plain,
% 1.30/1.50 ((node26(s52) | (~until27(s52)) | xuntil28(s52)) <=> (xuntil28(s52) | node26(s52) | (~until27(s52)))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9541,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s52) | (~until27(s52)) | xuntil28(s52))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s52) | node26(s52) | (~until27(s52))))),
% 1.30/1.50 inference(monotonicity,[status(thm)],[9540])).
% 1.30/1.50 tff(9542,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s52) | (~until27(s52)) | xuntil28(s52))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s52) | node26(s52) | (~until27(s52)))),
% 1.30/1.50 inference(transitivity,[status(thm)],[9541, 9539])).
% 1.30/1.50 tff(9543,plain,
% 1.30/1.50 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s52) | (~until27(s52)) | xuntil28(s52))),
% 1.30/1.50 inference(quant_inst,[status(thm)],[])).
% 1.30/1.50 tff(9544,plain,
% 1.30/1.50 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s52) | node26(s52) | (~until27(s52))),
% 1.30/1.50 inference(modus_ponens,[status(thm)],[9543, 9542])).
% 1.30/1.50 tff(9545,plain,
% 1.30/1.50 (xuntil28(s52) | (~until27(s52))),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9544, 8821, 9538])).
% 1.30/1.50 tff(9546,plain,
% 1.30/1.50 (xuntil28(s52)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9545, 9534])).
% 1.30/1.50 tff(9547,plain,
% 1.30/1.50 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s52, s53)) | (~xuntil28(s52)) | until27(s53))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s52, s53)) | (~xuntil28(s52)) | until27(s53))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9548,plain,
% 1.30/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s52, s53)) | (~xuntil28(s52)) | until27(s53))),
% 1.30/1.50 inference(quant_inst,[status(thm)],[])).
% 1.30/1.50 tff(9549,plain,
% 1.30/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s52, s53)) | (~xuntil28(s52)) | until27(s53)),
% 1.30/1.50 inference(modus_ponens,[status(thm)],[9548, 9547])).
% 1.30/1.50 tff(9550,plain,
% 1.30/1.50 ((~xuntil28(s52)) | until27(s53)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9549, 4638, 8839])).
% 1.30/1.50 tff(9551,plain,
% 1.30/1.50 (until27(s53)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9550, 9546])).
% 1.30/1.50 tff(9552,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s53) | node26(s53) | (~until27(s53)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s53) | node26(s53) | (~until27(s53)))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9553,plain,
% 1.30/1.50 ((node26(s53) | (~until27(s53)) | xuntil28(s53)) <=> (xuntil28(s53) | node26(s53) | (~until27(s53)))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9554,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s53) | (~until27(s53)) | xuntil28(s53))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s53) | node26(s53) | (~until27(s53))))),
% 1.30/1.50 inference(monotonicity,[status(thm)],[9553])).
% 1.30/1.50 tff(9555,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s53) | (~until27(s53)) | xuntil28(s53))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s53) | node26(s53) | (~until27(s53)))),
% 1.30/1.50 inference(transitivity,[status(thm)],[9554, 9552])).
% 1.30/1.50 tff(9556,plain,
% 1.30/1.50 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s53) | (~until27(s53)) | xuntil28(s53))),
% 1.30/1.50 inference(quant_inst,[status(thm)],[])).
% 1.30/1.50 tff(9557,plain,
% 1.30/1.50 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s53) | node26(s53) | (~until27(s53))),
% 1.30/1.50 inference(modus_ponens,[status(thm)],[9556, 9555])).
% 1.30/1.50 tff(9558,plain,
% 1.30/1.50 (xuntil28(s53)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9557, 8821, 9551, 8433])).
% 1.30/1.50 tff(9559,plain,
% 1.30/1.50 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s53, s54)) | (~xuntil28(s53)) | until27(s54))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s53, s54)) | (~xuntil28(s53)) | until27(s54))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9560,plain,
% 1.30/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s53, s54)) | (~xuntil28(s53)) | until27(s54))),
% 1.30/1.50 inference(quant_inst,[status(thm)],[])).
% 1.30/1.50 tff(9561,plain,
% 1.30/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s53, s54)) | (~xuntil28(s53)) | until27(s54)),
% 1.30/1.50 inference(modus_ponens,[status(thm)],[9560, 9559])).
% 1.30/1.50 tff(9562,plain,
% 1.30/1.50 ((~xuntil28(s53)) | until27(s54)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9561, 4705, 8839])).
% 1.30/1.50 tff(9563,plain,
% 1.30/1.50 (until27(s54)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9562, 9558])).
% 1.30/1.50 tff(9564,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s54) | node26(s54) | (~until27(s54)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s54) | node26(s54) | (~until27(s54)))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9565,plain,
% 1.30/1.50 ((node26(s54) | (~until27(s54)) | xuntil28(s54)) <=> (xuntil28(s54) | node26(s54) | (~until27(s54)))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9566,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s54) | (~until27(s54)) | xuntil28(s54))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s54) | node26(s54) | (~until27(s54))))),
% 1.30/1.50 inference(monotonicity,[status(thm)],[9565])).
% 1.30/1.50 tff(9567,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s54) | (~until27(s54)) | xuntil28(s54))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s54) | node26(s54) | (~until27(s54)))),
% 1.30/1.50 inference(transitivity,[status(thm)],[9566, 9564])).
% 1.30/1.50 tff(9568,plain,
% 1.30/1.50 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s54) | (~until27(s54)) | xuntil28(s54))),
% 1.30/1.50 inference(quant_inst,[status(thm)],[])).
% 1.30/1.50 tff(9569,plain,
% 1.30/1.50 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s54) | node26(s54) | (~until27(s54))),
% 1.30/1.50 inference(modus_ponens,[status(thm)],[9568, 9567])).
% 1.30/1.50 tff(9570,plain,
% 1.30/1.50 (xuntil28(s54) | node26(s54)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9569, 8821, 9563])).
% 1.30/1.50 tff(9571,plain,
% 1.30/1.50 (xuntil28(s54)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9570, 8429])).
% 1.30/1.50 tff(9572,plain,
% 1.30/1.50 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s54, s55)) | (~xuntil28(s54)) | until27(s55))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s54, s55)) | (~xuntil28(s54)) | until27(s55))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9573,plain,
% 1.30/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s54, s55)) | (~xuntil28(s54)) | until27(s55))),
% 1.30/1.50 inference(quant_inst,[status(thm)],[])).
% 1.30/1.50 tff(9574,plain,
% 1.30/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s54, s55)) | (~xuntil28(s54)) | until27(s55)),
% 1.30/1.50 inference(modus_ponens,[status(thm)],[9573, 9572])).
% 1.30/1.50 tff(9575,plain,
% 1.30/1.50 ((~xuntil28(s54)) | until27(s55)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9574, 4804, 8839])).
% 1.30/1.50 tff(9576,plain,
% 1.30/1.50 (until27(s55)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9575, 9571])).
% 1.30/1.50 tff(9577,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s55) | node26(s55) | (~until27(s55)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s55) | node26(s55) | (~until27(s55)))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9578,plain,
% 1.30/1.50 ((node26(s55) | (~until27(s55)) | xuntil28(s55)) <=> (xuntil28(s55) | node26(s55) | (~until27(s55)))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9579,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s55) | (~until27(s55)) | xuntil28(s55))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s55) | node26(s55) | (~until27(s55))))),
% 1.30/1.50 inference(monotonicity,[status(thm)],[9578])).
% 1.30/1.50 tff(9580,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s55) | (~until27(s55)) | xuntil28(s55))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s55) | node26(s55) | (~until27(s55)))),
% 1.30/1.50 inference(transitivity,[status(thm)],[9579, 9577])).
% 1.30/1.50 tff(9581,plain,
% 1.30/1.50 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s55) | (~until27(s55)) | xuntil28(s55))),
% 1.30/1.50 inference(quant_inst,[status(thm)],[])).
% 1.30/1.50 tff(9582,plain,
% 1.30/1.50 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s55) | node26(s55) | (~until27(s55))),
% 1.30/1.50 inference(modus_ponens,[status(thm)],[9581, 9580])).
% 1.30/1.50 tff(9583,plain,
% 1.30/1.50 (xuntil28(s55)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9582, 8821, 9576, 8420])).
% 1.30/1.50 tff(9584,plain,
% 1.30/1.50 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s55, s56)) | (~xuntil28(s55)) | until27(s56))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s55, s56)) | (~xuntil28(s55)) | until27(s56))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9585,plain,
% 1.30/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s55, s56)) | (~xuntil28(s55)) | until27(s56))),
% 1.30/1.50 inference(quant_inst,[status(thm)],[])).
% 1.30/1.50 tff(9586,plain,
% 1.30/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s55, s56)) | (~xuntil28(s55)) | until27(s56)),
% 1.30/1.50 inference(modus_ponens,[status(thm)],[9585, 9584])).
% 1.30/1.50 tff(9587,plain,
% 1.30/1.50 ((~xuntil28(s55)) | until27(s56)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9586, 4882, 8839])).
% 1.30/1.50 tff(9588,plain,
% 1.30/1.50 (until27(s56)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9587, 9583])).
% 1.30/1.50 tff(9589,plain,
% 1.30/1.50 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s56) | (~node26(s56)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s56) | (~node26(s56)))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9590,plain,
% 1.30/1.50 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s56) | (~node26(s56)))),
% 1.30/1.50 inference(quant_inst,[status(thm)],[])).
% 1.30/1.50 tff(9591,plain,
% 1.30/1.50 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s56) | (~node26(s56))),
% 1.30/1.50 inference(modus_ponens,[status(thm)],[9590, 9589])).
% 1.30/1.50 tff(9592,plain,
% 1.30/1.50 (~node26(s56)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9591, 3949, 8411])).
% 1.30/1.50 tff(9593,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s56) | node26(s56) | (~until27(s56)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s56) | node26(s56) | (~until27(s56)))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9594,plain,
% 1.30/1.50 ((node26(s56) | (~until27(s56)) | xuntil28(s56)) <=> (xuntil28(s56) | node26(s56) | (~until27(s56)))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9595,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s56) | (~until27(s56)) | xuntil28(s56))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s56) | node26(s56) | (~until27(s56))))),
% 1.30/1.50 inference(monotonicity,[status(thm)],[9594])).
% 1.30/1.50 tff(9596,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s56) | (~until27(s56)) | xuntil28(s56))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s56) | node26(s56) | (~until27(s56)))),
% 1.30/1.50 inference(transitivity,[status(thm)],[9595, 9593])).
% 1.30/1.50 tff(9597,plain,
% 1.30/1.50 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s56) | (~until27(s56)) | xuntil28(s56))),
% 1.30/1.50 inference(quant_inst,[status(thm)],[])).
% 1.30/1.50 tff(9598,plain,
% 1.30/1.50 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s56) | node26(s56) | (~until27(s56))),
% 1.30/1.50 inference(modus_ponens,[status(thm)],[9597, 9596])).
% 1.30/1.50 tff(9599,plain,
% 1.30/1.50 (xuntil28(s56) | (~until27(s56))),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9598, 8821, 9592])).
% 1.30/1.50 tff(9600,plain,
% 1.30/1.50 (xuntil28(s56)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9599, 9588])).
% 1.30/1.50 tff(9601,plain,
% 1.30/1.50 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s56, s57)) | (~xuntil28(s56)) | until27(s57))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s56, s57)) | (~xuntil28(s56)) | until27(s57))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9602,plain,
% 1.30/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s56, s57)) | (~xuntil28(s56)) | until27(s57))),
% 1.30/1.50 inference(quant_inst,[status(thm)],[])).
% 1.30/1.50 tff(9603,plain,
% 1.30/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s56, s57)) | (~xuntil28(s56)) | until27(s57)),
% 1.30/1.50 inference(modus_ponens,[status(thm)],[9602, 9601])).
% 1.30/1.50 tff(9604,plain,
% 1.30/1.50 ((~xuntil28(s56)) | until27(s57)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9603, 4943, 8839])).
% 1.30/1.50 tff(9605,plain,
% 1.30/1.50 (until27(s57)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9604, 9600])).
% 1.30/1.50 tff(9606,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s57) | node26(s57) | (~until27(s57)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s57) | node26(s57) | (~until27(s57)))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9607,plain,
% 1.30/1.50 ((node26(s57) | (~until27(s57)) | xuntil28(s57)) <=> (xuntil28(s57) | node26(s57) | (~until27(s57)))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9608,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s57) | (~until27(s57)) | xuntil28(s57))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s57) | node26(s57) | (~until27(s57))))),
% 1.30/1.50 inference(monotonicity,[status(thm)],[9607])).
% 1.30/1.50 tff(9609,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s57) | (~until27(s57)) | xuntil28(s57))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s57) | node26(s57) | (~until27(s57)))),
% 1.30/1.50 inference(transitivity,[status(thm)],[9608, 9606])).
% 1.30/1.50 tff(9610,plain,
% 1.30/1.50 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s57) | (~until27(s57)) | xuntil28(s57))),
% 1.30/1.50 inference(quant_inst,[status(thm)],[])).
% 1.30/1.50 tff(9611,plain,
% 1.30/1.50 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s57) | node26(s57) | (~until27(s57))),
% 1.30/1.50 inference(modus_ponens,[status(thm)],[9610, 9609])).
% 1.30/1.50 tff(9612,plain,
% 1.30/1.50 (xuntil28(s57)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9611, 8821, 9605, 8404])).
% 1.30/1.50 tff(9613,plain,
% 1.30/1.50 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s57, s58)) | (~xuntil28(s57)) | until27(s58))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s57, s58)) | (~xuntil28(s57)) | until27(s58))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9614,plain,
% 1.30/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s57, s58)) | (~xuntil28(s57)) | until27(s58))),
% 1.30/1.50 inference(quant_inst,[status(thm)],[])).
% 1.30/1.50 tff(9615,plain,
% 1.30/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s57, s58)) | (~xuntil28(s57)) | until27(s58)),
% 1.30/1.50 inference(modus_ponens,[status(thm)],[9614, 9613])).
% 1.30/1.50 tff(9616,plain,
% 1.30/1.50 ((~xuntil28(s57)) | until27(s58)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9615, 5038, 8839])).
% 1.30/1.50 tff(9617,plain,
% 1.30/1.50 (until27(s58)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9616, 9612])).
% 1.30/1.50 tff(9618,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s58) | node26(s58) | (~until27(s58)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s58) | node26(s58) | (~until27(s58)))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9619,plain,
% 1.30/1.50 ((node26(s58) | (~until27(s58)) | xuntil28(s58)) <=> (xuntil28(s58) | node26(s58) | (~until27(s58)))),
% 1.30/1.50 inference(rewrite,[status(thm)],[])).
% 1.30/1.50 tff(9620,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s58) | (~until27(s58)) | xuntil28(s58))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s58) | node26(s58) | (~until27(s58))))),
% 1.30/1.50 inference(monotonicity,[status(thm)],[9619])).
% 1.30/1.50 tff(9621,plain,
% 1.30/1.50 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s58) | (~until27(s58)) | xuntil28(s58))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s58) | node26(s58) | (~until27(s58)))),
% 1.30/1.50 inference(transitivity,[status(thm)],[9620, 9618])).
% 1.30/1.50 tff(9622,plain,
% 1.30/1.50 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s58) | (~until27(s58)) | xuntil28(s58))),
% 1.30/1.50 inference(quant_inst,[status(thm)],[])).
% 1.30/1.50 tff(9623,plain,
% 1.30/1.50 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s58) | node26(s58) | (~until27(s58))),
% 1.30/1.50 inference(modus_ponens,[status(thm)],[9622, 9621])).
% 1.30/1.50 tff(9624,plain,
% 1.30/1.50 (xuntil28(s58) | node26(s58)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9623, 8821, 9617])).
% 1.30/1.50 tff(9625,plain,
% 1.30/1.50 (xuntil28(s58)),
% 1.30/1.50 inference(unit_resolution,[status(thm)],[9624, 8400])).
% 1.30/1.51 tff(9626,plain,
% 1.30/1.51 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s58, s59)) | (~xuntil28(s58)) | until27(s59))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s58, s59)) | (~xuntil28(s58)) | until27(s59))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9627,plain,
% 1.30/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s58, s59)) | (~xuntil28(s58)) | until27(s59))),
% 1.30/1.51 inference(quant_inst,[status(thm)],[])).
% 1.30/1.51 tff(9628,plain,
% 1.30/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s58, s59)) | (~xuntil28(s58)) | until27(s59)),
% 1.30/1.51 inference(modus_ponens,[status(thm)],[9627, 9626])).
% 1.30/1.51 tff(9629,plain,
% 1.30/1.51 ((~xuntil28(s58)) | until27(s59)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9628, 5102, 8839])).
% 1.30/1.51 tff(9630,plain,
% 1.30/1.51 (until27(s59)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9629, 9625])).
% 1.30/1.51 tff(9631,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s59) | node26(s59) | (~until27(s59)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s59) | node26(s59) | (~until27(s59)))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9632,plain,
% 1.30/1.51 ((node26(s59) | (~until27(s59)) | xuntil28(s59)) <=> (xuntil28(s59) | node26(s59) | (~until27(s59)))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9633,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s59) | (~until27(s59)) | xuntil28(s59))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s59) | node26(s59) | (~until27(s59))))),
% 1.30/1.51 inference(monotonicity,[status(thm)],[9632])).
% 1.30/1.51 tff(9634,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s59) | (~until27(s59)) | xuntil28(s59))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s59) | node26(s59) | (~until27(s59)))),
% 1.30/1.51 inference(transitivity,[status(thm)],[9633, 9631])).
% 1.30/1.51 tff(9635,plain,
% 1.30/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s59) | (~until27(s59)) | xuntil28(s59))),
% 1.30/1.51 inference(quant_inst,[status(thm)],[])).
% 1.30/1.51 tff(9636,plain,
% 1.30/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s59) | node26(s59) | (~until27(s59))),
% 1.30/1.51 inference(modus_ponens,[status(thm)],[9635, 9634])).
% 1.30/1.51 tff(9637,plain,
% 1.30/1.51 (xuntil28(s59)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9636, 8821, 9630, 8391])).
% 1.30/1.51 tff(9638,plain,
% 1.30/1.51 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s59, s60)) | (~xuntil28(s59)) | until27(s60))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s59, s60)) | (~xuntil28(s59)) | until27(s60))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9639,plain,
% 1.30/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s59, s60)) | (~xuntil28(s59)) | until27(s60))),
% 1.30/1.51 inference(quant_inst,[status(thm)],[])).
% 1.30/1.51 tff(9640,plain,
% 1.30/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s59, s60)) | (~xuntil28(s59)) | until27(s60)),
% 1.30/1.51 inference(modus_ponens,[status(thm)],[9639, 9638])).
% 1.30/1.51 tff(9641,plain,
% 1.30/1.51 ((~xuntil28(s59)) | until27(s60)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9640, 5177, 8839])).
% 1.30/1.51 tff(9642,plain,
% 1.30/1.51 (until27(s60)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9641, 9637])).
% 1.30/1.51 tff(9643,plain,
% 1.30/1.51 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s60) | (~node26(s60)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s60) | (~node26(s60)))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9644,plain,
% 1.30/1.51 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s60) | (~node26(s60)))),
% 1.30/1.51 inference(quant_inst,[status(thm)],[])).
% 1.30/1.51 tff(9645,plain,
% 1.30/1.51 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s60) | (~node26(s60))),
% 1.30/1.51 inference(modus_ponens,[status(thm)],[9644, 9643])).
% 1.30/1.51 tff(9646,plain,
% 1.30/1.51 (~node26(s60)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9645, 3949, 8382])).
% 1.30/1.51 tff(9647,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s60) | node26(s60) | (~until27(s60)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s60) | node26(s60) | (~until27(s60)))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9648,plain,
% 1.30/1.51 ((node26(s60) | (~until27(s60)) | xuntil28(s60)) <=> (xuntil28(s60) | node26(s60) | (~until27(s60)))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9649,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s60) | (~until27(s60)) | xuntil28(s60))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s60) | node26(s60) | (~until27(s60))))),
% 1.30/1.51 inference(monotonicity,[status(thm)],[9648])).
% 1.30/1.51 tff(9650,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s60) | (~until27(s60)) | xuntil28(s60))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s60) | node26(s60) | (~until27(s60)))),
% 1.30/1.51 inference(transitivity,[status(thm)],[9649, 9647])).
% 1.30/1.51 tff(9651,plain,
% 1.30/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s60) | (~until27(s60)) | xuntil28(s60))),
% 1.30/1.51 inference(quant_inst,[status(thm)],[])).
% 1.30/1.51 tff(9652,plain,
% 1.30/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s60) | node26(s60) | (~until27(s60))),
% 1.30/1.51 inference(modus_ponens,[status(thm)],[9651, 9650])).
% 1.30/1.51 tff(9653,plain,
% 1.30/1.51 (xuntil28(s60) | (~until27(s60))),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9652, 8821, 9646])).
% 1.30/1.51 tff(9654,plain,
% 1.30/1.51 (xuntil28(s60)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9653, 9642])).
% 1.30/1.51 tff(9655,plain,
% 1.30/1.51 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s60, s61)) | (~xuntil28(s60)) | until27(s61))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s60, s61)) | (~xuntil28(s60)) | until27(s61))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9656,plain,
% 1.30/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s60, s61)) | (~xuntil28(s60)) | until27(s61))),
% 1.30/1.51 inference(quant_inst,[status(thm)],[])).
% 1.30/1.51 tff(9657,plain,
% 1.30/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s60, s61)) | (~xuntil28(s60)) | until27(s61)),
% 1.30/1.51 inference(modus_ponens,[status(thm)],[9656, 9655])).
% 1.30/1.51 tff(9658,plain,
% 1.30/1.51 ((~xuntil28(s60)) | until27(s61)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9657, 5266, 8839])).
% 1.30/1.51 tff(9659,plain,
% 1.30/1.51 (until27(s61)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9658, 9654])).
% 1.30/1.51 tff(9660,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s61) | node26(s61) | (~until27(s61)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s61) | node26(s61) | (~until27(s61)))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9661,plain,
% 1.30/1.51 ((node26(s61) | (~until27(s61)) | xuntil28(s61)) <=> (xuntil28(s61) | node26(s61) | (~until27(s61)))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9662,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s61) | (~until27(s61)) | xuntil28(s61))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s61) | node26(s61) | (~until27(s61))))),
% 1.30/1.51 inference(monotonicity,[status(thm)],[9661])).
% 1.30/1.51 tff(9663,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s61) | (~until27(s61)) | xuntil28(s61))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s61) | node26(s61) | (~until27(s61)))),
% 1.30/1.51 inference(transitivity,[status(thm)],[9662, 9660])).
% 1.30/1.51 tff(9664,plain,
% 1.30/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s61) | (~until27(s61)) | xuntil28(s61))),
% 1.30/1.51 inference(quant_inst,[status(thm)],[])).
% 1.30/1.51 tff(9665,plain,
% 1.30/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s61) | node26(s61) | (~until27(s61))),
% 1.30/1.51 inference(modus_ponens,[status(thm)],[9664, 9663])).
% 1.30/1.51 tff(9666,plain,
% 1.30/1.51 (xuntil28(s61)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9665, 8821, 9659, 8375])).
% 1.30/1.51 tff(9667,plain,
% 1.30/1.51 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s61, s62)) | (~xuntil28(s61)) | until27(s62))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s61, s62)) | (~xuntil28(s61)) | until27(s62))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9668,plain,
% 1.30/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s61, s62)) | (~xuntil28(s61)) | until27(s62))),
% 1.30/1.51 inference(quant_inst,[status(thm)],[])).
% 1.30/1.51 tff(9669,plain,
% 1.30/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s61, s62)) | (~xuntil28(s61)) | until27(s62)),
% 1.30/1.51 inference(modus_ponens,[status(thm)],[9668, 9667])).
% 1.30/1.51 tff(9670,plain,
% 1.30/1.51 ((~xuntil28(s61)) | until27(s62)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9669, 5333, 8839])).
% 1.30/1.51 tff(9671,plain,
% 1.30/1.51 (until27(s62)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9670, 9666])).
% 1.30/1.51 tff(9672,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s62) | node26(s62) | (~until27(s62)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s62) | node26(s62) | (~until27(s62)))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9673,plain,
% 1.30/1.51 ((node26(s62) | (~until27(s62)) | xuntil28(s62)) <=> (xuntil28(s62) | node26(s62) | (~until27(s62)))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9674,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s62) | (~until27(s62)) | xuntil28(s62))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s62) | node26(s62) | (~until27(s62))))),
% 1.30/1.51 inference(monotonicity,[status(thm)],[9673])).
% 1.30/1.51 tff(9675,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s62) | (~until27(s62)) | xuntil28(s62))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s62) | node26(s62) | (~until27(s62)))),
% 1.30/1.51 inference(transitivity,[status(thm)],[9674, 9672])).
% 1.30/1.51 tff(9676,plain,
% 1.30/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s62) | (~until27(s62)) | xuntil28(s62))),
% 1.30/1.51 inference(quant_inst,[status(thm)],[])).
% 1.30/1.51 tff(9677,plain,
% 1.30/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s62) | node26(s62) | (~until27(s62))),
% 1.30/1.51 inference(modus_ponens,[status(thm)],[9676, 9675])).
% 1.30/1.51 tff(9678,plain,
% 1.30/1.51 (xuntil28(s62) | node26(s62)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9677, 8821, 9671])).
% 1.30/1.51 tff(9679,plain,
% 1.30/1.51 (xuntil28(s62)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9678, 8371])).
% 1.30/1.51 tff(9680,plain,
% 1.30/1.51 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s62, s63)) | (~xuntil28(s62)) | until27(s63))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s62, s63)) | (~xuntil28(s62)) | until27(s63))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9681,plain,
% 1.30/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s62, s63)) | (~xuntil28(s62)) | until27(s63))),
% 1.30/1.51 inference(quant_inst,[status(thm)],[])).
% 1.30/1.51 tff(9682,plain,
% 1.30/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s62, s63)) | (~xuntil28(s62)) | until27(s63)),
% 1.30/1.51 inference(modus_ponens,[status(thm)],[9681, 9680])).
% 1.30/1.51 tff(9683,plain,
% 1.30/1.51 ((~xuntil28(s62)) | until27(s63)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9682, 5432, 8839])).
% 1.30/1.51 tff(9684,plain,
% 1.30/1.51 (until27(s63)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9683, 9679])).
% 1.30/1.51 tff(9685,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s63) | node26(s63) | (~until27(s63)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s63) | node26(s63) | (~until27(s63)))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9686,plain,
% 1.30/1.51 ((node26(s63) | (~until27(s63)) | xuntil28(s63)) <=> (xuntil28(s63) | node26(s63) | (~until27(s63)))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9687,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s63) | (~until27(s63)) | xuntil28(s63))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s63) | node26(s63) | (~until27(s63))))),
% 1.30/1.51 inference(monotonicity,[status(thm)],[9686])).
% 1.30/1.51 tff(9688,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s63) | (~until27(s63)) | xuntil28(s63))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s63) | node26(s63) | (~until27(s63)))),
% 1.30/1.51 inference(transitivity,[status(thm)],[9687, 9685])).
% 1.30/1.51 tff(9689,plain,
% 1.30/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s63) | (~until27(s63)) | xuntil28(s63))),
% 1.30/1.51 inference(quant_inst,[status(thm)],[])).
% 1.30/1.51 tff(9690,plain,
% 1.30/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s63) | node26(s63) | (~until27(s63))),
% 1.30/1.51 inference(modus_ponens,[status(thm)],[9689, 9688])).
% 1.30/1.51 tff(9691,plain,
% 1.30/1.51 (xuntil28(s63)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9690, 8821, 9684, 8362])).
% 1.30/1.51 tff(9692,plain,
% 1.30/1.51 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s63, s64)) | (~xuntil28(s63)) | until27(s64))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s63, s64)) | (~xuntil28(s63)) | until27(s64))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9693,plain,
% 1.30/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s63, s64)) | (~xuntil28(s63)) | until27(s64))),
% 1.30/1.51 inference(quant_inst,[status(thm)],[])).
% 1.30/1.51 tff(9694,plain,
% 1.30/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s63, s64)) | (~xuntil28(s63)) | until27(s64)),
% 1.30/1.51 inference(modus_ponens,[status(thm)],[9693, 9692])).
% 1.30/1.51 tff(9695,plain,
% 1.30/1.51 ((~xuntil28(s63)) | until27(s64)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9694, 5510, 8839])).
% 1.30/1.51 tff(9696,plain,
% 1.30/1.51 (until27(s64)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9695, 9691])).
% 1.30/1.51 tff(9697,plain,
% 1.30/1.51 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s64) | (~node26(s64)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s64) | (~node26(s64)))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9698,plain,
% 1.30/1.51 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s64) | (~node26(s64)))),
% 1.30/1.51 inference(quant_inst,[status(thm)],[])).
% 1.30/1.51 tff(9699,plain,
% 1.30/1.51 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s64) | (~node26(s64))),
% 1.30/1.51 inference(modus_ponens,[status(thm)],[9698, 9697])).
% 1.30/1.51 tff(9700,plain,
% 1.30/1.51 (~node26(s64)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9699, 3949, 8353])).
% 1.30/1.51 tff(9701,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s64) | node26(s64) | (~until27(s64)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s64) | node26(s64) | (~until27(s64)))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9702,plain,
% 1.30/1.51 ((node26(s64) | (~until27(s64)) | xuntil28(s64)) <=> (xuntil28(s64) | node26(s64) | (~until27(s64)))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9703,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s64) | (~until27(s64)) | xuntil28(s64))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s64) | node26(s64) | (~until27(s64))))),
% 1.30/1.51 inference(monotonicity,[status(thm)],[9702])).
% 1.30/1.51 tff(9704,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s64) | (~until27(s64)) | xuntil28(s64))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s64) | node26(s64) | (~until27(s64)))),
% 1.30/1.51 inference(transitivity,[status(thm)],[9703, 9701])).
% 1.30/1.51 tff(9705,plain,
% 1.30/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s64) | (~until27(s64)) | xuntil28(s64))),
% 1.30/1.51 inference(quant_inst,[status(thm)],[])).
% 1.30/1.51 tff(9706,plain,
% 1.30/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s64) | node26(s64) | (~until27(s64))),
% 1.30/1.51 inference(modus_ponens,[status(thm)],[9705, 9704])).
% 1.30/1.51 tff(9707,plain,
% 1.30/1.51 (xuntil28(s64) | (~until27(s64))),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9706, 8821, 9700])).
% 1.30/1.51 tff(9708,plain,
% 1.30/1.51 (xuntil28(s64)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9707, 9696])).
% 1.30/1.51 tff(9709,plain,
% 1.30/1.51 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s64, s65)) | (~xuntil28(s64)) | until27(s65))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s64, s65)) | (~xuntil28(s64)) | until27(s65))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9710,plain,
% 1.30/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s64, s65)) | (~xuntil28(s64)) | until27(s65))),
% 1.30/1.51 inference(quant_inst,[status(thm)],[])).
% 1.30/1.51 tff(9711,plain,
% 1.30/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s64, s65)) | (~xuntil28(s64)) | until27(s65)),
% 1.30/1.51 inference(modus_ponens,[status(thm)],[9710, 9709])).
% 1.30/1.51 tff(9712,plain,
% 1.30/1.51 ((~xuntil28(s64)) | until27(s65)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9711, 5571, 8839])).
% 1.30/1.51 tff(9713,plain,
% 1.30/1.51 (until27(s65)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9712, 9708])).
% 1.30/1.51 tff(9714,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s65) | node26(s65) | (~until27(s65)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s65) | node26(s65) | (~until27(s65)))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9715,plain,
% 1.30/1.51 ((node26(s65) | (~until27(s65)) | xuntil28(s65)) <=> (xuntil28(s65) | node26(s65) | (~until27(s65)))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9716,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s65) | (~until27(s65)) | xuntil28(s65))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s65) | node26(s65) | (~until27(s65))))),
% 1.30/1.51 inference(monotonicity,[status(thm)],[9715])).
% 1.30/1.51 tff(9717,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s65) | (~until27(s65)) | xuntil28(s65))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s65) | node26(s65) | (~until27(s65)))),
% 1.30/1.51 inference(transitivity,[status(thm)],[9716, 9714])).
% 1.30/1.51 tff(9718,plain,
% 1.30/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s65) | (~until27(s65)) | xuntil28(s65))),
% 1.30/1.51 inference(quant_inst,[status(thm)],[])).
% 1.30/1.51 tff(9719,plain,
% 1.30/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s65) | node26(s65) | (~until27(s65))),
% 1.30/1.51 inference(modus_ponens,[status(thm)],[9718, 9717])).
% 1.30/1.51 tff(9720,plain,
% 1.30/1.51 (xuntil28(s65)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9719, 8821, 9713, 8346])).
% 1.30/1.51 tff(9721,plain,
% 1.30/1.51 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s65, s66)) | (~xuntil28(s65)) | until27(s66))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s65, s66)) | (~xuntil28(s65)) | until27(s66))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9722,plain,
% 1.30/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s65, s66)) | (~xuntil28(s65)) | until27(s66))),
% 1.30/1.51 inference(quant_inst,[status(thm)],[])).
% 1.30/1.51 tff(9723,plain,
% 1.30/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s65, s66)) | (~xuntil28(s65)) | until27(s66)),
% 1.30/1.51 inference(modus_ponens,[status(thm)],[9722, 9721])).
% 1.30/1.51 tff(9724,plain,
% 1.30/1.51 ((~xuntil28(s65)) | until27(s66)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9723, 5666, 8839])).
% 1.30/1.51 tff(9725,plain,
% 1.30/1.51 (until27(s66)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9724, 9720])).
% 1.30/1.51 tff(9726,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s66) | node26(s66) | (~until27(s66)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s66) | node26(s66) | (~until27(s66)))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9727,plain,
% 1.30/1.51 ((node26(s66) | (~until27(s66)) | xuntil28(s66)) <=> (xuntil28(s66) | node26(s66) | (~until27(s66)))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9728,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s66) | (~until27(s66)) | xuntil28(s66))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s66) | node26(s66) | (~until27(s66))))),
% 1.30/1.51 inference(monotonicity,[status(thm)],[9727])).
% 1.30/1.51 tff(9729,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s66) | (~until27(s66)) | xuntil28(s66))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s66) | node26(s66) | (~until27(s66)))),
% 1.30/1.51 inference(transitivity,[status(thm)],[9728, 9726])).
% 1.30/1.51 tff(9730,plain,
% 1.30/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s66) | (~until27(s66)) | xuntil28(s66))),
% 1.30/1.51 inference(quant_inst,[status(thm)],[])).
% 1.30/1.51 tff(9731,plain,
% 1.30/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s66) | node26(s66) | (~until27(s66))),
% 1.30/1.51 inference(modus_ponens,[status(thm)],[9730, 9729])).
% 1.30/1.51 tff(9732,plain,
% 1.30/1.51 (xuntil28(s66) | node26(s66)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9731, 8821, 9725])).
% 1.30/1.51 tff(9733,plain,
% 1.30/1.51 (xuntil28(s66)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9732, 8342])).
% 1.30/1.51 tff(9734,plain,
% 1.30/1.51 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s66, s67)) | (~xuntil28(s66)) | until27(s67))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s66, s67)) | (~xuntil28(s66)) | until27(s67))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9735,plain,
% 1.30/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s66, s67)) | (~xuntil28(s66)) | until27(s67))),
% 1.30/1.51 inference(quant_inst,[status(thm)],[])).
% 1.30/1.51 tff(9736,plain,
% 1.30/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s66, s67)) | (~xuntil28(s66)) | until27(s67)),
% 1.30/1.51 inference(modus_ponens,[status(thm)],[9735, 9734])).
% 1.30/1.51 tff(9737,plain,
% 1.30/1.51 ((~xuntil28(s66)) | until27(s67)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9736, 5730, 8839])).
% 1.30/1.51 tff(9738,plain,
% 1.30/1.51 (until27(s67)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9737, 9733])).
% 1.30/1.51 tff(9739,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s67) | node26(s67) | (~until27(s67)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s67) | node26(s67) | (~until27(s67)))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9740,plain,
% 1.30/1.51 ((node26(s67) | (~until27(s67)) | xuntil28(s67)) <=> (xuntil28(s67) | node26(s67) | (~until27(s67)))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9741,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s67) | (~until27(s67)) | xuntil28(s67))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s67) | node26(s67) | (~until27(s67))))),
% 1.30/1.51 inference(monotonicity,[status(thm)],[9740])).
% 1.30/1.51 tff(9742,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s67) | (~until27(s67)) | xuntil28(s67))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s67) | node26(s67) | (~until27(s67)))),
% 1.30/1.51 inference(transitivity,[status(thm)],[9741, 9739])).
% 1.30/1.51 tff(9743,plain,
% 1.30/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s67) | (~until27(s67)) | xuntil28(s67))),
% 1.30/1.51 inference(quant_inst,[status(thm)],[])).
% 1.30/1.51 tff(9744,plain,
% 1.30/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s67) | node26(s67) | (~until27(s67))),
% 1.30/1.51 inference(modus_ponens,[status(thm)],[9743, 9742])).
% 1.30/1.51 tff(9745,plain,
% 1.30/1.51 (xuntil28(s67)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9744, 8821, 9738, 8333])).
% 1.30/1.51 tff(9746,plain,
% 1.30/1.51 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s67, s68)) | (~xuntil28(s67)) | until27(s68))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s67, s68)) | (~xuntil28(s67)) | until27(s68))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9747,plain,
% 1.30/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s67, s68)) | (~xuntil28(s67)) | until27(s68))),
% 1.30/1.51 inference(quant_inst,[status(thm)],[])).
% 1.30/1.51 tff(9748,plain,
% 1.30/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s67, s68)) | (~xuntil28(s67)) | until27(s68)),
% 1.30/1.51 inference(modus_ponens,[status(thm)],[9747, 9746])).
% 1.30/1.51 tff(9749,plain,
% 1.30/1.51 ((~xuntil28(s67)) | until27(s68)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9748, 5805, 8839])).
% 1.30/1.51 tff(9750,plain,
% 1.30/1.51 (until27(s68)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9749, 9745])).
% 1.30/1.51 tff(9751,plain,
% 1.30/1.51 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s68) | (~node26(s68)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s68) | (~node26(s68)))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9752,plain,
% 1.30/1.51 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s68) | (~node26(s68)))),
% 1.30/1.51 inference(quant_inst,[status(thm)],[])).
% 1.30/1.51 tff(9753,plain,
% 1.30/1.51 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s68) | (~node26(s68))),
% 1.30/1.51 inference(modus_ponens,[status(thm)],[9752, 9751])).
% 1.30/1.51 tff(9754,plain,
% 1.30/1.51 (~node26(s68)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9753, 3949, 8324])).
% 1.30/1.51 tff(9755,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s68) | node26(s68) | (~until27(s68)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s68) | node26(s68) | (~until27(s68)))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9756,plain,
% 1.30/1.51 ((node26(s68) | (~until27(s68)) | xuntil28(s68)) <=> (xuntil28(s68) | node26(s68) | (~until27(s68)))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9757,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s68) | (~until27(s68)) | xuntil28(s68))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s68) | node26(s68) | (~until27(s68))))),
% 1.30/1.51 inference(monotonicity,[status(thm)],[9756])).
% 1.30/1.51 tff(9758,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s68) | (~until27(s68)) | xuntil28(s68))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s68) | node26(s68) | (~until27(s68)))),
% 1.30/1.51 inference(transitivity,[status(thm)],[9757, 9755])).
% 1.30/1.51 tff(9759,plain,
% 1.30/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s68) | (~until27(s68)) | xuntil28(s68))),
% 1.30/1.51 inference(quant_inst,[status(thm)],[])).
% 1.30/1.51 tff(9760,plain,
% 1.30/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s68) | node26(s68) | (~until27(s68))),
% 1.30/1.51 inference(modus_ponens,[status(thm)],[9759, 9758])).
% 1.30/1.51 tff(9761,plain,
% 1.30/1.51 (xuntil28(s68) | (~until27(s68))),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9760, 8821, 9754])).
% 1.30/1.51 tff(9762,plain,
% 1.30/1.51 (xuntil28(s68)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9761, 9750])).
% 1.30/1.51 tff(9763,plain,
% 1.30/1.51 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s68, s69)) | (~xuntil28(s68)) | until27(s69))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s68, s69)) | (~xuntil28(s68)) | until27(s69))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9764,plain,
% 1.30/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s68, s69)) | (~xuntil28(s68)) | until27(s69))),
% 1.30/1.51 inference(quant_inst,[status(thm)],[])).
% 1.30/1.51 tff(9765,plain,
% 1.30/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s68, s69)) | (~xuntil28(s68)) | until27(s69)),
% 1.30/1.51 inference(modus_ponens,[status(thm)],[9764, 9763])).
% 1.30/1.51 tff(9766,plain,
% 1.30/1.51 ((~xuntil28(s68)) | until27(s69)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9765, 5894, 8839])).
% 1.30/1.51 tff(9767,plain,
% 1.30/1.51 (until27(s69)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9766, 9762])).
% 1.30/1.51 tff(9768,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s69) | node26(s69) | (~until27(s69)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s69) | node26(s69) | (~until27(s69)))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9769,plain,
% 1.30/1.51 ((node26(s69) | (~until27(s69)) | xuntil28(s69)) <=> (xuntil28(s69) | node26(s69) | (~until27(s69)))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9770,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s69) | (~until27(s69)) | xuntil28(s69))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s69) | node26(s69) | (~until27(s69))))),
% 1.30/1.51 inference(monotonicity,[status(thm)],[9769])).
% 1.30/1.51 tff(9771,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s69) | (~until27(s69)) | xuntil28(s69))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s69) | node26(s69) | (~until27(s69)))),
% 1.30/1.51 inference(transitivity,[status(thm)],[9770, 9768])).
% 1.30/1.51 tff(9772,plain,
% 1.30/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s69) | (~until27(s69)) | xuntil28(s69))),
% 1.30/1.51 inference(quant_inst,[status(thm)],[])).
% 1.30/1.51 tff(9773,plain,
% 1.30/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s69) | node26(s69) | (~until27(s69))),
% 1.30/1.51 inference(modus_ponens,[status(thm)],[9772, 9771])).
% 1.30/1.51 tff(9774,plain,
% 1.30/1.51 (xuntil28(s69)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9773, 8821, 9767, 8317])).
% 1.30/1.51 tff(9775,plain,
% 1.30/1.51 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s69, s70)) | (~xuntil28(s69)) | until27(s70))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s69, s70)) | (~xuntil28(s69)) | until27(s70))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9776,plain,
% 1.30/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s69, s70)) | (~xuntil28(s69)) | until27(s70))),
% 1.30/1.51 inference(quant_inst,[status(thm)],[])).
% 1.30/1.51 tff(9777,plain,
% 1.30/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s69, s70)) | (~xuntil28(s69)) | until27(s70)),
% 1.30/1.51 inference(modus_ponens,[status(thm)],[9776, 9775])).
% 1.30/1.51 tff(9778,plain,
% 1.30/1.51 ((~xuntil28(s69)) | until27(s70)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9777, 5961, 8839])).
% 1.30/1.51 tff(9779,plain,
% 1.30/1.51 (until27(s70)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9778, 9774])).
% 1.30/1.51 tff(9780,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s70) | node26(s70) | (~until27(s70)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s70) | node26(s70) | (~until27(s70)))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9781,plain,
% 1.30/1.51 ((node26(s70) | (~until27(s70)) | xuntil28(s70)) <=> (xuntil28(s70) | node26(s70) | (~until27(s70)))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9782,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s70) | (~until27(s70)) | xuntil28(s70))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s70) | node26(s70) | (~until27(s70))))),
% 1.30/1.51 inference(monotonicity,[status(thm)],[9781])).
% 1.30/1.51 tff(9783,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s70) | (~until27(s70)) | xuntil28(s70))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s70) | node26(s70) | (~until27(s70)))),
% 1.30/1.51 inference(transitivity,[status(thm)],[9782, 9780])).
% 1.30/1.51 tff(9784,plain,
% 1.30/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s70) | (~until27(s70)) | xuntil28(s70))),
% 1.30/1.51 inference(quant_inst,[status(thm)],[])).
% 1.30/1.51 tff(9785,plain,
% 1.30/1.51 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s70) | node26(s70) | (~until27(s70))),
% 1.30/1.51 inference(modus_ponens,[status(thm)],[9784, 9783])).
% 1.30/1.51 tff(9786,plain,
% 1.30/1.51 (xuntil28(s70) | node26(s70)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9785, 8821, 9779])).
% 1.30/1.51 tff(9787,plain,
% 1.30/1.51 (xuntil28(s70)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9786, 8313])).
% 1.30/1.51 tff(9788,plain,
% 1.30/1.51 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s70, s71)) | (~xuntil28(s70)) | until27(s71))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s70, s71)) | (~xuntil28(s70)) | until27(s71))),
% 1.30/1.51 inference(rewrite,[status(thm)],[])).
% 1.30/1.51 tff(9789,plain,
% 1.30/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s70, s71)) | (~xuntil28(s70)) | until27(s71))),
% 1.30/1.51 inference(quant_inst,[status(thm)],[])).
% 1.30/1.51 tff(9790,plain,
% 1.30/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s70, s71)) | (~xuntil28(s70)) | until27(s71)),
% 1.30/1.51 inference(modus_ponens,[status(thm)],[9789, 9788])).
% 1.30/1.51 tff(9791,plain,
% 1.30/1.51 ((~xuntil28(s70)) | until27(s71)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9790, 6060, 8839])).
% 1.30/1.51 tff(9792,plain,
% 1.30/1.51 (until27(s71)),
% 1.30/1.51 inference(unit_resolution,[status(thm)],[9791, 9787])).
% 1.30/1.51 tff(9793,plain,
% 1.30/1.51 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s71) | node26(s71) | (~until27(s71)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s71) | node26(s71) | (~until27(s71)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9794,plain,
% 1.30/1.52 ((node26(s71) | (~until27(s71)) | xuntil28(s71)) <=> (xuntil28(s71) | node26(s71) | (~until27(s71)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9795,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s71) | (~until27(s71)) | xuntil28(s71))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s71) | node26(s71) | (~until27(s71))))),
% 1.30/1.52 inference(monotonicity,[status(thm)],[9794])).
% 1.30/1.52 tff(9796,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s71) | (~until27(s71)) | xuntil28(s71))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s71) | node26(s71) | (~until27(s71)))),
% 1.30/1.52 inference(transitivity,[status(thm)],[9795, 9793])).
% 1.30/1.52 tff(9797,plain,
% 1.30/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s71) | (~until27(s71)) | xuntil28(s71))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9798,plain,
% 1.30/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s71) | node26(s71) | (~until27(s71))),
% 1.30/1.52 inference(modus_ponens,[status(thm)],[9797, 9796])).
% 1.30/1.52 tff(9799,plain,
% 1.30/1.52 (xuntil28(s71)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9798, 8821, 9792, 8304])).
% 1.30/1.52 tff(9800,plain,
% 1.30/1.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s71, s72)) | (~xuntil28(s71)) | until27(s72))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s71, s72)) | (~xuntil28(s71)) | until27(s72))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9801,plain,
% 1.30/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s71, s72)) | (~xuntil28(s71)) | until27(s72))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9802,plain,
% 1.30/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s71, s72)) | (~xuntil28(s71)) | until27(s72)),
% 1.30/1.52 inference(modus_ponens,[status(thm)],[9801, 9800])).
% 1.30/1.52 tff(9803,plain,
% 1.30/1.52 ((~xuntil28(s71)) | until27(s72)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9802, 6138, 8839])).
% 1.30/1.52 tff(9804,plain,
% 1.30/1.52 (until27(s72)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9803, 9799])).
% 1.30/1.52 tff(9805,plain,
% 1.30/1.52 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s72) | (~node26(s72)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s72) | (~node26(s72)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9806,plain,
% 1.30/1.52 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s72) | (~node26(s72)))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9807,plain,
% 1.30/1.52 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s72) | (~node26(s72))),
% 1.30/1.52 inference(modus_ponens,[status(thm)],[9806, 9805])).
% 1.30/1.52 tff(9808,plain,
% 1.30/1.52 (~node26(s72)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9807, 3949, 8295])).
% 1.30/1.52 tff(9809,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s72) | node26(s72) | (~until27(s72)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s72) | node26(s72) | (~until27(s72)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9810,plain,
% 1.30/1.52 ((node26(s72) | (~until27(s72)) | xuntil28(s72)) <=> (xuntil28(s72) | node26(s72) | (~until27(s72)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9811,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s72) | (~until27(s72)) | xuntil28(s72))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s72) | node26(s72) | (~until27(s72))))),
% 1.30/1.52 inference(monotonicity,[status(thm)],[9810])).
% 1.30/1.52 tff(9812,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s72) | (~until27(s72)) | xuntil28(s72))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s72) | node26(s72) | (~until27(s72)))),
% 1.30/1.52 inference(transitivity,[status(thm)],[9811, 9809])).
% 1.30/1.52 tff(9813,plain,
% 1.30/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s72) | (~until27(s72)) | xuntil28(s72))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9814,plain,
% 1.30/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s72) | node26(s72) | (~until27(s72))),
% 1.30/1.52 inference(modus_ponens,[status(thm)],[9813, 9812])).
% 1.30/1.52 tff(9815,plain,
% 1.30/1.52 (xuntil28(s72) | (~until27(s72))),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9814, 8821, 9808])).
% 1.30/1.52 tff(9816,plain,
% 1.30/1.52 (xuntil28(s72)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9815, 9804])).
% 1.30/1.52 tff(9817,plain,
% 1.30/1.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s72, s73)) | (~xuntil28(s72)) | until27(s73))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s72, s73)) | (~xuntil28(s72)) | until27(s73))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9818,plain,
% 1.30/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s72, s73)) | (~xuntil28(s72)) | until27(s73))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9819,plain,
% 1.30/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s72, s73)) | (~xuntil28(s72)) | until27(s73)),
% 1.30/1.52 inference(modus_ponens,[status(thm)],[9818, 9817])).
% 1.30/1.52 tff(9820,plain,
% 1.30/1.52 ((~xuntil28(s72)) | until27(s73)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9819, 6199, 8839])).
% 1.30/1.52 tff(9821,plain,
% 1.30/1.52 (until27(s73)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9820, 9816])).
% 1.30/1.52 tff(9822,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s73) | node26(s73) | (~until27(s73)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s73) | node26(s73) | (~until27(s73)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9823,plain,
% 1.30/1.52 ((node26(s73) | (~until27(s73)) | xuntil28(s73)) <=> (xuntil28(s73) | node26(s73) | (~until27(s73)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9824,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s73) | (~until27(s73)) | xuntil28(s73))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s73) | node26(s73) | (~until27(s73))))),
% 1.30/1.52 inference(monotonicity,[status(thm)],[9823])).
% 1.30/1.52 tff(9825,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s73) | (~until27(s73)) | xuntil28(s73))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s73) | node26(s73) | (~until27(s73)))),
% 1.30/1.52 inference(transitivity,[status(thm)],[9824, 9822])).
% 1.30/1.52 tff(9826,plain,
% 1.30/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s73) | (~until27(s73)) | xuntil28(s73))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9827,plain,
% 1.30/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s73) | node26(s73) | (~until27(s73))),
% 1.30/1.52 inference(modus_ponens,[status(thm)],[9826, 9825])).
% 1.30/1.52 tff(9828,plain,
% 1.30/1.52 (xuntil28(s73)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9827, 8821, 9821, 8288])).
% 1.30/1.52 tff(9829,plain,
% 1.30/1.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s73, s74)) | (~xuntil28(s73)) | until27(s74))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s73, s74)) | (~xuntil28(s73)) | until27(s74))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9830,plain,
% 1.30/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s73, s74)) | (~xuntil28(s73)) | until27(s74))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9831,plain,
% 1.30/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s73, s74)) | (~xuntil28(s73)) | until27(s74)),
% 1.30/1.52 inference(modus_ponens,[status(thm)],[9830, 9829])).
% 1.30/1.52 tff(9832,plain,
% 1.30/1.52 ((~xuntil28(s73)) | until27(s74)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9831, 6294, 8839])).
% 1.30/1.52 tff(9833,plain,
% 1.30/1.52 (until27(s74)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9832, 9828])).
% 1.30/1.52 tff(9834,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s74) | node26(s74) | (~until27(s74)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s74) | node26(s74) | (~until27(s74)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9835,plain,
% 1.30/1.52 ((node26(s74) | (~until27(s74)) | xuntil28(s74)) <=> (xuntil28(s74) | node26(s74) | (~until27(s74)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9836,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s74) | (~until27(s74)) | xuntil28(s74))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s74) | node26(s74) | (~until27(s74))))),
% 1.30/1.52 inference(monotonicity,[status(thm)],[9835])).
% 1.30/1.52 tff(9837,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s74) | (~until27(s74)) | xuntil28(s74))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s74) | node26(s74) | (~until27(s74)))),
% 1.30/1.52 inference(transitivity,[status(thm)],[9836, 9834])).
% 1.30/1.52 tff(9838,plain,
% 1.30/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s74) | (~until27(s74)) | xuntil28(s74))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9839,plain,
% 1.30/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s74) | node26(s74) | (~until27(s74))),
% 1.30/1.52 inference(modus_ponens,[status(thm)],[9838, 9837])).
% 1.30/1.52 tff(9840,plain,
% 1.30/1.52 (xuntil28(s74) | node26(s74)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9839, 8821, 9833])).
% 1.30/1.52 tff(9841,plain,
% 1.30/1.52 (xuntil28(s74)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9840, 8284])).
% 1.30/1.52 tff(9842,plain,
% 1.30/1.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s74, s75)) | (~xuntil28(s74)) | until27(s75))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s74, s75)) | (~xuntil28(s74)) | until27(s75))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9843,plain,
% 1.30/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s74, s75)) | (~xuntil28(s74)) | until27(s75))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9844,plain,
% 1.30/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s74, s75)) | (~xuntil28(s74)) | until27(s75)),
% 1.30/1.52 inference(modus_ponens,[status(thm)],[9843, 9842])).
% 1.30/1.52 tff(9845,plain,
% 1.30/1.52 ((~xuntil28(s74)) | until27(s75)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9844, 6358, 8839])).
% 1.30/1.52 tff(9846,plain,
% 1.30/1.52 (until27(s75)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9845, 9841])).
% 1.30/1.52 tff(9847,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s75) | node26(s75) | (~until27(s75)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s75) | node26(s75) | (~until27(s75)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9848,plain,
% 1.30/1.52 ((node26(s75) | (~until27(s75)) | xuntil28(s75)) <=> (xuntil28(s75) | node26(s75) | (~until27(s75)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9849,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s75) | (~until27(s75)) | xuntil28(s75))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s75) | node26(s75) | (~until27(s75))))),
% 1.30/1.52 inference(monotonicity,[status(thm)],[9848])).
% 1.30/1.52 tff(9850,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s75) | (~until27(s75)) | xuntil28(s75))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s75) | node26(s75) | (~until27(s75)))),
% 1.30/1.52 inference(transitivity,[status(thm)],[9849, 9847])).
% 1.30/1.52 tff(9851,plain,
% 1.30/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s75) | (~until27(s75)) | xuntil28(s75))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9852,plain,
% 1.30/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s75) | node26(s75) | (~until27(s75))),
% 1.30/1.52 inference(modus_ponens,[status(thm)],[9851, 9850])).
% 1.30/1.52 tff(9853,plain,
% 1.30/1.52 (xuntil28(s75)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9852, 8821, 9846, 8275])).
% 1.30/1.52 tff(9854,plain,
% 1.30/1.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s75, s76)) | (~xuntil28(s75)) | until27(s76))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s75, s76)) | (~xuntil28(s75)) | until27(s76))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9855,plain,
% 1.30/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s75, s76)) | (~xuntil28(s75)) | until27(s76))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9856,plain,
% 1.30/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s75, s76)) | (~xuntil28(s75)) | until27(s76)),
% 1.30/1.52 inference(modus_ponens,[status(thm)],[9855, 9854])).
% 1.30/1.52 tff(9857,plain,
% 1.30/1.52 ((~xuntil28(s75)) | until27(s76)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9856, 6433, 8839])).
% 1.30/1.52 tff(9858,plain,
% 1.30/1.52 (until27(s76)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9857, 9853])).
% 1.30/1.52 tff(9859,plain,
% 1.30/1.52 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s76) | (~node26(s76)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s76) | (~node26(s76)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9860,plain,
% 1.30/1.52 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s76) | (~node26(s76)))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9861,plain,
% 1.30/1.52 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s76) | (~node26(s76))),
% 1.30/1.52 inference(modus_ponens,[status(thm)],[9860, 9859])).
% 1.30/1.52 tff(9862,plain,
% 1.30/1.52 (~node26(s76)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9861, 3949, 8266])).
% 1.30/1.52 tff(9863,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s76) | node26(s76) | (~until27(s76)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s76) | node26(s76) | (~until27(s76)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9864,plain,
% 1.30/1.52 ((node26(s76) | (~until27(s76)) | xuntil28(s76)) <=> (xuntil28(s76) | node26(s76) | (~until27(s76)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9865,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s76) | (~until27(s76)) | xuntil28(s76))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s76) | node26(s76) | (~until27(s76))))),
% 1.30/1.52 inference(monotonicity,[status(thm)],[9864])).
% 1.30/1.52 tff(9866,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s76) | (~until27(s76)) | xuntil28(s76))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s76) | node26(s76) | (~until27(s76)))),
% 1.30/1.52 inference(transitivity,[status(thm)],[9865, 9863])).
% 1.30/1.52 tff(9867,plain,
% 1.30/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s76) | (~until27(s76)) | xuntil28(s76))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9868,plain,
% 1.30/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s76) | node26(s76) | (~until27(s76))),
% 1.30/1.52 inference(modus_ponens,[status(thm)],[9867, 9866])).
% 1.30/1.52 tff(9869,plain,
% 1.30/1.52 (xuntil28(s76) | (~until27(s76))),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9868, 8821, 9862])).
% 1.30/1.52 tff(9870,plain,
% 1.30/1.52 (xuntil28(s76)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9869, 9858])).
% 1.30/1.52 tff(9871,plain,
% 1.30/1.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s76, s77)) | (~xuntil28(s76)) | until27(s77))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s76, s77)) | (~xuntil28(s76)) | until27(s77))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9872,plain,
% 1.30/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s76, s77)) | (~xuntil28(s76)) | until27(s77))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9873,plain,
% 1.30/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s76, s77)) | (~xuntil28(s76)) | until27(s77)),
% 1.30/1.52 inference(modus_ponens,[status(thm)],[9872, 9871])).
% 1.30/1.52 tff(9874,plain,
% 1.30/1.52 ((~xuntil28(s76)) | until27(s77)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9873, 6522, 8839])).
% 1.30/1.52 tff(9875,plain,
% 1.30/1.52 (until27(s77)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9874, 9870])).
% 1.30/1.52 tff(9876,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s77) | node26(s77) | (~until27(s77)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s77) | node26(s77) | (~until27(s77)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9877,plain,
% 1.30/1.52 ((node26(s77) | (~until27(s77)) | xuntil28(s77)) <=> (xuntil28(s77) | node26(s77) | (~until27(s77)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9878,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s77) | (~until27(s77)) | xuntil28(s77))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s77) | node26(s77) | (~until27(s77))))),
% 1.30/1.52 inference(monotonicity,[status(thm)],[9877])).
% 1.30/1.52 tff(9879,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s77) | (~until27(s77)) | xuntil28(s77))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s77) | node26(s77) | (~until27(s77)))),
% 1.30/1.52 inference(transitivity,[status(thm)],[9878, 9876])).
% 1.30/1.52 tff(9880,plain,
% 1.30/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s77) | (~until27(s77)) | xuntil28(s77))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9881,plain,
% 1.30/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s77) | node26(s77) | (~until27(s77))),
% 1.30/1.52 inference(modus_ponens,[status(thm)],[9880, 9879])).
% 1.30/1.52 tff(9882,plain,
% 1.30/1.52 (xuntil28(s77)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9881, 8821, 9875, 8259])).
% 1.30/1.52 tff(9883,plain,
% 1.30/1.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s77, s78)) | (~xuntil28(s77)) | until27(s78))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s77, s78)) | (~xuntil28(s77)) | until27(s78))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9884,plain,
% 1.30/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s77, s78)) | (~xuntil28(s77)) | until27(s78))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9885,plain,
% 1.30/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s77, s78)) | (~xuntil28(s77)) | until27(s78)),
% 1.30/1.52 inference(modus_ponens,[status(thm)],[9884, 9883])).
% 1.30/1.52 tff(9886,plain,
% 1.30/1.52 ((~xuntil28(s77)) | until27(s78)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9885, 6589, 8839])).
% 1.30/1.52 tff(9887,plain,
% 1.30/1.52 (until27(s78)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9886, 9882])).
% 1.30/1.52 tff(9888,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s78) | node26(s78) | (~until27(s78)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s78) | node26(s78) | (~until27(s78)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9889,plain,
% 1.30/1.52 ((node26(s78) | (~until27(s78)) | xuntil28(s78)) <=> (xuntil28(s78) | node26(s78) | (~until27(s78)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9890,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s78) | (~until27(s78)) | xuntil28(s78))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s78) | node26(s78) | (~until27(s78))))),
% 1.30/1.52 inference(monotonicity,[status(thm)],[9889])).
% 1.30/1.52 tff(9891,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s78) | (~until27(s78)) | xuntil28(s78))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s78) | node26(s78) | (~until27(s78)))),
% 1.30/1.52 inference(transitivity,[status(thm)],[9890, 9888])).
% 1.30/1.52 tff(9892,plain,
% 1.30/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s78) | (~until27(s78)) | xuntil28(s78))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9893,plain,
% 1.30/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s78) | node26(s78) | (~until27(s78))),
% 1.30/1.52 inference(modus_ponens,[status(thm)],[9892, 9891])).
% 1.30/1.52 tff(9894,plain,
% 1.30/1.52 (xuntil28(s78) | node26(s78)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9893, 8821, 9887])).
% 1.30/1.52 tff(9895,plain,
% 1.30/1.52 (xuntil28(s78)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9894, 8255])).
% 1.30/1.52 tff(9896,plain,
% 1.30/1.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s78, s79)) | (~xuntil28(s78)) | until27(s79))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s78, s79)) | (~xuntil28(s78)) | until27(s79))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9897,plain,
% 1.30/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s78, s79)) | (~xuntil28(s78)) | until27(s79))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9898,plain,
% 1.30/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s78, s79)) | (~xuntil28(s78)) | until27(s79)),
% 1.30/1.52 inference(modus_ponens,[status(thm)],[9897, 9896])).
% 1.30/1.52 tff(9899,plain,
% 1.30/1.52 ((~xuntil28(s78)) | until27(s79)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9898, 6688, 8839])).
% 1.30/1.52 tff(9900,plain,
% 1.30/1.52 (until27(s79)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9899, 9895])).
% 1.30/1.52 tff(9901,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s79) | node26(s79) | (~until27(s79)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s79) | node26(s79) | (~until27(s79)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9902,plain,
% 1.30/1.52 ((node26(s79) | (~until27(s79)) | xuntil28(s79)) <=> (xuntil28(s79) | node26(s79) | (~until27(s79)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9903,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s79) | (~until27(s79)) | xuntil28(s79))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s79) | node26(s79) | (~until27(s79))))),
% 1.30/1.52 inference(monotonicity,[status(thm)],[9902])).
% 1.30/1.52 tff(9904,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s79) | (~until27(s79)) | xuntil28(s79))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s79) | node26(s79) | (~until27(s79)))),
% 1.30/1.52 inference(transitivity,[status(thm)],[9903, 9901])).
% 1.30/1.52 tff(9905,plain,
% 1.30/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s79) | (~until27(s79)) | xuntil28(s79))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9906,plain,
% 1.30/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s79) | node26(s79) | (~until27(s79))),
% 1.30/1.52 inference(modus_ponens,[status(thm)],[9905, 9904])).
% 1.30/1.52 tff(9907,plain,
% 1.30/1.52 (xuntil28(s79)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9906, 8821, 9900, 8246])).
% 1.30/1.52 tff(9908,plain,
% 1.30/1.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s79, s80)) | (~xuntil28(s79)) | until27(s80))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s79, s80)) | (~xuntil28(s79)) | until27(s80))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9909,plain,
% 1.30/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s79, s80)) | (~xuntil28(s79)) | until27(s80))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9910,plain,
% 1.30/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s79, s80)) | (~xuntil28(s79)) | until27(s80)),
% 1.30/1.52 inference(modus_ponens,[status(thm)],[9909, 9908])).
% 1.30/1.52 tff(9911,plain,
% 1.30/1.52 ((~xuntil28(s79)) | until27(s80)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9910, 6766, 8839])).
% 1.30/1.52 tff(9912,plain,
% 1.30/1.52 (until27(s80)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9911, 9907])).
% 1.30/1.52 tff(9913,plain,
% 1.30/1.52 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s80) | (~node26(s80)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s80) | (~node26(s80)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9914,plain,
% 1.30/1.52 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s80) | (~node26(s80)))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9915,plain,
% 1.30/1.52 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s80) | (~node26(s80))),
% 1.30/1.52 inference(modus_ponens,[status(thm)],[9914, 9913])).
% 1.30/1.52 tff(9916,plain,
% 1.30/1.52 (~node26(s80)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9915, 3949, 8237])).
% 1.30/1.52 tff(9917,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s80) | node26(s80) | (~until27(s80)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s80) | node26(s80) | (~until27(s80)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9918,plain,
% 1.30/1.52 ((node26(s80) | (~until27(s80)) | xuntil28(s80)) <=> (xuntil28(s80) | node26(s80) | (~until27(s80)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9919,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s80) | (~until27(s80)) | xuntil28(s80))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s80) | node26(s80) | (~until27(s80))))),
% 1.30/1.52 inference(monotonicity,[status(thm)],[9918])).
% 1.30/1.52 tff(9920,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s80) | (~until27(s80)) | xuntil28(s80))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s80) | node26(s80) | (~until27(s80)))),
% 1.30/1.52 inference(transitivity,[status(thm)],[9919, 9917])).
% 1.30/1.52 tff(9921,plain,
% 1.30/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s80) | (~until27(s80)) | xuntil28(s80))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9922,plain,
% 1.30/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s80) | node26(s80) | (~until27(s80))),
% 1.30/1.52 inference(modus_ponens,[status(thm)],[9921, 9920])).
% 1.30/1.52 tff(9923,plain,
% 1.30/1.52 (xuntil28(s80) | (~until27(s80))),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9922, 8821, 9916])).
% 1.30/1.52 tff(9924,plain,
% 1.30/1.52 (xuntil28(s80)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9923, 9912])).
% 1.30/1.52 tff(9925,plain,
% 1.30/1.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s80, s81)) | (~xuntil28(s80)) | until27(s81))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s80, s81)) | (~xuntil28(s80)) | until27(s81))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9926,plain,
% 1.30/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s80, s81)) | (~xuntil28(s80)) | until27(s81))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9927,plain,
% 1.30/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s80, s81)) | (~xuntil28(s80)) | until27(s81)),
% 1.30/1.52 inference(modus_ponens,[status(thm)],[9926, 9925])).
% 1.30/1.52 tff(9928,plain,
% 1.30/1.52 ((~xuntil28(s80)) | until27(s81)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9927, 6827, 8839])).
% 1.30/1.52 tff(9929,plain,
% 1.30/1.52 (until27(s81)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9928, 9924])).
% 1.30/1.52 tff(9930,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s81) | node26(s81) | (~until27(s81)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s81) | node26(s81) | (~until27(s81)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9931,plain,
% 1.30/1.52 ((node26(s81) | (~until27(s81)) | xuntil28(s81)) <=> (xuntil28(s81) | node26(s81) | (~until27(s81)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9932,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s81) | (~until27(s81)) | xuntil28(s81))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s81) | node26(s81) | (~until27(s81))))),
% 1.30/1.52 inference(monotonicity,[status(thm)],[9931])).
% 1.30/1.52 tff(9933,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s81) | (~until27(s81)) | xuntil28(s81))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s81) | node26(s81) | (~until27(s81)))),
% 1.30/1.52 inference(transitivity,[status(thm)],[9932, 9930])).
% 1.30/1.52 tff(9934,plain,
% 1.30/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s81) | (~until27(s81)) | xuntil28(s81))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9935,plain,
% 1.30/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s81) | node26(s81) | (~until27(s81))),
% 1.30/1.52 inference(modus_ponens,[status(thm)],[9934, 9933])).
% 1.30/1.52 tff(9936,plain,
% 1.30/1.52 (xuntil28(s81)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9935, 8821, 9929, 8230])).
% 1.30/1.52 tff(9937,plain,
% 1.30/1.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s81, s82)) | (~xuntil28(s81)) | until27(s82))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s81, s82)) | (~xuntil28(s81)) | until27(s82))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9938,plain,
% 1.30/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s81, s82)) | (~xuntil28(s81)) | until27(s82))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9939,plain,
% 1.30/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s81, s82)) | (~xuntil28(s81)) | until27(s82)),
% 1.30/1.52 inference(modus_ponens,[status(thm)],[9938, 9937])).
% 1.30/1.52 tff(9940,plain,
% 1.30/1.52 ((~xuntil28(s81)) | until27(s82)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9939, 6922, 8839])).
% 1.30/1.52 tff(9941,plain,
% 1.30/1.52 (until27(s82)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9940, 9936])).
% 1.30/1.52 tff(9942,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s82) | node26(s82) | (~until27(s82)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s82) | node26(s82) | (~until27(s82)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9943,plain,
% 1.30/1.52 ((node26(s82) | (~until27(s82)) | xuntil28(s82)) <=> (xuntil28(s82) | node26(s82) | (~until27(s82)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9944,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s82) | (~until27(s82)) | xuntil28(s82))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s82) | node26(s82) | (~until27(s82))))),
% 1.30/1.52 inference(monotonicity,[status(thm)],[9943])).
% 1.30/1.52 tff(9945,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s82) | (~until27(s82)) | xuntil28(s82))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s82) | node26(s82) | (~until27(s82)))),
% 1.30/1.52 inference(transitivity,[status(thm)],[9944, 9942])).
% 1.30/1.52 tff(9946,plain,
% 1.30/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s82) | (~until27(s82)) | xuntil28(s82))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9947,plain,
% 1.30/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s82) | node26(s82) | (~until27(s82))),
% 1.30/1.52 inference(modus_ponens,[status(thm)],[9946, 9945])).
% 1.30/1.52 tff(9948,plain,
% 1.30/1.52 (xuntil28(s82) | node26(s82)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9947, 8821, 9941])).
% 1.30/1.52 tff(9949,plain,
% 1.30/1.52 (xuntil28(s82)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9948, 8226])).
% 1.30/1.52 tff(9950,plain,
% 1.30/1.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s82, s83)) | (~xuntil28(s82)) | until27(s83))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s82, s83)) | (~xuntil28(s82)) | until27(s83))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9951,plain,
% 1.30/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s82, s83)) | (~xuntil28(s82)) | until27(s83))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9952,plain,
% 1.30/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s82, s83)) | (~xuntil28(s82)) | until27(s83)),
% 1.30/1.52 inference(modus_ponens,[status(thm)],[9951, 9950])).
% 1.30/1.52 tff(9953,plain,
% 1.30/1.52 ((~xuntil28(s82)) | until27(s83)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9952, 6986, 8839])).
% 1.30/1.52 tff(9954,plain,
% 1.30/1.52 (until27(s83)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9953, 9949])).
% 1.30/1.52 tff(9955,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s83) | node26(s83) | (~until27(s83)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s83) | node26(s83) | (~until27(s83)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9956,plain,
% 1.30/1.52 ((node26(s83) | (~until27(s83)) | xuntil28(s83)) <=> (xuntil28(s83) | node26(s83) | (~until27(s83)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9957,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s83) | (~until27(s83)) | xuntil28(s83))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s83) | node26(s83) | (~until27(s83))))),
% 1.30/1.52 inference(monotonicity,[status(thm)],[9956])).
% 1.30/1.52 tff(9958,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s83) | (~until27(s83)) | xuntil28(s83))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s83) | node26(s83) | (~until27(s83)))),
% 1.30/1.52 inference(transitivity,[status(thm)],[9957, 9955])).
% 1.30/1.52 tff(9959,plain,
% 1.30/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s83) | (~until27(s83)) | xuntil28(s83))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9960,plain,
% 1.30/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s83) | node26(s83) | (~until27(s83))),
% 1.30/1.52 inference(modus_ponens,[status(thm)],[9959, 9958])).
% 1.30/1.52 tff(9961,plain,
% 1.30/1.52 (xuntil28(s83)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9960, 8821, 9954, 8217])).
% 1.30/1.52 tff(9962,plain,
% 1.30/1.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s83, s84)) | (~xuntil28(s83)) | until27(s84))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s83, s84)) | (~xuntil28(s83)) | until27(s84))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9963,plain,
% 1.30/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s83, s84)) | (~xuntil28(s83)) | until27(s84))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9964,plain,
% 1.30/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s83, s84)) | (~xuntil28(s83)) | until27(s84)),
% 1.30/1.52 inference(modus_ponens,[status(thm)],[9963, 9962])).
% 1.30/1.52 tff(9965,plain,
% 1.30/1.52 ((~xuntil28(s83)) | until27(s84)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9964, 7061, 8839])).
% 1.30/1.52 tff(9966,plain,
% 1.30/1.52 (until27(s84)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9965, 9961])).
% 1.30/1.52 tff(9967,plain,
% 1.30/1.52 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s84) | (~node26(s84)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s84) | (~node26(s84)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9968,plain,
% 1.30/1.52 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s84) | (~node26(s84)))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9969,plain,
% 1.30/1.52 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s84) | (~node26(s84))),
% 1.30/1.52 inference(modus_ponens,[status(thm)],[9968, 9967])).
% 1.30/1.52 tff(9970,plain,
% 1.30/1.52 (~node26(s84)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9969, 3949, 8208])).
% 1.30/1.52 tff(9971,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s84) | node26(s84) | (~until27(s84)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s84) | node26(s84) | (~until27(s84)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9972,plain,
% 1.30/1.52 ((node26(s84) | (~until27(s84)) | xuntil28(s84)) <=> (xuntil28(s84) | node26(s84) | (~until27(s84)))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9973,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s84) | (~until27(s84)) | xuntil28(s84))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s84) | node26(s84) | (~until27(s84))))),
% 1.30/1.52 inference(monotonicity,[status(thm)],[9972])).
% 1.30/1.52 tff(9974,plain,
% 1.30/1.52 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s84) | (~until27(s84)) | xuntil28(s84))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s84) | node26(s84) | (~until27(s84)))),
% 1.30/1.52 inference(transitivity,[status(thm)],[9973, 9971])).
% 1.30/1.52 tff(9975,plain,
% 1.30/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s84) | (~until27(s84)) | xuntil28(s84))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9976,plain,
% 1.30/1.52 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s84) | node26(s84) | (~until27(s84))),
% 1.30/1.52 inference(modus_ponens,[status(thm)],[9975, 9974])).
% 1.30/1.52 tff(9977,plain,
% 1.30/1.52 (xuntil28(s84) | (~until27(s84))),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9976, 8821, 9970])).
% 1.30/1.52 tff(9978,plain,
% 1.30/1.52 (xuntil28(s84)),
% 1.30/1.52 inference(unit_resolution,[status(thm)],[9977, 9966])).
% 1.30/1.52 tff(9979,plain,
% 1.30/1.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s84, s85)) | (~xuntil28(s84)) | until27(s85))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s84, s85)) | (~xuntil28(s84)) | until27(s85))),
% 1.30/1.52 inference(rewrite,[status(thm)],[])).
% 1.30/1.52 tff(9980,plain,
% 1.30/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s84, s85)) | (~xuntil28(s84)) | until27(s85))),
% 1.30/1.52 inference(quant_inst,[status(thm)],[])).
% 1.30/1.52 tff(9981,plain,
% 1.30/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s84, s85)) | (~xuntil28(s84)) | until27(s85)),
% 1.30/1.53 inference(modus_ponens,[status(thm)],[9980, 9979])).
% 1.30/1.53 tff(9982,plain,
% 1.30/1.53 ((~xuntil28(s84)) | until27(s85)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[9981, 7150, 8839])).
% 1.30/1.53 tff(9983,plain,
% 1.30/1.53 (until27(s85)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[9982, 9978])).
% 1.30/1.53 tff(9984,plain,
% 1.30/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s85) | node26(s85) | (~until27(s85)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s85) | node26(s85) | (~until27(s85)))),
% 1.30/1.53 inference(rewrite,[status(thm)],[])).
% 1.30/1.53 tff(9985,plain,
% 1.30/1.53 ((node26(s85) | (~until27(s85)) | xuntil28(s85)) <=> (xuntil28(s85) | node26(s85) | (~until27(s85)))),
% 1.30/1.53 inference(rewrite,[status(thm)],[])).
% 1.30/1.53 tff(9986,plain,
% 1.30/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s85) | (~until27(s85)) | xuntil28(s85))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s85) | node26(s85) | (~until27(s85))))),
% 1.30/1.53 inference(monotonicity,[status(thm)],[9985])).
% 1.30/1.53 tff(9987,plain,
% 1.30/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s85) | (~until27(s85)) | xuntil28(s85))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s85) | node26(s85) | (~until27(s85)))),
% 1.30/1.53 inference(transitivity,[status(thm)],[9986, 9984])).
% 1.30/1.53 tff(9988,plain,
% 1.30/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s85) | (~until27(s85)) | xuntil28(s85))),
% 1.30/1.53 inference(quant_inst,[status(thm)],[])).
% 1.30/1.53 tff(9989,plain,
% 1.30/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s85) | node26(s85) | (~until27(s85))),
% 1.30/1.53 inference(modus_ponens,[status(thm)],[9988, 9987])).
% 1.30/1.53 tff(9990,plain,
% 1.30/1.53 (xuntil28(s85)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[9989, 8821, 9983, 8201])).
% 1.30/1.53 tff(9991,plain,
% 1.30/1.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s85, s86)) | (~xuntil28(s85)) | until27(s86))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s85, s86)) | (~xuntil28(s85)) | until27(s86))),
% 1.30/1.53 inference(rewrite,[status(thm)],[])).
% 1.30/1.53 tff(9992,plain,
% 1.30/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s85, s86)) | (~xuntil28(s85)) | until27(s86))),
% 1.30/1.53 inference(quant_inst,[status(thm)],[])).
% 1.30/1.53 tff(9993,plain,
% 1.30/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s85, s86)) | (~xuntil28(s85)) | until27(s86)),
% 1.30/1.53 inference(modus_ponens,[status(thm)],[9992, 9991])).
% 1.30/1.53 tff(9994,plain,
% 1.30/1.53 ((~xuntil28(s85)) | until27(s86)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[9993, 7217, 8839])).
% 1.30/1.53 tff(9995,plain,
% 1.30/1.53 (until27(s86)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[9994, 9990])).
% 1.30/1.53 tff(9996,plain,
% 1.30/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s86) | node26(s86) | (~until27(s86)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s86) | node26(s86) | (~until27(s86)))),
% 1.30/1.53 inference(rewrite,[status(thm)],[])).
% 1.30/1.53 tff(9997,plain,
% 1.30/1.53 ((node26(s86) | (~until27(s86)) | xuntil28(s86)) <=> (xuntil28(s86) | node26(s86) | (~until27(s86)))),
% 1.30/1.53 inference(rewrite,[status(thm)],[])).
% 1.30/1.53 tff(9998,plain,
% 1.30/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s86) | (~until27(s86)) | xuntil28(s86))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s86) | node26(s86) | (~until27(s86))))),
% 1.30/1.53 inference(monotonicity,[status(thm)],[9997])).
% 1.30/1.53 tff(9999,plain,
% 1.30/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s86) | (~until27(s86)) | xuntil28(s86))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s86) | node26(s86) | (~until27(s86)))),
% 1.30/1.53 inference(transitivity,[status(thm)],[9998, 9996])).
% 1.30/1.53 tff(10000,plain,
% 1.30/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s86) | (~until27(s86)) | xuntil28(s86))),
% 1.30/1.53 inference(quant_inst,[status(thm)],[])).
% 1.30/1.53 tff(10001,plain,
% 1.30/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s86) | node26(s86) | (~until27(s86))),
% 1.30/1.53 inference(modus_ponens,[status(thm)],[10000, 9999])).
% 1.30/1.53 tff(10002,plain,
% 1.30/1.53 (xuntil28(s86) | node26(s86)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[10001, 8821, 9995])).
% 1.30/1.53 tff(10003,plain,
% 1.30/1.53 (xuntil28(s86)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[10002, 8197])).
% 1.30/1.53 tff(10004,plain,
% 1.30/1.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s86, s87)) | (~xuntil28(s86)) | until27(s87))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s86, s87)) | (~xuntil28(s86)) | until27(s87))),
% 1.30/1.53 inference(rewrite,[status(thm)],[])).
% 1.30/1.53 tff(10005,plain,
% 1.30/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s86, s87)) | (~xuntil28(s86)) | until27(s87))),
% 1.30/1.53 inference(quant_inst,[status(thm)],[])).
% 1.30/1.53 tff(10006,plain,
% 1.30/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s86, s87)) | (~xuntil28(s86)) | until27(s87)),
% 1.30/1.53 inference(modus_ponens,[status(thm)],[10005, 10004])).
% 1.30/1.53 tff(10007,plain,
% 1.30/1.53 ((~xuntil28(s86)) | until27(s87)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[10006, 7316, 8839])).
% 1.30/1.53 tff(10008,plain,
% 1.30/1.53 (until27(s87)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[10007, 10003])).
% 1.30/1.53 tff(10009,plain,
% 1.30/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s87) | node26(s87) | (~until27(s87)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s87) | node26(s87) | (~until27(s87)))),
% 1.30/1.53 inference(rewrite,[status(thm)],[])).
% 1.30/1.53 tff(10010,plain,
% 1.30/1.53 ((node26(s87) | (~until27(s87)) | xuntil28(s87)) <=> (xuntil28(s87) | node26(s87) | (~until27(s87)))),
% 1.30/1.53 inference(rewrite,[status(thm)],[])).
% 1.30/1.53 tff(10011,plain,
% 1.30/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s87) | (~until27(s87)) | xuntil28(s87))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s87) | node26(s87) | (~until27(s87))))),
% 1.30/1.53 inference(monotonicity,[status(thm)],[10010])).
% 1.30/1.53 tff(10012,plain,
% 1.30/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s87) | (~until27(s87)) | xuntil28(s87))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s87) | node26(s87) | (~until27(s87)))),
% 1.30/1.53 inference(transitivity,[status(thm)],[10011, 10009])).
% 1.30/1.53 tff(10013,plain,
% 1.30/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s87) | (~until27(s87)) | xuntil28(s87))),
% 1.30/1.53 inference(quant_inst,[status(thm)],[])).
% 1.30/1.53 tff(10014,plain,
% 1.30/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s87) | node26(s87) | (~until27(s87))),
% 1.30/1.53 inference(modus_ponens,[status(thm)],[10013, 10012])).
% 1.30/1.53 tff(10015,plain,
% 1.30/1.53 (xuntil28(s87)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[10014, 8821, 10008, 8188])).
% 1.30/1.53 tff(10016,plain,
% 1.30/1.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s87, s88)) | (~xuntil28(s87)) | until27(s88))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s87, s88)) | (~xuntil28(s87)) | until27(s88))),
% 1.30/1.53 inference(rewrite,[status(thm)],[])).
% 1.30/1.53 tff(10017,plain,
% 1.30/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s87, s88)) | (~xuntil28(s87)) | until27(s88))),
% 1.30/1.53 inference(quant_inst,[status(thm)],[])).
% 1.30/1.53 tff(10018,plain,
% 1.30/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s87, s88)) | (~xuntil28(s87)) | until27(s88)),
% 1.30/1.53 inference(modus_ponens,[status(thm)],[10017, 10016])).
% 1.30/1.53 tff(10019,plain,
% 1.30/1.53 ((~xuntil28(s87)) | until27(s88)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[10018, 7394, 8839])).
% 1.30/1.53 tff(10020,plain,
% 1.30/1.53 (until27(s88)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[10019, 10015])).
% 1.30/1.53 tff(10021,plain,
% 1.30/1.53 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s88) | (~node26(s88)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s88) | (~node26(s88)))),
% 1.30/1.53 inference(rewrite,[status(thm)],[])).
% 1.30/1.53 tff(10022,plain,
% 1.30/1.53 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s88) | (~node26(s88)))),
% 1.30/1.53 inference(quant_inst,[status(thm)],[])).
% 1.30/1.53 tff(10023,plain,
% 1.30/1.53 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s88) | (~node26(s88))),
% 1.30/1.53 inference(modus_ponens,[status(thm)],[10022, 10021])).
% 1.30/1.53 tff(10024,plain,
% 1.30/1.53 (~node26(s88)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[10023, 3949, 8179])).
% 1.30/1.53 tff(10025,plain,
% 1.30/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s88) | node26(s88) | (~until27(s88)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s88) | node26(s88) | (~until27(s88)))),
% 1.30/1.53 inference(rewrite,[status(thm)],[])).
% 1.30/1.53 tff(10026,plain,
% 1.30/1.53 ((node26(s88) | (~until27(s88)) | xuntil28(s88)) <=> (xuntil28(s88) | node26(s88) | (~until27(s88)))),
% 1.30/1.53 inference(rewrite,[status(thm)],[])).
% 1.30/1.53 tff(10027,plain,
% 1.30/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s88) | (~until27(s88)) | xuntil28(s88))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s88) | node26(s88) | (~until27(s88))))),
% 1.30/1.53 inference(monotonicity,[status(thm)],[10026])).
% 1.30/1.53 tff(10028,plain,
% 1.30/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s88) | (~until27(s88)) | xuntil28(s88))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s88) | node26(s88) | (~until27(s88)))),
% 1.30/1.53 inference(transitivity,[status(thm)],[10027, 10025])).
% 1.30/1.53 tff(10029,plain,
% 1.30/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s88) | (~until27(s88)) | xuntil28(s88))),
% 1.30/1.53 inference(quant_inst,[status(thm)],[])).
% 1.30/1.53 tff(10030,plain,
% 1.30/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s88) | node26(s88) | (~until27(s88))),
% 1.30/1.53 inference(modus_ponens,[status(thm)],[10029, 10028])).
% 1.30/1.53 tff(10031,plain,
% 1.30/1.53 (xuntil28(s88) | (~until27(s88))),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[10030, 8821, 10024])).
% 1.30/1.53 tff(10032,plain,
% 1.30/1.53 (xuntil28(s88)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[10031, 10020])).
% 1.30/1.53 tff(10033,plain,
% 1.30/1.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s88, s89)) | (~xuntil28(s88)) | until27(s89))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s88, s89)) | (~xuntil28(s88)) | until27(s89))),
% 1.30/1.53 inference(rewrite,[status(thm)],[])).
% 1.30/1.53 tff(10034,plain,
% 1.30/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s88, s89)) | (~xuntil28(s88)) | until27(s89))),
% 1.30/1.53 inference(quant_inst,[status(thm)],[])).
% 1.30/1.53 tff(10035,plain,
% 1.30/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s88, s89)) | (~xuntil28(s88)) | until27(s89)),
% 1.30/1.53 inference(modus_ponens,[status(thm)],[10034, 10033])).
% 1.30/1.53 tff(10036,plain,
% 1.30/1.53 ((~xuntil28(s88)) | until27(s89)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[10035, 7455, 8839])).
% 1.30/1.53 tff(10037,plain,
% 1.30/1.53 (until27(s89)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[10036, 10032])).
% 1.30/1.53 tff(10038,plain,
% 1.30/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s89) | node26(s89) | (~until27(s89)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s89) | node26(s89) | (~until27(s89)))),
% 1.30/1.53 inference(rewrite,[status(thm)],[])).
% 1.30/1.53 tff(10039,plain,
% 1.30/1.53 ((node26(s89) | (~until27(s89)) | xuntil28(s89)) <=> (xuntil28(s89) | node26(s89) | (~until27(s89)))),
% 1.30/1.53 inference(rewrite,[status(thm)],[])).
% 1.30/1.53 tff(10040,plain,
% 1.30/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s89) | (~until27(s89)) | xuntil28(s89))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s89) | node26(s89) | (~until27(s89))))),
% 1.30/1.53 inference(monotonicity,[status(thm)],[10039])).
% 1.30/1.53 tff(10041,plain,
% 1.30/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s89) | (~until27(s89)) | xuntil28(s89))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s89) | node26(s89) | (~until27(s89)))),
% 1.30/1.53 inference(transitivity,[status(thm)],[10040, 10038])).
% 1.30/1.53 tff(10042,plain,
% 1.30/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s89) | (~until27(s89)) | xuntil28(s89))),
% 1.30/1.53 inference(quant_inst,[status(thm)],[])).
% 1.30/1.53 tff(10043,plain,
% 1.30/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s89) | node26(s89) | (~until27(s89))),
% 1.30/1.53 inference(modus_ponens,[status(thm)],[10042, 10041])).
% 1.30/1.53 tff(10044,plain,
% 1.30/1.53 (xuntil28(s89)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[10043, 8821, 10037, 8172])).
% 1.30/1.53 tff(10045,plain,
% 1.30/1.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s89, s90)) | (~xuntil28(s89)) | until27(s90))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s89, s90)) | (~xuntil28(s89)) | until27(s90))),
% 1.30/1.53 inference(rewrite,[status(thm)],[])).
% 1.30/1.53 tff(10046,plain,
% 1.30/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s89, s90)) | (~xuntil28(s89)) | until27(s90))),
% 1.30/1.53 inference(quant_inst,[status(thm)],[])).
% 1.30/1.53 tff(10047,plain,
% 1.30/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s89, s90)) | (~xuntil28(s89)) | until27(s90)),
% 1.30/1.53 inference(modus_ponens,[status(thm)],[10046, 10045])).
% 1.30/1.53 tff(10048,plain,
% 1.30/1.53 ((~xuntil28(s89)) | until27(s90)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[10047, 7550, 8839])).
% 1.30/1.53 tff(10049,plain,
% 1.30/1.53 (until27(s90)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[10048, 10044])).
% 1.30/1.53 tff(10050,plain,
% 1.30/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s90) | node26(s90) | (~until27(s90)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s90) | node26(s90) | (~until27(s90)))),
% 1.30/1.53 inference(rewrite,[status(thm)],[])).
% 1.30/1.53 tff(10051,plain,
% 1.30/1.53 ((node26(s90) | (~until27(s90)) | xuntil28(s90)) <=> (xuntil28(s90) | node26(s90) | (~until27(s90)))),
% 1.30/1.53 inference(rewrite,[status(thm)],[])).
% 1.30/1.53 tff(10052,plain,
% 1.30/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s90) | (~until27(s90)) | xuntil28(s90))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s90) | node26(s90) | (~until27(s90))))),
% 1.30/1.53 inference(monotonicity,[status(thm)],[10051])).
% 1.30/1.53 tff(10053,plain,
% 1.30/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s90) | (~until27(s90)) | xuntil28(s90))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s90) | node26(s90) | (~until27(s90)))),
% 1.30/1.53 inference(transitivity,[status(thm)],[10052, 10050])).
% 1.30/1.53 tff(10054,plain,
% 1.30/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s90) | (~until27(s90)) | xuntil28(s90))),
% 1.30/1.53 inference(quant_inst,[status(thm)],[])).
% 1.30/1.53 tff(10055,plain,
% 1.30/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s90) | node26(s90) | (~until27(s90))),
% 1.30/1.53 inference(modus_ponens,[status(thm)],[10054, 10053])).
% 1.30/1.53 tff(10056,plain,
% 1.30/1.53 (xuntil28(s90) | node26(s90)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[10055, 8821, 10049])).
% 1.30/1.53 tff(10057,plain,
% 1.30/1.53 (xuntil28(s90)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[10056, 8168])).
% 1.30/1.53 tff(10058,plain,
% 1.30/1.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s90, s91)) | (~xuntil28(s90)) | until27(s91))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s90, s91)) | (~xuntil28(s90)) | until27(s91))),
% 1.30/1.53 inference(rewrite,[status(thm)],[])).
% 1.30/1.53 tff(10059,plain,
% 1.30/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s90, s91)) | (~xuntil28(s90)) | until27(s91))),
% 1.30/1.53 inference(quant_inst,[status(thm)],[])).
% 1.30/1.53 tff(10060,plain,
% 1.30/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s90, s91)) | (~xuntil28(s90)) | until27(s91)),
% 1.30/1.53 inference(modus_ponens,[status(thm)],[10059, 10058])).
% 1.30/1.53 tff(10061,plain,
% 1.30/1.53 ((~xuntil28(s90)) | until27(s91)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[10060, 7614, 8839])).
% 1.30/1.53 tff(10062,plain,
% 1.30/1.53 (until27(s91)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[10061, 10057])).
% 1.30/1.53 tff(10063,plain,
% 1.30/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s91) | node26(s91) | (~until27(s91)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s91) | node26(s91) | (~until27(s91)))),
% 1.30/1.53 inference(rewrite,[status(thm)],[])).
% 1.30/1.53 tff(10064,plain,
% 1.30/1.53 ((node26(s91) | (~until27(s91)) | xuntil28(s91)) <=> (xuntil28(s91) | node26(s91) | (~until27(s91)))),
% 1.30/1.53 inference(rewrite,[status(thm)],[])).
% 1.30/1.53 tff(10065,plain,
% 1.30/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s91) | (~until27(s91)) | xuntil28(s91))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s91) | node26(s91) | (~until27(s91))))),
% 1.30/1.53 inference(monotonicity,[status(thm)],[10064])).
% 1.30/1.53 tff(10066,plain,
% 1.30/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s91) | (~until27(s91)) | xuntil28(s91))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s91) | node26(s91) | (~until27(s91)))),
% 1.30/1.53 inference(transitivity,[status(thm)],[10065, 10063])).
% 1.30/1.53 tff(10067,plain,
% 1.30/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s91) | (~until27(s91)) | xuntil28(s91))),
% 1.30/1.53 inference(quant_inst,[status(thm)],[])).
% 1.30/1.53 tff(10068,plain,
% 1.30/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s91) | node26(s91) | (~until27(s91))),
% 1.30/1.53 inference(modus_ponens,[status(thm)],[10067, 10066])).
% 1.30/1.53 tff(10069,plain,
% 1.30/1.53 (xuntil28(s91)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[10068, 8821, 10062, 8159])).
% 1.30/1.53 tff(10070,plain,
% 1.30/1.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s91, s92)) | (~xuntil28(s91)) | until27(s92))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s91, s92)) | (~xuntil28(s91)) | until27(s92))),
% 1.30/1.53 inference(rewrite,[status(thm)],[])).
% 1.30/1.53 tff(10071,plain,
% 1.30/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s91, s92)) | (~xuntil28(s91)) | until27(s92))),
% 1.30/1.53 inference(quant_inst,[status(thm)],[])).
% 1.30/1.53 tff(10072,plain,
% 1.30/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s91, s92)) | (~xuntil28(s91)) | until27(s92)),
% 1.30/1.53 inference(modus_ponens,[status(thm)],[10071, 10070])).
% 1.30/1.53 tff(10073,plain,
% 1.30/1.53 ((~xuntil28(s91)) | until27(s92)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[10072, 7689, 8839])).
% 1.30/1.53 tff(10074,plain,
% 1.30/1.53 (until27(s92)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[10073, 10069])).
% 1.30/1.53 tff(10075,plain,
% 1.30/1.53 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s92) | (~node26(s92)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s92) | (~node26(s92)))),
% 1.30/1.53 inference(rewrite,[status(thm)],[])).
% 1.30/1.53 tff(10076,plain,
% 1.30/1.53 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s92) | (~node26(s92)))),
% 1.30/1.53 inference(quant_inst,[status(thm)],[])).
% 1.30/1.53 tff(10077,plain,
% 1.30/1.53 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s92) | (~node26(s92))),
% 1.30/1.53 inference(modus_ponens,[status(thm)],[10076, 10075])).
% 1.30/1.53 tff(10078,plain,
% 1.30/1.53 (~node26(s92)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[10077, 3949, 8150])).
% 1.30/1.53 tff(10079,plain,
% 1.30/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s92) | node26(s92) | (~until27(s92)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s92) | node26(s92) | (~until27(s92)))),
% 1.30/1.53 inference(rewrite,[status(thm)],[])).
% 1.30/1.53 tff(10080,plain,
% 1.30/1.53 ((node26(s92) | (~until27(s92)) | xuntil28(s92)) <=> (xuntil28(s92) | node26(s92) | (~until27(s92)))),
% 1.30/1.53 inference(rewrite,[status(thm)],[])).
% 1.30/1.53 tff(10081,plain,
% 1.30/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s92) | (~until27(s92)) | xuntil28(s92))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s92) | node26(s92) | (~until27(s92))))),
% 1.30/1.53 inference(monotonicity,[status(thm)],[10080])).
% 1.30/1.53 tff(10082,plain,
% 1.30/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s92) | (~until27(s92)) | xuntil28(s92))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s92) | node26(s92) | (~until27(s92)))),
% 1.30/1.53 inference(transitivity,[status(thm)],[10081, 10079])).
% 1.30/1.53 tff(10083,plain,
% 1.30/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s92) | (~until27(s92)) | xuntil28(s92))),
% 1.30/1.53 inference(quant_inst,[status(thm)],[])).
% 1.30/1.53 tff(10084,plain,
% 1.30/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s92) | node26(s92) | (~until27(s92))),
% 1.30/1.53 inference(modus_ponens,[status(thm)],[10083, 10082])).
% 1.30/1.53 tff(10085,plain,
% 1.30/1.53 (xuntil28(s92) | (~until27(s92))),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[10084, 8821, 10078])).
% 1.30/1.53 tff(10086,plain,
% 1.30/1.53 (xuntil28(s92)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[10085, 10074])).
% 1.30/1.53 tff(10087,plain,
% 1.30/1.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s92, s93)) | (~xuntil28(s92)) | until27(s93))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s92, s93)) | (~xuntil28(s92)) | until27(s93))),
% 1.30/1.53 inference(rewrite,[status(thm)],[])).
% 1.30/1.53 tff(10088,plain,
% 1.30/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s92, s93)) | (~xuntil28(s92)) | until27(s93))),
% 1.30/1.53 inference(quant_inst,[status(thm)],[])).
% 1.30/1.53 tff(10089,plain,
% 1.30/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s92, s93)) | (~xuntil28(s92)) | until27(s93)),
% 1.30/1.53 inference(modus_ponens,[status(thm)],[10088, 10087])).
% 1.30/1.53 tff(10090,plain,
% 1.30/1.53 ((~xuntil28(s92)) | until27(s93)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[10089, 7778, 8839])).
% 1.30/1.53 tff(10091,plain,
% 1.30/1.53 (until27(s93)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[10090, 10086])).
% 1.30/1.53 tff(10092,plain,
% 1.30/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s93) | node26(s93) | (~until27(s93)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s93) | node26(s93) | (~until27(s93)))),
% 1.30/1.53 inference(rewrite,[status(thm)],[])).
% 1.30/1.53 tff(10093,plain,
% 1.30/1.53 ((node26(s93) | (~until27(s93)) | xuntil28(s93)) <=> (xuntil28(s93) | node26(s93) | (~until27(s93)))),
% 1.30/1.53 inference(rewrite,[status(thm)],[])).
% 1.30/1.53 tff(10094,plain,
% 1.30/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s93) | (~until27(s93)) | xuntil28(s93))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s93) | node26(s93) | (~until27(s93))))),
% 1.30/1.53 inference(monotonicity,[status(thm)],[10093])).
% 1.30/1.53 tff(10095,plain,
% 1.30/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s93) | (~until27(s93)) | xuntil28(s93))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s93) | node26(s93) | (~until27(s93)))),
% 1.30/1.53 inference(transitivity,[status(thm)],[10094, 10092])).
% 1.30/1.53 tff(10096,plain,
% 1.30/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s93) | (~until27(s93)) | xuntil28(s93))),
% 1.30/1.53 inference(quant_inst,[status(thm)],[])).
% 1.30/1.53 tff(10097,plain,
% 1.30/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s93) | node26(s93) | (~until27(s93))),
% 1.30/1.53 inference(modus_ponens,[status(thm)],[10096, 10095])).
% 1.30/1.53 tff(10098,plain,
% 1.30/1.53 (xuntil28(s93)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[10097, 8821, 10091, 8143])).
% 1.30/1.53 tff(10099,plain,
% 1.30/1.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s93, s94)) | (~xuntil28(s93)) | until27(s94))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s93, s94)) | (~xuntil28(s93)) | until27(s94))),
% 1.30/1.53 inference(rewrite,[status(thm)],[])).
% 1.30/1.53 tff(10100,plain,
% 1.30/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s93, s94)) | (~xuntil28(s93)) | until27(s94))),
% 1.30/1.53 inference(quant_inst,[status(thm)],[])).
% 1.30/1.53 tff(10101,plain,
% 1.30/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s93, s94)) | (~xuntil28(s93)) | until27(s94)),
% 1.30/1.53 inference(modus_ponens,[status(thm)],[10100, 10099])).
% 1.30/1.53 tff(10102,plain,
% 1.30/1.53 ((~xuntil28(s93)) | until27(s94)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[10101, 7845, 8839])).
% 1.30/1.53 tff(10103,plain,
% 1.30/1.53 (until27(s94)),
% 1.30/1.53 inference(unit_resolution,[status(thm)],[10102, 10098])).
% 1.30/1.53 tff(10104,plain,
% 1.30/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s94) | node26(s94) | (~until27(s94)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s94) | node26(s94) | (~until27(s94)))),
% 1.30/1.53 inference(rewrite,[status(thm)],[])).
% 1.30/1.53 tff(10105,plain,
% 1.30/1.53 ((node26(s94) | (~until27(s94)) | xuntil28(s94)) <=> (xuntil28(s94) | node26(s94) | (~until27(s94)))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(10106,plain,
% 1.37/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s94) | (~until27(s94)) | xuntil28(s94))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s94) | node26(s94) | (~until27(s94))))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[10105])).
% 1.37/1.53 tff(10107,plain,
% 1.37/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s94) | (~until27(s94)) | xuntil28(s94))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s94) | node26(s94) | (~until27(s94)))),
% 1.37/1.53 inference(transitivity,[status(thm)],[10106, 10104])).
% 1.37/1.53 tff(10108,plain,
% 1.37/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s94) | (~until27(s94)) | xuntil28(s94))),
% 1.37/1.53 inference(quant_inst,[status(thm)],[])).
% 1.37/1.53 tff(10109,plain,
% 1.37/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s94) | node26(s94) | (~until27(s94))),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[10108, 10107])).
% 1.37/1.53 tff(10110,plain,
% 1.37/1.53 (xuntil28(s94) | node26(s94)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[10109, 8821, 10103])).
% 1.37/1.53 tff(10111,plain,
% 1.37/1.53 (xuntil28(s94)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[10110, 8139])).
% 1.37/1.53 tff(10112,plain,
% 1.37/1.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s94, s95)) | (~xuntil28(s94)) | until27(s95))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s94, s95)) | (~xuntil28(s94)) | until27(s95))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(10113,plain,
% 1.37/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s94, s95)) | (~xuntil28(s94)) | until27(s95))),
% 1.37/1.53 inference(quant_inst,[status(thm)],[])).
% 1.37/1.53 tff(10114,plain,
% 1.37/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s94, s95)) | (~xuntil28(s94)) | until27(s95)),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[10113, 10112])).
% 1.37/1.53 tff(10115,plain,
% 1.37/1.53 ((~xuntil28(s94)) | until27(s95)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[10114, 7944, 8839])).
% 1.37/1.53 tff(10116,plain,
% 1.37/1.53 (until27(s95)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[10115, 10111])).
% 1.37/1.53 tff(10117,plain,
% 1.37/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s95) | node26(s95) | (~until27(s95)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s95) | node26(s95) | (~until27(s95)))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(10118,plain,
% 1.37/1.53 ((node26(s95) | (~until27(s95)) | xuntil28(s95)) <=> (xuntil28(s95) | node26(s95) | (~until27(s95)))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(10119,plain,
% 1.37/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s95) | (~until27(s95)) | xuntil28(s95))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s95) | node26(s95) | (~until27(s95))))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[10118])).
% 1.37/1.53 tff(10120,plain,
% 1.37/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s95) | (~until27(s95)) | xuntil28(s95))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s95) | node26(s95) | (~until27(s95)))),
% 1.37/1.53 inference(transitivity,[status(thm)],[10119, 10117])).
% 1.37/1.53 tff(10121,plain,
% 1.37/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s95) | (~until27(s95)) | xuntil28(s95))),
% 1.37/1.53 inference(quant_inst,[status(thm)],[])).
% 1.37/1.53 tff(10122,plain,
% 1.37/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s95) | node26(s95) | (~until27(s95))),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[10121, 10120])).
% 1.37/1.53 tff(10123,plain,
% 1.37/1.53 (xuntil28(s95)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[10122, 8821, 10116, 8130])).
% 1.37/1.53 tff(10124,plain,
% 1.37/1.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s95, s96)) | (~xuntil28(s95)) | until27(s96))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s95, s96)) | (~xuntil28(s95)) | until27(s96))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(10125,plain,
% 1.37/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s95, s96)) | (~xuntil28(s95)) | until27(s96))),
% 1.37/1.53 inference(quant_inst,[status(thm)],[])).
% 1.37/1.53 tff(10126,plain,
% 1.37/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s95, s96)) | (~xuntil28(s95)) | until27(s96)),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[10125, 10124])).
% 1.37/1.53 tff(10127,plain,
% 1.37/1.53 ((~xuntil28(s95)) | until27(s96)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[10126, 8022, 8839])).
% 1.37/1.53 tff(10128,plain,
% 1.37/1.53 (until27(s96)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[10127, 10123])).
% 1.37/1.53 tff(10129,plain,
% 1.37/1.53 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s96) | (~node26(s96)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s96) | (~node26(s96)))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(10130,plain,
% 1.37/1.53 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s96) | (~node26(s96)))),
% 1.37/1.53 inference(quant_inst,[status(thm)],[])).
% 1.37/1.53 tff(10131,plain,
% 1.37/1.53 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s96) | (~node26(s96))),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[10130, 10129])).
% 1.37/1.53 tff(10132,plain,
% 1.37/1.53 (~node26(s96)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[10131, 3949, 8121])).
% 1.37/1.53 tff(10133,plain,
% 1.37/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s96) | node26(s96) | (~until27(s96)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s96) | node26(s96) | (~until27(s96)))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(10134,plain,
% 1.37/1.53 ((node26(s96) | (~until27(s96)) | xuntil28(s96)) <=> (xuntil28(s96) | node26(s96) | (~until27(s96)))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(10135,plain,
% 1.37/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s96) | (~until27(s96)) | xuntil28(s96))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s96) | node26(s96) | (~until27(s96))))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[10134])).
% 1.37/1.53 tff(10136,plain,
% 1.37/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s96) | (~until27(s96)) | xuntil28(s96))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s96) | node26(s96) | (~until27(s96)))),
% 1.37/1.53 inference(transitivity,[status(thm)],[10135, 10133])).
% 1.37/1.53 tff(10137,plain,
% 1.37/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s96) | (~until27(s96)) | xuntil28(s96))),
% 1.37/1.53 inference(quant_inst,[status(thm)],[])).
% 1.37/1.53 tff(10138,plain,
% 1.37/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s96) | node26(s96) | (~until27(s96))),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[10137, 10136])).
% 1.37/1.53 tff(10139,plain,
% 1.37/1.53 (xuntil28(s96) | (~until27(s96))),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[10138, 8821, 10132])).
% 1.37/1.53 tff(10140,plain,
% 1.37/1.53 (xuntil28(s96)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[10139, 10128])).
% 1.37/1.53 tff(10141,plain,
% 1.37/1.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s96, s97)) | (~xuntil28(s96)) | until27(s97))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s96, s97)) | (~xuntil28(s96)) | until27(s97))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(10142,plain,
% 1.37/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s96, s97)) | (~xuntil28(s96)) | until27(s97))),
% 1.37/1.53 inference(quant_inst,[status(thm)],[])).
% 1.37/1.53 tff(10143,plain,
% 1.37/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s96, s97)) | (~xuntil28(s96)) | until27(s97)),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[10142, 10141])).
% 1.37/1.53 tff(10144,plain,
% 1.37/1.53 ((~xuntil28(s96)) | until27(s97)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[10143, 8083, 8839])).
% 1.37/1.53 tff(10145,plain,
% 1.37/1.53 (until27(s97)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[10144, 10140])).
% 1.37/1.53 tff(10146,plain,
% 1.37/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s97) | node26(s97) | (~until27(s97)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s97) | node26(s97) | (~until27(s97)))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(10147,plain,
% 1.37/1.53 ((node26(s97) | (~until27(s97)) | xuntil28(s97)) <=> (xuntil28(s97) | node26(s97) | (~until27(s97)))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(10148,plain,
% 1.37/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s97) | (~until27(s97)) | xuntil28(s97))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s97) | node26(s97) | (~until27(s97))))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[10147])).
% 1.37/1.53 tff(10149,plain,
% 1.37/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s97) | (~until27(s97)) | xuntil28(s97))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s97) | node26(s97) | (~until27(s97)))),
% 1.37/1.53 inference(transitivity,[status(thm)],[10148, 10146])).
% 1.37/1.53 tff(10150,plain,
% 1.37/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s97) | (~until27(s97)) | xuntil28(s97))),
% 1.37/1.53 inference(quant_inst,[status(thm)],[])).
% 1.37/1.53 tff(10151,plain,
% 1.37/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s97) | node26(s97) | (~until27(s97))),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[10150, 10149])).
% 1.37/1.53 tff(10152,plain,
% 1.37/1.53 (xuntil28(s97)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[10151, 8821, 10145, 8114])).
% 1.37/1.53 tff(10153,plain,
% 1.37/1.53 (succ(s97, s98) <=> succ(s97, s98)),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(10154,axiom,(succ(s97, s98)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound98')).
% 1.37/1.53 tff(10155,plain,
% 1.37/1.53 (succ(s97, s98)),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[10154, 10153])).
% 1.37/1.53 tff(10156,plain,
% 1.37/1.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s97, s98)) | (~xuntil28(s97)) | until27(s98))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s97, s98)) | (~xuntil28(s97)) | until27(s98))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(10157,plain,
% 1.37/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s97, s98)) | (~xuntil28(s97)) | until27(s98))),
% 1.37/1.53 inference(quant_inst,[status(thm)],[])).
% 1.37/1.53 tff(10158,plain,
% 1.37/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s97, s98)) | (~xuntil28(s97)) | until27(s98)),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[10157, 10156])).
% 1.37/1.53 tff(10159,plain,
% 1.37/1.53 ((~xuntil28(s97)) | until27(s98)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[10158, 10155, 8839])).
% 1.37/1.53 tff(10160,plain,
% 1.37/1.53 (until27(s98)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[10159, 10152])).
% 1.37/1.53 tff(10161,plain,
% 1.37/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s98) | node26(s98) | (~until27(s98)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s98) | node26(s98) | (~until27(s98)))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(10162,plain,
% 1.37/1.53 ((node26(s98) | (~until27(s98)) | xuntil28(s98)) <=> (xuntil28(s98) | node26(s98) | (~until27(s98)))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(10163,plain,
% 1.37/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s98) | (~until27(s98)) | xuntil28(s98))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s98) | node26(s98) | (~until27(s98))))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[10162])).
% 1.37/1.53 tff(10164,plain,
% 1.37/1.53 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s98) | (~until27(s98)) | xuntil28(s98))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s98) | node26(s98) | (~until27(s98)))),
% 1.37/1.53 inference(transitivity,[status(thm)],[10163, 10161])).
% 1.37/1.53 tff(10165,plain,
% 1.37/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s98) | (~until27(s98)) | xuntil28(s98))),
% 1.37/1.53 inference(quant_inst,[status(thm)],[])).
% 1.37/1.53 tff(10166,plain,
% 1.37/1.53 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s98) | node26(s98) | (~until27(s98))),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[10165, 10164])).
% 1.37/1.53 tff(10167,plain,
% 1.37/1.53 (xuntil28(s98) | node26(s98)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[10166, 8821, 10160])).
% 1.37/1.53 tff(10168,plain,
% 1.37/1.53 (xuntil28(s98)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[10167, 3953])).
% 1.37/1.53 tff(10169,plain,
% 1.37/1.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s98, s99)) | (~xuntil28(s98)) | until27(s99))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s98, s99)) | (~xuntil28(s98)) | until27(s99))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10170,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s98, s99)) | (~xuntil28(s98)) | until27(s99))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10171,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s98, s99)) | (~xuntil28(s98)) | until27(s99)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10170, 10169])).
% 1.37/1.54 tff(10172,plain,
% 1.37/1.54 ((~xuntil28(s98)) | until27(s99)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10171, 3920, 8839])).
% 1.37/1.54 tff(10173,plain,
% 1.37/1.54 (until27(s99)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10172, 10168])).
% 1.37/1.54 tff(10174,plain,
% 1.37/1.54 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s99) | node26(s99) | (~until27(s99)))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s99) | node26(s99) | (~until27(s99)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10175,plain,
% 1.37/1.54 ((node26(s99) | (~until27(s99)) | xuntil28(s99)) <=> (xuntil28(s99) | node26(s99) | (~until27(s99)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10176,plain,
% 1.37/1.54 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s99) | (~until27(s99)) | xuntil28(s99))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (xuntil28(s99) | node26(s99) | (~until27(s99))))),
% 1.37/1.54 inference(monotonicity,[status(thm)],[10175])).
% 1.37/1.54 tff(10177,plain,
% 1.37/1.54 (((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s99) | (~until27(s99)) | xuntil28(s99))) <=> ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s99) | node26(s99) | (~until27(s99)))),
% 1.37/1.54 inference(transitivity,[status(thm)],[10176, 10174])).
% 1.37/1.54 tff(10178,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | (node26(s99) | (~until27(s99)) | xuntil28(s99))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10179,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | (~until27(X)) | xuntil28(X))) | xuntil28(s99) | node26(s99) | (~until27(s99))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10178, 10177])).
% 1.37/1.54 tff(10180,plain,
% 1.37/1.54 (node26(s99)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10179, 8821, 10173, 3917])).
% 1.37/1.54 tff(10181,plain,
% 1.37/1.54 (((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s99) | (~node26(s99)))) <=> ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s99) | (~node26(s99)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10182,plain,
% 1.37/1.54 ((~![X: $i] : (always25(X) | (~node26(X)))) | (always25(s99) | (~node26(s99)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10183,plain,
% 1.37/1.54 ((~![X: $i] : (always25(X) | (~node26(X)))) | always25(s99) | (~node26(s99))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10182, 10181])).
% 1.37/1.54 tff(10184,plain,
% 1.37/1.54 ($false),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10183, 3949, 3916, 10180])).
% 1.37/1.54 tff(10185,plain,(always25(s99) | xuntil28(s99)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.54 tff(10186,plain,
% 1.37/1.54 (xuntil28(s99)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10185, 3916])).
% 1.37/1.54 tff(10187,assumption,(node26(s99)), introduced(assumption)).
% 1.37/1.54 tff(10188,plain,
% 1.37/1.54 ($false),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10183, 3949, 3916, 10187])).
% 1.37/1.54 tff(10189,plain,((~node26(s99)) | always25(s99)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.54 tff(10190,plain,
% 1.37/1.54 (~node26(s99)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10189, 3916])).
% 1.37/1.54 tff(10191,plain,
% 1.37/1.54 (^[X: $i] : refl(((~last(X)) | (~xuntil2p30(X))) <=> ((~last(X)) | (~xuntil2p30(X))))),
% 1.37/1.54 inference(bind,[status(th)],[])).
% 1.37/1.54 tff(10192,plain,
% 1.37/1.54 (![X: $i] : ((~last(X)) | (~xuntil2p30(X))) <=> ![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 1.37/1.54 inference(quant_intro,[status(thm)],[10191])).
% 1.37/1.54 tff(10193,plain,
% 1.37/1.54 (![X: $i] : ((~last(X)) | (~xuntil2p30(X))) <=> ![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10194,axiom,(![X: $i] : ((~last(X)) | (~xuntil2p30(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty25')).
% 1.37/1.54 tff(10195,plain,
% 1.37/1.54 (![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10194, 10193])).
% 1.37/1.54 tff(10196,plain,(
% 1.37/1.54 ![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 1.37/1.54 inference(skolemize,[status(sab)],[10195])).
% 1.37/1.54 tff(10197,plain,
% 1.37/1.54 (![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10196, 10192])).
% 1.37/1.54 tff(10198,plain,
% 1.37/1.54 (last(s99) <=> last(s99)),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10199,axiom,(last(s99)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound100')).
% 1.37/1.54 tff(10200,plain,
% 1.37/1.54 (last(s99)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10199, 10198])).
% 1.37/1.54 tff(10201,plain,
% 1.37/1.54 (((~![X: $i] : ((~last(X)) | (~xuntil2p30(X)))) | ((~last(s99)) | (~xuntil2p30(s99)))) <=> ((~![X: $i] : ((~last(X)) | (~xuntil2p30(X)))) | (~last(s99)) | (~xuntil2p30(s99)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10202,plain,
% 1.37/1.54 ((~![X: $i] : ((~last(X)) | (~xuntil2p30(X)))) | ((~last(s99)) | (~xuntil2p30(s99)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10203,plain,
% 1.37/1.54 ((~![X: $i] : ((~last(X)) | (~xuntil2p30(X)))) | (~last(s99)) | (~xuntil2p30(s99))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10202, 10201])).
% 1.37/1.54 tff(10204,plain,
% 1.37/1.54 (~xuntil2p30(s99)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10203, 10200, 10197])).
% 1.37/1.54 tff(10205,plain,
% 1.37/1.54 (^[X: $i] : refl((node26(X) | xuntil2p30(X) | (~until2p29(X))) <=> (node26(X) | xuntil2p30(X) | (~until2p29(X))))),
% 1.37/1.54 inference(bind,[status(th)],[])).
% 1.37/1.54 tff(10206,plain,
% 1.37/1.54 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X))) <=> ![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 1.37/1.54 inference(quant_intro,[status(thm)],[10205])).
% 1.37/1.54 tff(10207,plain,
% 1.37/1.54 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X))) <=> ![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10208,plain,
% 1.37/1.54 (^[X: $i] : rewrite(((node26(X) | xuntil2p30(X)) | (~until2p29(X))) <=> (node26(X) | xuntil2p30(X) | (~until2p29(X))))),
% 1.37/1.54 inference(bind,[status(th)],[])).
% 1.37/1.54 tff(10209,plain,
% 1.37/1.54 (![X: $i] : ((node26(X) | xuntil2p30(X)) | (~until2p29(X))) <=> ![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 1.37/1.54 inference(quant_intro,[status(thm)],[10208])).
% 1.37/1.54 tff(10210,axiom,(![X: $i] : ((node26(X) | xuntil2p30(X)) | (~until2p29(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty23')).
% 1.37/1.54 tff(10211,plain,
% 1.37/1.54 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10210, 10209])).
% 1.37/1.54 tff(10212,plain,
% 1.37/1.54 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10211, 10207])).
% 1.37/1.54 tff(10213,plain,(
% 1.37/1.54 ![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 1.37/1.54 inference(skolemize,[status(sab)],[10212])).
% 1.37/1.54 tff(10214,plain,
% 1.37/1.54 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10213, 10206])).
% 1.37/1.54 tff(10215,plain,
% 1.37/1.54 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s99) | xuntil2p30(s99) | (~until2p29(s99)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s99) | xuntil2p30(s99) | (~until2p29(s99)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10216,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s99) | xuntil2p30(s99) | (~until2p29(s99)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10217,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s99) | xuntil2p30(s99) | (~until2p29(s99))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10216, 10215])).
% 1.37/1.54 tff(10218,plain,
% 1.37/1.54 (node26(s99) | (~until2p29(s99))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10217, 10214, 10204])).
% 1.37/1.54 tff(10219,plain,
% 1.37/1.54 (~until2p29(s99)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10218, 10190])).
% 1.37/1.54 tff(10220,plain,
% 1.37/1.54 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))) <=> ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))))),
% 1.37/1.54 inference(bind,[status(th)],[])).
% 1.37/1.54 tff(10221,plain,
% 1.37/1.54 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 1.37/1.54 inference(quant_intro,[status(thm)],[10220])).
% 1.37/1.54 tff(10222,plain,
% 1.37/1.54 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10223,plain,
% 1.37/1.54 (^[Y: $i, X: $i] : rewrite(((until2p29(Y) | (~succ(X, Y))) | (~xuntil2p30(X))) <=> ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))))),
% 1.37/1.54 inference(bind,[status(th)],[])).
% 1.37/1.54 tff(10224,plain,
% 1.37/1.54 (![Y: $i, X: $i] : ((until2p29(Y) | (~succ(X, Y))) | (~xuntil2p30(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 1.37/1.54 inference(quant_intro,[status(thm)],[10223])).
% 1.37/1.54 tff(10225,axiom,(![Y: $i, X: $i] : ((until2p29(Y) | (~succ(X, Y))) | (~xuntil2p30(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty24')).
% 1.37/1.54 tff(10226,plain,
% 1.37/1.54 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10225, 10224])).
% 1.37/1.54 tff(10227,plain,
% 1.37/1.54 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10226, 10222])).
% 1.37/1.54 tff(10228,plain,(
% 1.37/1.54 ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 1.37/1.54 inference(skolemize,[status(sab)],[10227])).
% 1.37/1.54 tff(10229,plain,
% 1.37/1.54 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10228, 10221])).
% 1.37/1.54 tff(10230,plain,
% 1.37/1.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s98, s99)) | until2p29(s99) | (~xuntil2p30(s98)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s98, s99)) | until2p29(s99) | (~xuntil2p30(s98)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10231,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s98, s99)) | until2p29(s99) | (~xuntil2p30(s98)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10232,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s98, s99)) | until2p29(s99) | (~xuntil2p30(s98))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10231, 10230])).
% 1.37/1.54 tff(10233,plain,
% 1.37/1.54 (until2p29(s99) | (~xuntil2p30(s98))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10232, 3920, 10229])).
% 1.37/1.54 tff(10234,plain,
% 1.37/1.54 (~xuntil2p30(s98)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10233, 10219])).
% 1.37/1.54 tff(10235,plain,
% 1.37/1.54 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s98) | xuntil2p30(s98) | (~until2p29(s98)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s98) | xuntil2p30(s98) | (~until2p29(s98)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10236,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s98) | xuntil2p30(s98) | (~until2p29(s98)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10237,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s98) | xuntil2p30(s98) | (~until2p29(s98))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10236, 10235])).
% 1.37/1.54 tff(10238,plain,
% 1.37/1.54 (xuntil2p30(s98) | (~until2p29(s98))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10237, 10214, 3953])).
% 1.37/1.54 tff(10239,plain,
% 1.37/1.54 (~until2p29(s98)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10238, 10234])).
% 1.37/1.54 tff(10240,plain,
% 1.37/1.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s97, s98)) | until2p29(s98) | (~xuntil2p30(s97)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s97, s98)) | until2p29(s98) | (~xuntil2p30(s97)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10241,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s97, s98)) | until2p29(s98) | (~xuntil2p30(s97)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10242,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s97, s98)) | until2p29(s98) | (~xuntil2p30(s97))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10241, 10240])).
% 1.37/1.54 tff(10243,plain,
% 1.37/1.54 (until2p29(s98) | (~xuntil2p30(s97))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10242, 10155, 10229])).
% 1.37/1.54 tff(10244,plain,
% 1.37/1.54 (~xuntil2p30(s97)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10243, 10239])).
% 1.37/1.54 tff(10245,plain,
% 1.37/1.54 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s97) | xuntil2p30(s97) | (~until2p29(s97)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s97) | xuntil2p30(s97) | (~until2p29(s97)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10246,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s97) | xuntil2p30(s97) | (~until2p29(s97)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10247,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s97) | xuntil2p30(s97) | (~until2p29(s97))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10246, 10245])).
% 1.37/1.54 tff(10248,plain,
% 1.37/1.54 (xuntil2p30(s97) | (~until2p29(s97))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10247, 10214, 8114])).
% 1.37/1.54 tff(10249,plain,
% 1.37/1.54 (~until2p29(s97)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10248, 10244])).
% 1.37/1.54 tff(10250,plain,
% 1.37/1.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s96, s97)) | until2p29(s97) | (~xuntil2p30(s96)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s96, s97)) | until2p29(s97) | (~xuntil2p30(s96)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10251,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s96, s97)) | until2p29(s97) | (~xuntil2p30(s96)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10252,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s96, s97)) | until2p29(s97) | (~xuntil2p30(s96))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10251, 10250])).
% 1.37/1.54 tff(10253,plain,
% 1.37/1.54 (until2p29(s97) | (~xuntil2p30(s96))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10252, 8083, 10229])).
% 1.37/1.54 tff(10254,plain,
% 1.37/1.54 (~xuntil2p30(s96)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10253, 10249])).
% 1.37/1.54 tff(10255,plain,
% 1.37/1.54 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s96) | xuntil2p30(s96) | (~until2p29(s96)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s96) | xuntil2p30(s96) | (~until2p29(s96)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10256,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s96) | xuntil2p30(s96) | (~until2p29(s96)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10257,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s96) | xuntil2p30(s96) | (~until2p29(s96))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10256, 10255])).
% 1.37/1.54 tff(10258,plain,
% 1.37/1.54 (xuntil2p30(s96) | (~until2p29(s96))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10257, 10214, 10132])).
% 1.37/1.54 tff(10259,plain,
% 1.37/1.54 (~until2p29(s96)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10258, 10254])).
% 1.37/1.54 tff(10260,plain,
% 1.37/1.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s95, s96)) | until2p29(s96) | (~xuntil2p30(s95)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s95, s96)) | until2p29(s96) | (~xuntil2p30(s95)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10261,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s95, s96)) | until2p29(s96) | (~xuntil2p30(s95)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10262,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s95, s96)) | until2p29(s96) | (~xuntil2p30(s95))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10261, 10260])).
% 1.37/1.54 tff(10263,plain,
% 1.37/1.54 (until2p29(s96) | (~xuntil2p30(s95))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10262, 8022, 10229])).
% 1.37/1.54 tff(10264,plain,
% 1.37/1.54 (~xuntil2p30(s95)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10263, 10259])).
% 1.37/1.54 tff(10265,plain,
% 1.37/1.54 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s95) | xuntil2p30(s95) | (~until2p29(s95)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s95) | xuntil2p30(s95) | (~until2p29(s95)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10266,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s95) | xuntil2p30(s95) | (~until2p29(s95)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10267,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s95) | xuntil2p30(s95) | (~until2p29(s95))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10266, 10265])).
% 1.37/1.54 tff(10268,plain,
% 1.37/1.54 (xuntil2p30(s95) | (~until2p29(s95))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10267, 10214, 8130])).
% 1.37/1.54 tff(10269,plain,
% 1.37/1.54 (~until2p29(s95)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10268, 10264])).
% 1.37/1.54 tff(10270,plain,
% 1.37/1.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s94, s95)) | until2p29(s95) | (~xuntil2p30(s94)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s94, s95)) | until2p29(s95) | (~xuntil2p30(s94)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10271,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s94, s95)) | until2p29(s95) | (~xuntil2p30(s94)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10272,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s94, s95)) | until2p29(s95) | (~xuntil2p30(s94))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10271, 10270])).
% 1.37/1.54 tff(10273,plain,
% 1.37/1.54 (until2p29(s95) | (~xuntil2p30(s94))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10272, 7944, 10229])).
% 1.37/1.54 tff(10274,plain,
% 1.37/1.54 (~xuntil2p30(s94)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10273, 10269])).
% 1.37/1.54 tff(10275,plain,
% 1.37/1.54 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s94) | xuntil2p30(s94) | (~until2p29(s94)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s94) | xuntil2p30(s94) | (~until2p29(s94)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10276,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s94) | xuntil2p30(s94) | (~until2p29(s94)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10277,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s94) | xuntil2p30(s94) | (~until2p29(s94))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10276, 10275])).
% 1.37/1.54 tff(10278,plain,
% 1.37/1.54 (xuntil2p30(s94) | (~until2p29(s94))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10277, 10214, 8139])).
% 1.37/1.54 tff(10279,plain,
% 1.37/1.54 (~until2p29(s94)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10278, 10274])).
% 1.37/1.54 tff(10280,plain,
% 1.37/1.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s93, s94)) | until2p29(s94) | (~xuntil2p30(s93)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s93, s94)) | until2p29(s94) | (~xuntil2p30(s93)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10281,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s93, s94)) | until2p29(s94) | (~xuntil2p30(s93)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10282,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s93, s94)) | until2p29(s94) | (~xuntil2p30(s93))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10281, 10280])).
% 1.37/1.54 tff(10283,plain,
% 1.37/1.54 (until2p29(s94) | (~xuntil2p30(s93))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10282, 7845, 10229])).
% 1.37/1.54 tff(10284,plain,
% 1.37/1.54 (~xuntil2p30(s93)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10283, 10279])).
% 1.37/1.54 tff(10285,plain,
% 1.37/1.54 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s93) | xuntil2p30(s93) | (~until2p29(s93)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s93) | xuntil2p30(s93) | (~until2p29(s93)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10286,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s93) | xuntil2p30(s93) | (~until2p29(s93)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10287,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s93) | xuntil2p30(s93) | (~until2p29(s93))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10286, 10285])).
% 1.37/1.54 tff(10288,plain,
% 1.37/1.54 (xuntil2p30(s93) | (~until2p29(s93))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10287, 10214, 8143])).
% 1.37/1.54 tff(10289,plain,
% 1.37/1.54 (~until2p29(s93)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10288, 10284])).
% 1.37/1.54 tff(10290,plain,
% 1.37/1.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s92, s93)) | until2p29(s93) | (~xuntil2p30(s92)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s92, s93)) | until2p29(s93) | (~xuntil2p30(s92)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10291,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s92, s93)) | until2p29(s93) | (~xuntil2p30(s92)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10292,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s92, s93)) | until2p29(s93) | (~xuntil2p30(s92))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10291, 10290])).
% 1.37/1.54 tff(10293,plain,
% 1.37/1.54 (until2p29(s93) | (~xuntil2p30(s92))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10292, 7778, 10229])).
% 1.37/1.54 tff(10294,plain,
% 1.37/1.54 (~xuntil2p30(s92)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10293, 10289])).
% 1.37/1.54 tff(10295,plain,
% 1.37/1.54 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s92) | xuntil2p30(s92) | (~until2p29(s92)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s92) | xuntil2p30(s92) | (~until2p29(s92)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10296,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s92) | xuntil2p30(s92) | (~until2p29(s92)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10297,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s92) | xuntil2p30(s92) | (~until2p29(s92))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10296, 10295])).
% 1.37/1.54 tff(10298,plain,
% 1.37/1.54 (xuntil2p30(s92) | (~until2p29(s92))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10297, 10214, 10078])).
% 1.37/1.54 tff(10299,plain,
% 1.37/1.54 (~until2p29(s92)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10298, 10294])).
% 1.37/1.54 tff(10300,plain,
% 1.37/1.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s91, s92)) | until2p29(s92) | (~xuntil2p30(s91)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s91, s92)) | until2p29(s92) | (~xuntil2p30(s91)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10301,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s91, s92)) | until2p29(s92) | (~xuntil2p30(s91)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10302,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s91, s92)) | until2p29(s92) | (~xuntil2p30(s91))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10301, 10300])).
% 1.37/1.54 tff(10303,plain,
% 1.37/1.54 (until2p29(s92) | (~xuntil2p30(s91))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10302, 7689, 10229])).
% 1.37/1.54 tff(10304,plain,
% 1.37/1.54 (~xuntil2p30(s91)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10303, 10299])).
% 1.37/1.54 tff(10305,plain,
% 1.37/1.54 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s91) | xuntil2p30(s91) | (~until2p29(s91)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s91) | xuntil2p30(s91) | (~until2p29(s91)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10306,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s91) | xuntil2p30(s91) | (~until2p29(s91)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10307,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s91) | xuntil2p30(s91) | (~until2p29(s91))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10306, 10305])).
% 1.37/1.54 tff(10308,plain,
% 1.37/1.54 (xuntil2p30(s91) | (~until2p29(s91))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10307, 10214, 8159])).
% 1.37/1.54 tff(10309,plain,
% 1.37/1.54 (~until2p29(s91)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10308, 10304])).
% 1.37/1.54 tff(10310,plain,
% 1.37/1.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s90, s91)) | until2p29(s91) | (~xuntil2p30(s90)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s90, s91)) | until2p29(s91) | (~xuntil2p30(s90)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10311,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s90, s91)) | until2p29(s91) | (~xuntil2p30(s90)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10312,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s90, s91)) | until2p29(s91) | (~xuntil2p30(s90))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10311, 10310])).
% 1.37/1.54 tff(10313,plain,
% 1.37/1.54 (until2p29(s91) | (~xuntil2p30(s90))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10312, 7614, 10229])).
% 1.37/1.54 tff(10314,plain,
% 1.37/1.54 (~xuntil2p30(s90)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10313, 10309])).
% 1.37/1.54 tff(10315,plain,
% 1.37/1.54 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s90) | xuntil2p30(s90) | (~until2p29(s90)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s90) | xuntil2p30(s90) | (~until2p29(s90)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10316,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s90) | xuntil2p30(s90) | (~until2p29(s90)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10317,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s90) | xuntil2p30(s90) | (~until2p29(s90))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10316, 10315])).
% 1.37/1.54 tff(10318,plain,
% 1.37/1.54 (xuntil2p30(s90) | (~until2p29(s90))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10317, 10214, 8168])).
% 1.37/1.54 tff(10319,plain,
% 1.37/1.54 (~until2p29(s90)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10318, 10314])).
% 1.37/1.54 tff(10320,plain,
% 1.37/1.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s89, s90)) | until2p29(s90) | (~xuntil2p30(s89)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s89, s90)) | until2p29(s90) | (~xuntil2p30(s89)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10321,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s89, s90)) | until2p29(s90) | (~xuntil2p30(s89)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10322,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s89, s90)) | until2p29(s90) | (~xuntil2p30(s89))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10321, 10320])).
% 1.37/1.54 tff(10323,plain,
% 1.37/1.54 (until2p29(s90) | (~xuntil2p30(s89))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10322, 7550, 10229])).
% 1.37/1.54 tff(10324,plain,
% 1.37/1.54 (~xuntil2p30(s89)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10323, 10319])).
% 1.37/1.54 tff(10325,plain,
% 1.37/1.54 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s89) | xuntil2p30(s89) | (~until2p29(s89)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s89) | xuntil2p30(s89) | (~until2p29(s89)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10326,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s89) | xuntil2p30(s89) | (~until2p29(s89)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10327,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s89) | xuntil2p30(s89) | (~until2p29(s89))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10326, 10325])).
% 1.37/1.54 tff(10328,plain,
% 1.37/1.54 (xuntil2p30(s89) | (~until2p29(s89))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10327, 10214, 8172])).
% 1.37/1.54 tff(10329,plain,
% 1.37/1.54 (~until2p29(s89)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10328, 10324])).
% 1.37/1.54 tff(10330,plain,
% 1.37/1.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s88, s89)) | until2p29(s89) | (~xuntil2p30(s88)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s88, s89)) | until2p29(s89) | (~xuntil2p30(s88)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10331,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s88, s89)) | until2p29(s89) | (~xuntil2p30(s88)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10332,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s88, s89)) | until2p29(s89) | (~xuntil2p30(s88))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10331, 10330])).
% 1.37/1.54 tff(10333,plain,
% 1.37/1.54 (until2p29(s89) | (~xuntil2p30(s88))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10332, 7455, 10229])).
% 1.37/1.54 tff(10334,plain,
% 1.37/1.54 (~xuntil2p30(s88)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10333, 10329])).
% 1.37/1.54 tff(10335,plain,
% 1.37/1.54 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s88) | xuntil2p30(s88) | (~until2p29(s88)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s88) | xuntil2p30(s88) | (~until2p29(s88)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10336,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s88) | xuntil2p30(s88) | (~until2p29(s88)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10337,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s88) | xuntil2p30(s88) | (~until2p29(s88))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10336, 10335])).
% 1.37/1.54 tff(10338,plain,
% 1.37/1.54 (xuntil2p30(s88) | (~until2p29(s88))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10337, 10214, 10024])).
% 1.37/1.54 tff(10339,plain,
% 1.37/1.54 (~until2p29(s88)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10338, 10334])).
% 1.37/1.54 tff(10340,plain,
% 1.37/1.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s87, s88)) | until2p29(s88) | (~xuntil2p30(s87)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s87, s88)) | until2p29(s88) | (~xuntil2p30(s87)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10341,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s87, s88)) | until2p29(s88) | (~xuntil2p30(s87)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10342,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s87, s88)) | until2p29(s88) | (~xuntil2p30(s87))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10341, 10340])).
% 1.37/1.54 tff(10343,plain,
% 1.37/1.54 (until2p29(s88) | (~xuntil2p30(s87))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10342, 7394, 10229])).
% 1.37/1.54 tff(10344,plain,
% 1.37/1.54 (~xuntil2p30(s87)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10343, 10339])).
% 1.37/1.54 tff(10345,plain,
% 1.37/1.54 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s87) | xuntil2p30(s87) | (~until2p29(s87)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s87) | xuntil2p30(s87) | (~until2p29(s87)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10346,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s87) | xuntil2p30(s87) | (~until2p29(s87)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10347,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s87) | xuntil2p30(s87) | (~until2p29(s87))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10346, 10345])).
% 1.37/1.54 tff(10348,plain,
% 1.37/1.54 (xuntil2p30(s87) | (~until2p29(s87))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10347, 10214, 8188])).
% 1.37/1.54 tff(10349,plain,
% 1.37/1.54 (~until2p29(s87)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10348, 10344])).
% 1.37/1.54 tff(10350,plain,
% 1.37/1.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s86, s87)) | until2p29(s87) | (~xuntil2p30(s86)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s86, s87)) | until2p29(s87) | (~xuntil2p30(s86)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10351,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s86, s87)) | until2p29(s87) | (~xuntil2p30(s86)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10352,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s86, s87)) | until2p29(s87) | (~xuntil2p30(s86))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10351, 10350])).
% 1.37/1.54 tff(10353,plain,
% 1.37/1.54 (until2p29(s87) | (~xuntil2p30(s86))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10352, 7316, 10229])).
% 1.37/1.54 tff(10354,plain,
% 1.37/1.54 (~xuntil2p30(s86)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10353, 10349])).
% 1.37/1.54 tff(10355,plain,
% 1.37/1.54 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s86) | xuntil2p30(s86) | (~until2p29(s86)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s86) | xuntil2p30(s86) | (~until2p29(s86)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10356,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s86) | xuntil2p30(s86) | (~until2p29(s86)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10357,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s86) | xuntil2p30(s86) | (~until2p29(s86))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10356, 10355])).
% 1.37/1.54 tff(10358,plain,
% 1.37/1.54 (xuntil2p30(s86) | (~until2p29(s86))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10357, 10214, 8197])).
% 1.37/1.54 tff(10359,plain,
% 1.37/1.54 (~until2p29(s86)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10358, 10354])).
% 1.37/1.54 tff(10360,plain,
% 1.37/1.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s85, s86)) | until2p29(s86) | (~xuntil2p30(s85)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s85, s86)) | until2p29(s86) | (~xuntil2p30(s85)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10361,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s85, s86)) | until2p29(s86) | (~xuntil2p30(s85)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10362,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s85, s86)) | until2p29(s86) | (~xuntil2p30(s85))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10361, 10360])).
% 1.37/1.54 tff(10363,plain,
% 1.37/1.54 (until2p29(s86) | (~xuntil2p30(s85))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10362, 7217, 10229])).
% 1.37/1.54 tff(10364,plain,
% 1.37/1.54 (~xuntil2p30(s85)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10363, 10359])).
% 1.37/1.54 tff(10365,plain,
% 1.37/1.54 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s85) | xuntil2p30(s85) | (~until2p29(s85)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s85) | xuntil2p30(s85) | (~until2p29(s85)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10366,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s85) | xuntil2p30(s85) | (~until2p29(s85)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10367,plain,
% 1.37/1.54 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s85) | xuntil2p30(s85) | (~until2p29(s85))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[10366, 10365])).
% 1.37/1.54 tff(10368,plain,
% 1.37/1.54 (xuntil2p30(s85) | (~until2p29(s85))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10367, 10214, 8201])).
% 1.37/1.54 tff(10369,plain,
% 1.37/1.54 (~until2p29(s85)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[10368, 10364])).
% 1.37/1.54 tff(10370,plain,
% 1.37/1.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s84, s85)) | until2p29(s85) | (~xuntil2p30(s84)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s84, s85)) | until2p29(s85) | (~xuntil2p30(s84)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(10371,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s84, s85)) | until2p29(s85) | (~xuntil2p30(s84)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(10372,plain,
% 1.37/1.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s84, s85)) | until2p29(s85) | (~xuntil2p30(s84))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10371, 10370])).
% 1.37/1.55 tff(10373,plain,
% 1.37/1.55 (until2p29(s85) | (~xuntil2p30(s84))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10372, 7150, 10229])).
% 1.37/1.55 tff(10374,plain,
% 1.37/1.55 (~xuntil2p30(s84)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10373, 10369])).
% 1.37/1.55 tff(10375,plain,
% 1.37/1.55 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s84) | xuntil2p30(s84) | (~until2p29(s84)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s84) | xuntil2p30(s84) | (~until2p29(s84)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10376,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s84) | xuntil2p30(s84) | (~until2p29(s84)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10377,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s84) | xuntil2p30(s84) | (~until2p29(s84))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10376, 10375])).
% 1.37/1.55 tff(10378,plain,
% 1.37/1.55 (xuntil2p30(s84) | (~until2p29(s84))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10377, 10214, 9970])).
% 1.37/1.55 tff(10379,plain,
% 1.37/1.55 (~until2p29(s84)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10378, 10374])).
% 1.37/1.55 tff(10380,plain,
% 1.37/1.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s83, s84)) | until2p29(s84) | (~xuntil2p30(s83)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s83, s84)) | until2p29(s84) | (~xuntil2p30(s83)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10381,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s83, s84)) | until2p29(s84) | (~xuntil2p30(s83)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10382,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s83, s84)) | until2p29(s84) | (~xuntil2p30(s83))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10381, 10380])).
% 1.37/1.55 tff(10383,plain,
% 1.37/1.55 (until2p29(s84) | (~xuntil2p30(s83))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10382, 7061, 10229])).
% 1.37/1.55 tff(10384,plain,
% 1.37/1.55 (~xuntil2p30(s83)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10383, 10379])).
% 1.37/1.55 tff(10385,plain,
% 1.37/1.55 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s83) | xuntil2p30(s83) | (~until2p29(s83)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s83) | xuntil2p30(s83) | (~until2p29(s83)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10386,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s83) | xuntil2p30(s83) | (~until2p29(s83)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10387,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s83) | xuntil2p30(s83) | (~until2p29(s83))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10386, 10385])).
% 1.37/1.55 tff(10388,plain,
% 1.37/1.55 (xuntil2p30(s83) | (~until2p29(s83))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10387, 10214, 8217])).
% 1.37/1.55 tff(10389,plain,
% 1.37/1.55 (~until2p29(s83)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10388, 10384])).
% 1.37/1.55 tff(10390,plain,
% 1.37/1.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s82, s83)) | until2p29(s83) | (~xuntil2p30(s82)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s82, s83)) | until2p29(s83) | (~xuntil2p30(s82)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10391,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s82, s83)) | until2p29(s83) | (~xuntil2p30(s82)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10392,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s82, s83)) | until2p29(s83) | (~xuntil2p30(s82))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10391, 10390])).
% 1.37/1.55 tff(10393,plain,
% 1.37/1.55 (until2p29(s83) | (~xuntil2p30(s82))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10392, 6986, 10229])).
% 1.37/1.55 tff(10394,plain,
% 1.37/1.55 (~xuntil2p30(s82)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10393, 10389])).
% 1.37/1.55 tff(10395,plain,
% 1.37/1.55 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s82) | xuntil2p30(s82) | (~until2p29(s82)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s82) | xuntil2p30(s82) | (~until2p29(s82)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10396,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s82) | xuntil2p30(s82) | (~until2p29(s82)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10397,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s82) | xuntil2p30(s82) | (~until2p29(s82))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10396, 10395])).
% 1.37/1.55 tff(10398,plain,
% 1.37/1.55 (xuntil2p30(s82) | (~until2p29(s82))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10397, 10214, 8226])).
% 1.37/1.55 tff(10399,plain,
% 1.37/1.55 (~until2p29(s82)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10398, 10394])).
% 1.37/1.55 tff(10400,plain,
% 1.37/1.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s81, s82)) | until2p29(s82) | (~xuntil2p30(s81)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s81, s82)) | until2p29(s82) | (~xuntil2p30(s81)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10401,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s81, s82)) | until2p29(s82) | (~xuntil2p30(s81)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10402,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s81, s82)) | until2p29(s82) | (~xuntil2p30(s81))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10401, 10400])).
% 1.37/1.55 tff(10403,plain,
% 1.37/1.55 (until2p29(s82) | (~xuntil2p30(s81))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10402, 6922, 10229])).
% 1.37/1.55 tff(10404,plain,
% 1.37/1.55 (~xuntil2p30(s81)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10403, 10399])).
% 1.37/1.55 tff(10405,plain,
% 1.37/1.55 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s81) | xuntil2p30(s81) | (~until2p29(s81)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s81) | xuntil2p30(s81) | (~until2p29(s81)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10406,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s81) | xuntil2p30(s81) | (~until2p29(s81)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10407,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s81) | xuntil2p30(s81) | (~until2p29(s81))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10406, 10405])).
% 1.37/1.55 tff(10408,plain,
% 1.37/1.55 (xuntil2p30(s81) | (~until2p29(s81))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10407, 10214, 8230])).
% 1.37/1.55 tff(10409,plain,
% 1.37/1.55 (~until2p29(s81)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10408, 10404])).
% 1.37/1.55 tff(10410,plain,
% 1.37/1.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s80, s81)) | until2p29(s81) | (~xuntil2p30(s80)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s80, s81)) | until2p29(s81) | (~xuntil2p30(s80)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10411,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s80, s81)) | until2p29(s81) | (~xuntil2p30(s80)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10412,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s80, s81)) | until2p29(s81) | (~xuntil2p30(s80))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10411, 10410])).
% 1.37/1.55 tff(10413,plain,
% 1.37/1.55 (until2p29(s81) | (~xuntil2p30(s80))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10412, 6827, 10229])).
% 1.37/1.55 tff(10414,plain,
% 1.37/1.55 (~xuntil2p30(s80)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10413, 10409])).
% 1.37/1.55 tff(10415,plain,
% 1.37/1.55 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s80) | xuntil2p30(s80) | (~until2p29(s80)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s80) | xuntil2p30(s80) | (~until2p29(s80)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10416,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s80) | xuntil2p30(s80) | (~until2p29(s80)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10417,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s80) | xuntil2p30(s80) | (~until2p29(s80))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10416, 10415])).
% 1.37/1.55 tff(10418,plain,
% 1.37/1.55 (xuntil2p30(s80) | (~until2p29(s80))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10417, 10214, 9916])).
% 1.37/1.55 tff(10419,plain,
% 1.37/1.55 (~until2p29(s80)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10418, 10414])).
% 1.37/1.55 tff(10420,plain,
% 1.37/1.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s79, s80)) | until2p29(s80) | (~xuntil2p30(s79)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s79, s80)) | until2p29(s80) | (~xuntil2p30(s79)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10421,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s79, s80)) | until2p29(s80) | (~xuntil2p30(s79)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10422,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s79, s80)) | until2p29(s80) | (~xuntil2p30(s79))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10421, 10420])).
% 1.37/1.55 tff(10423,plain,
% 1.37/1.55 (until2p29(s80) | (~xuntil2p30(s79))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10422, 6766, 10229])).
% 1.37/1.55 tff(10424,plain,
% 1.37/1.55 (~xuntil2p30(s79)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10423, 10419])).
% 1.37/1.55 tff(10425,plain,
% 1.37/1.55 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s79) | xuntil2p30(s79) | (~until2p29(s79)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s79) | xuntil2p30(s79) | (~until2p29(s79)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10426,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s79) | xuntil2p30(s79) | (~until2p29(s79)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10427,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s79) | xuntil2p30(s79) | (~until2p29(s79))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10426, 10425])).
% 1.37/1.55 tff(10428,plain,
% 1.37/1.55 (xuntil2p30(s79) | (~until2p29(s79))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10427, 10214, 8246])).
% 1.37/1.55 tff(10429,plain,
% 1.37/1.55 (~until2p29(s79)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10428, 10424])).
% 1.37/1.55 tff(10430,plain,
% 1.37/1.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s78, s79)) | until2p29(s79) | (~xuntil2p30(s78)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s78, s79)) | until2p29(s79) | (~xuntil2p30(s78)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10431,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s78, s79)) | until2p29(s79) | (~xuntil2p30(s78)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10432,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s78, s79)) | until2p29(s79) | (~xuntil2p30(s78))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10431, 10430])).
% 1.37/1.55 tff(10433,plain,
% 1.37/1.55 (until2p29(s79) | (~xuntil2p30(s78))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10432, 6688, 10229])).
% 1.37/1.55 tff(10434,plain,
% 1.37/1.55 (~xuntil2p30(s78)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10433, 10429])).
% 1.37/1.55 tff(10435,plain,
% 1.37/1.55 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s78) | xuntil2p30(s78) | (~until2p29(s78)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s78) | xuntil2p30(s78) | (~until2p29(s78)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10436,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s78) | xuntil2p30(s78) | (~until2p29(s78)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10437,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s78) | xuntil2p30(s78) | (~until2p29(s78))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10436, 10435])).
% 1.37/1.55 tff(10438,plain,
% 1.37/1.55 (xuntil2p30(s78) | (~until2p29(s78))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10437, 10214, 8255])).
% 1.37/1.55 tff(10439,plain,
% 1.37/1.55 (~until2p29(s78)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10438, 10434])).
% 1.37/1.55 tff(10440,plain,
% 1.37/1.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s77, s78)) | until2p29(s78) | (~xuntil2p30(s77)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s77, s78)) | until2p29(s78) | (~xuntil2p30(s77)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10441,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s77, s78)) | until2p29(s78) | (~xuntil2p30(s77)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10442,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s77, s78)) | until2p29(s78) | (~xuntil2p30(s77))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10441, 10440])).
% 1.37/1.55 tff(10443,plain,
% 1.37/1.55 (until2p29(s78) | (~xuntil2p30(s77))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10442, 6589, 10229])).
% 1.37/1.55 tff(10444,plain,
% 1.37/1.55 (~xuntil2p30(s77)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10443, 10439])).
% 1.37/1.55 tff(10445,plain,
% 1.37/1.55 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s77) | xuntil2p30(s77) | (~until2p29(s77)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s77) | xuntil2p30(s77) | (~until2p29(s77)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10446,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s77) | xuntil2p30(s77) | (~until2p29(s77)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10447,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s77) | xuntil2p30(s77) | (~until2p29(s77))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10446, 10445])).
% 1.37/1.55 tff(10448,plain,
% 1.37/1.55 (xuntil2p30(s77) | (~until2p29(s77))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10447, 10214, 8259])).
% 1.37/1.55 tff(10449,plain,
% 1.37/1.55 (~until2p29(s77)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10448, 10444])).
% 1.37/1.55 tff(10450,plain,
% 1.37/1.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s76, s77)) | until2p29(s77) | (~xuntil2p30(s76)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s76, s77)) | until2p29(s77) | (~xuntil2p30(s76)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10451,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s76, s77)) | until2p29(s77) | (~xuntil2p30(s76)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10452,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s76, s77)) | until2p29(s77) | (~xuntil2p30(s76))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10451, 10450])).
% 1.37/1.55 tff(10453,plain,
% 1.37/1.55 (until2p29(s77) | (~xuntil2p30(s76))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10452, 6522, 10229])).
% 1.37/1.55 tff(10454,plain,
% 1.37/1.55 (~xuntil2p30(s76)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10453, 10449])).
% 1.37/1.55 tff(10455,plain,
% 1.37/1.55 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s76) | xuntil2p30(s76) | (~until2p29(s76)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s76) | xuntil2p30(s76) | (~until2p29(s76)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10456,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s76) | xuntil2p30(s76) | (~until2p29(s76)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10457,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s76) | xuntil2p30(s76) | (~until2p29(s76))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10456, 10455])).
% 1.37/1.55 tff(10458,plain,
% 1.37/1.55 (xuntil2p30(s76) | (~until2p29(s76))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10457, 10214, 9862])).
% 1.37/1.55 tff(10459,plain,
% 1.37/1.55 (~until2p29(s76)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10458, 10454])).
% 1.37/1.55 tff(10460,plain,
% 1.37/1.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s75, s76)) | until2p29(s76) | (~xuntil2p30(s75)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s75, s76)) | until2p29(s76) | (~xuntil2p30(s75)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10461,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s75, s76)) | until2p29(s76) | (~xuntil2p30(s75)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10462,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s75, s76)) | until2p29(s76) | (~xuntil2p30(s75))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10461, 10460])).
% 1.37/1.55 tff(10463,plain,
% 1.37/1.55 (until2p29(s76) | (~xuntil2p30(s75))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10462, 6433, 10229])).
% 1.37/1.55 tff(10464,plain,
% 1.37/1.55 (~xuntil2p30(s75)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10463, 10459])).
% 1.37/1.55 tff(10465,plain,
% 1.37/1.55 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s75) | xuntil2p30(s75) | (~until2p29(s75)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s75) | xuntil2p30(s75) | (~until2p29(s75)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10466,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s75) | xuntil2p30(s75) | (~until2p29(s75)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10467,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s75) | xuntil2p30(s75) | (~until2p29(s75))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10466, 10465])).
% 1.37/1.55 tff(10468,plain,
% 1.37/1.55 (xuntil2p30(s75) | (~until2p29(s75))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10467, 10214, 8275])).
% 1.37/1.55 tff(10469,plain,
% 1.37/1.55 (~until2p29(s75)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10468, 10464])).
% 1.37/1.55 tff(10470,plain,
% 1.37/1.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s74, s75)) | until2p29(s75) | (~xuntil2p30(s74)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s74, s75)) | until2p29(s75) | (~xuntil2p30(s74)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10471,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s74, s75)) | until2p29(s75) | (~xuntil2p30(s74)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10472,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s74, s75)) | until2p29(s75) | (~xuntil2p30(s74))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10471, 10470])).
% 1.37/1.55 tff(10473,plain,
% 1.37/1.55 (until2p29(s75) | (~xuntil2p30(s74))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10472, 6358, 10229])).
% 1.37/1.55 tff(10474,plain,
% 1.37/1.55 (~xuntil2p30(s74)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10473, 10469])).
% 1.37/1.55 tff(10475,plain,
% 1.37/1.55 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s74) | xuntil2p30(s74) | (~until2p29(s74)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s74) | xuntil2p30(s74) | (~until2p29(s74)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10476,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s74) | xuntil2p30(s74) | (~until2p29(s74)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10477,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s74) | xuntil2p30(s74) | (~until2p29(s74))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10476, 10475])).
% 1.37/1.55 tff(10478,plain,
% 1.37/1.55 (xuntil2p30(s74) | (~until2p29(s74))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10477, 10214, 8284])).
% 1.37/1.55 tff(10479,plain,
% 1.37/1.55 (~until2p29(s74)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10478, 10474])).
% 1.37/1.55 tff(10480,plain,
% 1.37/1.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s73, s74)) | until2p29(s74) | (~xuntil2p30(s73)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s73, s74)) | until2p29(s74) | (~xuntil2p30(s73)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10481,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s73, s74)) | until2p29(s74) | (~xuntil2p30(s73)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10482,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s73, s74)) | until2p29(s74) | (~xuntil2p30(s73))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10481, 10480])).
% 1.37/1.55 tff(10483,plain,
% 1.37/1.55 (until2p29(s74) | (~xuntil2p30(s73))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10482, 6294, 10229])).
% 1.37/1.55 tff(10484,plain,
% 1.37/1.55 (~xuntil2p30(s73)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10483, 10479])).
% 1.37/1.55 tff(10485,plain,
% 1.37/1.55 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s73) | xuntil2p30(s73) | (~until2p29(s73)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s73) | xuntil2p30(s73) | (~until2p29(s73)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10486,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s73) | xuntil2p30(s73) | (~until2p29(s73)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10487,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s73) | xuntil2p30(s73) | (~until2p29(s73))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10486, 10485])).
% 1.37/1.55 tff(10488,plain,
% 1.37/1.55 (xuntil2p30(s73) | (~until2p29(s73))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10487, 10214, 8288])).
% 1.37/1.55 tff(10489,plain,
% 1.37/1.55 (~until2p29(s73)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10488, 10484])).
% 1.37/1.55 tff(10490,plain,
% 1.37/1.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s72, s73)) | until2p29(s73) | (~xuntil2p30(s72)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s72, s73)) | until2p29(s73) | (~xuntil2p30(s72)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10491,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s72, s73)) | until2p29(s73) | (~xuntil2p30(s72)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10492,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s72, s73)) | until2p29(s73) | (~xuntil2p30(s72))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10491, 10490])).
% 1.37/1.55 tff(10493,plain,
% 1.37/1.55 (until2p29(s73) | (~xuntil2p30(s72))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10492, 6199, 10229])).
% 1.37/1.55 tff(10494,plain,
% 1.37/1.55 (~xuntil2p30(s72)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10493, 10489])).
% 1.37/1.55 tff(10495,plain,
% 1.37/1.55 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s72) | xuntil2p30(s72) | (~until2p29(s72)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s72) | xuntil2p30(s72) | (~until2p29(s72)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10496,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s72) | xuntil2p30(s72) | (~until2p29(s72)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10497,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s72) | xuntil2p30(s72) | (~until2p29(s72))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10496, 10495])).
% 1.37/1.55 tff(10498,plain,
% 1.37/1.55 (xuntil2p30(s72) | (~until2p29(s72))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10497, 10214, 9808])).
% 1.37/1.55 tff(10499,plain,
% 1.37/1.55 (~until2p29(s72)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10498, 10494])).
% 1.37/1.55 tff(10500,plain,
% 1.37/1.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s71, s72)) | until2p29(s72) | (~xuntil2p30(s71)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s71, s72)) | until2p29(s72) | (~xuntil2p30(s71)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10501,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s71, s72)) | until2p29(s72) | (~xuntil2p30(s71)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10502,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s71, s72)) | until2p29(s72) | (~xuntil2p30(s71))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10501, 10500])).
% 1.37/1.55 tff(10503,plain,
% 1.37/1.55 (until2p29(s72) | (~xuntil2p30(s71))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10502, 6138, 10229])).
% 1.37/1.55 tff(10504,plain,
% 1.37/1.55 (~xuntil2p30(s71)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10503, 10499])).
% 1.37/1.55 tff(10505,plain,
% 1.37/1.55 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s71) | xuntil2p30(s71) | (~until2p29(s71)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s71) | xuntil2p30(s71) | (~until2p29(s71)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10506,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s71) | xuntil2p30(s71) | (~until2p29(s71)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10507,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s71) | xuntil2p30(s71) | (~until2p29(s71))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10506, 10505])).
% 1.37/1.55 tff(10508,plain,
% 1.37/1.55 (xuntil2p30(s71) | (~until2p29(s71))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10507, 10214, 8304])).
% 1.37/1.55 tff(10509,plain,
% 1.37/1.55 (~until2p29(s71)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10508, 10504])).
% 1.37/1.55 tff(10510,plain,
% 1.37/1.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s70, s71)) | until2p29(s71) | (~xuntil2p30(s70)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s70, s71)) | until2p29(s71) | (~xuntil2p30(s70)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10511,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s70, s71)) | until2p29(s71) | (~xuntil2p30(s70)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10512,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s70, s71)) | until2p29(s71) | (~xuntil2p30(s70))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10511, 10510])).
% 1.37/1.55 tff(10513,plain,
% 1.37/1.55 (until2p29(s71) | (~xuntil2p30(s70))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10512, 6060, 10229])).
% 1.37/1.55 tff(10514,plain,
% 1.37/1.55 (~xuntil2p30(s70)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10513, 10509])).
% 1.37/1.55 tff(10515,plain,
% 1.37/1.55 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s70) | xuntil2p30(s70) | (~until2p29(s70)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s70) | xuntil2p30(s70) | (~until2p29(s70)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10516,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s70) | xuntil2p30(s70) | (~until2p29(s70)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10517,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s70) | xuntil2p30(s70) | (~until2p29(s70))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10516, 10515])).
% 1.37/1.55 tff(10518,plain,
% 1.37/1.55 (xuntil2p30(s70) | (~until2p29(s70))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10517, 10214, 8313])).
% 1.37/1.55 tff(10519,plain,
% 1.37/1.55 (~until2p29(s70)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10518, 10514])).
% 1.37/1.55 tff(10520,plain,
% 1.37/1.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s69, s70)) | until2p29(s70) | (~xuntil2p30(s69)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s69, s70)) | until2p29(s70) | (~xuntil2p30(s69)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10521,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s69, s70)) | until2p29(s70) | (~xuntil2p30(s69)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10522,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s69, s70)) | until2p29(s70) | (~xuntil2p30(s69))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10521, 10520])).
% 1.37/1.55 tff(10523,plain,
% 1.37/1.55 (until2p29(s70) | (~xuntil2p30(s69))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10522, 5961, 10229])).
% 1.37/1.55 tff(10524,plain,
% 1.37/1.55 (~xuntil2p30(s69)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10523, 10519])).
% 1.37/1.55 tff(10525,plain,
% 1.37/1.55 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s69) | xuntil2p30(s69) | (~until2p29(s69)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s69) | xuntil2p30(s69) | (~until2p29(s69)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10526,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s69) | xuntil2p30(s69) | (~until2p29(s69)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10527,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s69) | xuntil2p30(s69) | (~until2p29(s69))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10526, 10525])).
% 1.37/1.55 tff(10528,plain,
% 1.37/1.55 (xuntil2p30(s69) | (~until2p29(s69))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10527, 10214, 8317])).
% 1.37/1.55 tff(10529,plain,
% 1.37/1.55 (~until2p29(s69)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10528, 10524])).
% 1.37/1.55 tff(10530,plain,
% 1.37/1.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s68, s69)) | until2p29(s69) | (~xuntil2p30(s68)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s68, s69)) | until2p29(s69) | (~xuntil2p30(s68)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10531,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s68, s69)) | until2p29(s69) | (~xuntil2p30(s68)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10532,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s68, s69)) | until2p29(s69) | (~xuntil2p30(s68))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10531, 10530])).
% 1.37/1.55 tff(10533,plain,
% 1.37/1.55 (until2p29(s69) | (~xuntil2p30(s68))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10532, 5894, 10229])).
% 1.37/1.55 tff(10534,plain,
% 1.37/1.55 (~xuntil2p30(s68)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10533, 10529])).
% 1.37/1.55 tff(10535,plain,
% 1.37/1.55 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s68) | xuntil2p30(s68) | (~until2p29(s68)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s68) | xuntil2p30(s68) | (~until2p29(s68)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10536,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s68) | xuntil2p30(s68) | (~until2p29(s68)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10537,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s68) | xuntil2p30(s68) | (~until2p29(s68))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10536, 10535])).
% 1.37/1.55 tff(10538,plain,
% 1.37/1.55 (xuntil2p30(s68) | (~until2p29(s68))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10537, 10214, 9754])).
% 1.37/1.55 tff(10539,plain,
% 1.37/1.55 (~until2p29(s68)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10538, 10534])).
% 1.37/1.55 tff(10540,plain,
% 1.37/1.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s67, s68)) | until2p29(s68) | (~xuntil2p30(s67)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s67, s68)) | until2p29(s68) | (~xuntil2p30(s67)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10541,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s67, s68)) | until2p29(s68) | (~xuntil2p30(s67)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10542,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s67, s68)) | until2p29(s68) | (~xuntil2p30(s67))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10541, 10540])).
% 1.37/1.55 tff(10543,plain,
% 1.37/1.55 (until2p29(s68) | (~xuntil2p30(s67))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10542, 5805, 10229])).
% 1.37/1.55 tff(10544,plain,
% 1.37/1.55 (~xuntil2p30(s67)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10543, 10539])).
% 1.37/1.55 tff(10545,plain,
% 1.37/1.55 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s67) | xuntil2p30(s67) | (~until2p29(s67)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s67) | xuntil2p30(s67) | (~until2p29(s67)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10546,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s67) | xuntil2p30(s67) | (~until2p29(s67)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10547,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s67) | xuntil2p30(s67) | (~until2p29(s67))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10546, 10545])).
% 1.37/1.55 tff(10548,plain,
% 1.37/1.55 (xuntil2p30(s67) | (~until2p29(s67))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10547, 10214, 8333])).
% 1.37/1.55 tff(10549,plain,
% 1.37/1.55 (~until2p29(s67)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10548, 10544])).
% 1.37/1.55 tff(10550,plain,
% 1.37/1.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s66, s67)) | until2p29(s67) | (~xuntil2p30(s66)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s66, s67)) | until2p29(s67) | (~xuntil2p30(s66)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10551,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s66, s67)) | until2p29(s67) | (~xuntil2p30(s66)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10552,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s66, s67)) | until2p29(s67) | (~xuntil2p30(s66))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10551, 10550])).
% 1.37/1.55 tff(10553,plain,
% 1.37/1.55 (until2p29(s67) | (~xuntil2p30(s66))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10552, 5730, 10229])).
% 1.37/1.55 tff(10554,plain,
% 1.37/1.55 (~xuntil2p30(s66)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10553, 10549])).
% 1.37/1.55 tff(10555,plain,
% 1.37/1.55 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s66) | xuntil2p30(s66) | (~until2p29(s66)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s66) | xuntil2p30(s66) | (~until2p29(s66)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10556,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s66) | xuntil2p30(s66) | (~until2p29(s66)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10557,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s66) | xuntil2p30(s66) | (~until2p29(s66))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10556, 10555])).
% 1.37/1.55 tff(10558,plain,
% 1.37/1.55 (xuntil2p30(s66) | (~until2p29(s66))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10557, 10214, 8342])).
% 1.37/1.55 tff(10559,plain,
% 1.37/1.55 (~until2p29(s66)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10558, 10554])).
% 1.37/1.55 tff(10560,plain,
% 1.37/1.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s65, s66)) | until2p29(s66) | (~xuntil2p30(s65)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s65, s66)) | until2p29(s66) | (~xuntil2p30(s65)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10561,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s65, s66)) | until2p29(s66) | (~xuntil2p30(s65)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10562,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s65, s66)) | until2p29(s66) | (~xuntil2p30(s65))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10561, 10560])).
% 1.37/1.55 tff(10563,plain,
% 1.37/1.55 (until2p29(s66) | (~xuntil2p30(s65))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10562, 5666, 10229])).
% 1.37/1.55 tff(10564,plain,
% 1.37/1.55 (~xuntil2p30(s65)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10563, 10559])).
% 1.37/1.55 tff(10565,plain,
% 1.37/1.55 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s65) | xuntil2p30(s65) | (~until2p29(s65)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s65) | xuntil2p30(s65) | (~until2p29(s65)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10566,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s65) | xuntil2p30(s65) | (~until2p29(s65)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10567,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s65) | xuntil2p30(s65) | (~until2p29(s65))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10566, 10565])).
% 1.37/1.55 tff(10568,plain,
% 1.37/1.55 (xuntil2p30(s65) | (~until2p29(s65))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10567, 10214, 8346])).
% 1.37/1.55 tff(10569,plain,
% 1.37/1.55 (~until2p29(s65)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10568, 10564])).
% 1.37/1.55 tff(10570,plain,
% 1.37/1.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s64, s65)) | until2p29(s65) | (~xuntil2p30(s64)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s64, s65)) | until2p29(s65) | (~xuntil2p30(s64)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10571,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s64, s65)) | until2p29(s65) | (~xuntil2p30(s64)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10572,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s64, s65)) | until2p29(s65) | (~xuntil2p30(s64))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10571, 10570])).
% 1.37/1.55 tff(10573,plain,
% 1.37/1.55 (until2p29(s65) | (~xuntil2p30(s64))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10572, 5571, 10229])).
% 1.37/1.55 tff(10574,plain,
% 1.37/1.55 (~xuntil2p30(s64)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10573, 10569])).
% 1.37/1.55 tff(10575,plain,
% 1.37/1.55 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s64) | xuntil2p30(s64) | (~until2p29(s64)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s64) | xuntil2p30(s64) | (~until2p29(s64)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10576,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s64) | xuntil2p30(s64) | (~until2p29(s64)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10577,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s64) | xuntil2p30(s64) | (~until2p29(s64))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10576, 10575])).
% 1.37/1.55 tff(10578,plain,
% 1.37/1.55 (xuntil2p30(s64) | (~until2p29(s64))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10577, 10214, 9700])).
% 1.37/1.55 tff(10579,plain,
% 1.37/1.55 (~until2p29(s64)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10578, 10574])).
% 1.37/1.55 tff(10580,plain,
% 1.37/1.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s63, s64)) | until2p29(s64) | (~xuntil2p30(s63)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s63, s64)) | until2p29(s64) | (~xuntil2p30(s63)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10581,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s63, s64)) | until2p29(s64) | (~xuntil2p30(s63)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10582,plain,
% 1.37/1.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s63, s64)) | until2p29(s64) | (~xuntil2p30(s63))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10581, 10580])).
% 1.37/1.55 tff(10583,plain,
% 1.37/1.55 (until2p29(s64) | (~xuntil2p30(s63))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10582, 5510, 10229])).
% 1.37/1.55 tff(10584,plain,
% 1.37/1.55 (~xuntil2p30(s63)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10583, 10579])).
% 1.37/1.55 tff(10585,plain,
% 1.37/1.55 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s63) | xuntil2p30(s63) | (~until2p29(s63)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s63) | xuntil2p30(s63) | (~until2p29(s63)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(10586,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s63) | xuntil2p30(s63) | (~until2p29(s63)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(10587,plain,
% 1.37/1.55 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s63) | xuntil2p30(s63) | (~until2p29(s63))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[10586, 10585])).
% 1.37/1.55 tff(10588,plain,
% 1.37/1.55 (xuntil2p30(s63) | (~until2p29(s63))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10587, 10214, 8362])).
% 1.37/1.55 tff(10589,plain,
% 1.37/1.55 (~until2p29(s63)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[10588, 10584])).
% 1.37/1.55 tff(10590,plain,
% 1.37/1.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s62, s63)) | until2p29(s63) | (~xuntil2p30(s62)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s62, s63)) | until2p29(s63) | (~xuntil2p30(s62)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10591,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s62, s63)) | until2p29(s63) | (~xuntil2p30(s62)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10592,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s62, s63)) | until2p29(s63) | (~xuntil2p30(s62))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10591, 10590])).
% 1.37/1.56 tff(10593,plain,
% 1.37/1.56 (until2p29(s63) | (~xuntil2p30(s62))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10592, 5432, 10229])).
% 1.37/1.56 tff(10594,plain,
% 1.37/1.56 (~xuntil2p30(s62)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10593, 10589])).
% 1.37/1.56 tff(10595,plain,
% 1.37/1.56 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s62) | xuntil2p30(s62) | (~until2p29(s62)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s62) | xuntil2p30(s62) | (~until2p29(s62)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10596,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s62) | xuntil2p30(s62) | (~until2p29(s62)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10597,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s62) | xuntil2p30(s62) | (~until2p29(s62))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10596, 10595])).
% 1.37/1.56 tff(10598,plain,
% 1.37/1.56 (xuntil2p30(s62) | (~until2p29(s62))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10597, 10214, 8371])).
% 1.37/1.56 tff(10599,plain,
% 1.37/1.56 (~until2p29(s62)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10598, 10594])).
% 1.37/1.56 tff(10600,plain,
% 1.37/1.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s61, s62)) | until2p29(s62) | (~xuntil2p30(s61)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s61, s62)) | until2p29(s62) | (~xuntil2p30(s61)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10601,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s61, s62)) | until2p29(s62) | (~xuntil2p30(s61)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10602,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s61, s62)) | until2p29(s62) | (~xuntil2p30(s61))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10601, 10600])).
% 1.37/1.56 tff(10603,plain,
% 1.37/1.56 (until2p29(s62) | (~xuntil2p30(s61))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10602, 5333, 10229])).
% 1.37/1.56 tff(10604,plain,
% 1.37/1.56 (~xuntil2p30(s61)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10603, 10599])).
% 1.37/1.56 tff(10605,plain,
% 1.37/1.56 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s61) | xuntil2p30(s61) | (~until2p29(s61)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s61) | xuntil2p30(s61) | (~until2p29(s61)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10606,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s61) | xuntil2p30(s61) | (~until2p29(s61)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10607,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s61) | xuntil2p30(s61) | (~until2p29(s61))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10606, 10605])).
% 1.37/1.56 tff(10608,plain,
% 1.37/1.56 (xuntil2p30(s61) | (~until2p29(s61))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10607, 10214, 8375])).
% 1.37/1.56 tff(10609,plain,
% 1.37/1.56 (~until2p29(s61)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10608, 10604])).
% 1.37/1.56 tff(10610,plain,
% 1.37/1.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s60, s61)) | until2p29(s61) | (~xuntil2p30(s60)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s60, s61)) | until2p29(s61) | (~xuntil2p30(s60)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10611,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s60, s61)) | until2p29(s61) | (~xuntil2p30(s60)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10612,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s60, s61)) | until2p29(s61) | (~xuntil2p30(s60))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10611, 10610])).
% 1.37/1.56 tff(10613,plain,
% 1.37/1.56 (until2p29(s61) | (~xuntil2p30(s60))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10612, 5266, 10229])).
% 1.37/1.56 tff(10614,plain,
% 1.37/1.56 (~xuntil2p30(s60)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10613, 10609])).
% 1.37/1.56 tff(10615,plain,
% 1.37/1.56 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s60) | xuntil2p30(s60) | (~until2p29(s60)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s60) | xuntil2p30(s60) | (~until2p29(s60)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10616,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s60) | xuntil2p30(s60) | (~until2p29(s60)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10617,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s60) | xuntil2p30(s60) | (~until2p29(s60))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10616, 10615])).
% 1.37/1.56 tff(10618,plain,
% 1.37/1.56 (xuntil2p30(s60) | (~until2p29(s60))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10617, 10214, 9646])).
% 1.37/1.56 tff(10619,plain,
% 1.37/1.56 (~until2p29(s60)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10618, 10614])).
% 1.37/1.56 tff(10620,plain,
% 1.37/1.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s59, s60)) | until2p29(s60) | (~xuntil2p30(s59)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s59, s60)) | until2p29(s60) | (~xuntil2p30(s59)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10621,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s59, s60)) | until2p29(s60) | (~xuntil2p30(s59)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10622,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s59, s60)) | until2p29(s60) | (~xuntil2p30(s59))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10621, 10620])).
% 1.37/1.56 tff(10623,plain,
% 1.37/1.56 (until2p29(s60) | (~xuntil2p30(s59))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10622, 5177, 10229])).
% 1.37/1.56 tff(10624,plain,
% 1.37/1.56 (~xuntil2p30(s59)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10623, 10619])).
% 1.37/1.56 tff(10625,plain,
% 1.37/1.56 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s59) | xuntil2p30(s59) | (~until2p29(s59)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s59) | xuntil2p30(s59) | (~until2p29(s59)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10626,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s59) | xuntil2p30(s59) | (~until2p29(s59)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10627,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s59) | xuntil2p30(s59) | (~until2p29(s59))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10626, 10625])).
% 1.37/1.56 tff(10628,plain,
% 1.37/1.56 (xuntil2p30(s59) | (~until2p29(s59))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10627, 10214, 8391])).
% 1.37/1.56 tff(10629,plain,
% 1.37/1.56 (~until2p29(s59)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10628, 10624])).
% 1.37/1.56 tff(10630,plain,
% 1.37/1.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s58, s59)) | until2p29(s59) | (~xuntil2p30(s58)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s58, s59)) | until2p29(s59) | (~xuntil2p30(s58)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10631,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s58, s59)) | until2p29(s59) | (~xuntil2p30(s58)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10632,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s58, s59)) | until2p29(s59) | (~xuntil2p30(s58))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10631, 10630])).
% 1.37/1.56 tff(10633,plain,
% 1.37/1.56 (until2p29(s59) | (~xuntil2p30(s58))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10632, 5102, 10229])).
% 1.37/1.56 tff(10634,plain,
% 1.37/1.56 (~xuntil2p30(s58)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10633, 10629])).
% 1.37/1.56 tff(10635,plain,
% 1.37/1.56 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s58) | xuntil2p30(s58) | (~until2p29(s58)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s58) | xuntil2p30(s58) | (~until2p29(s58)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10636,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s58) | xuntil2p30(s58) | (~until2p29(s58)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10637,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s58) | xuntil2p30(s58) | (~until2p29(s58))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10636, 10635])).
% 1.37/1.56 tff(10638,plain,
% 1.37/1.56 (xuntil2p30(s58) | (~until2p29(s58))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10637, 10214, 8400])).
% 1.37/1.56 tff(10639,plain,
% 1.37/1.56 (~until2p29(s58)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10638, 10634])).
% 1.37/1.56 tff(10640,plain,
% 1.37/1.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s57, s58)) | until2p29(s58) | (~xuntil2p30(s57)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s57, s58)) | until2p29(s58) | (~xuntil2p30(s57)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10641,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s57, s58)) | until2p29(s58) | (~xuntil2p30(s57)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10642,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s57, s58)) | until2p29(s58) | (~xuntil2p30(s57))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10641, 10640])).
% 1.37/1.56 tff(10643,plain,
% 1.37/1.56 (until2p29(s58) | (~xuntil2p30(s57))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10642, 5038, 10229])).
% 1.37/1.56 tff(10644,plain,
% 1.37/1.56 (~xuntil2p30(s57)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10643, 10639])).
% 1.37/1.56 tff(10645,plain,
% 1.37/1.56 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s57) | xuntil2p30(s57) | (~until2p29(s57)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s57) | xuntil2p30(s57) | (~until2p29(s57)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10646,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s57) | xuntil2p30(s57) | (~until2p29(s57)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10647,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s57) | xuntil2p30(s57) | (~until2p29(s57))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10646, 10645])).
% 1.37/1.56 tff(10648,plain,
% 1.37/1.56 (xuntil2p30(s57) | (~until2p29(s57))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10647, 10214, 8404])).
% 1.37/1.56 tff(10649,plain,
% 1.37/1.56 (~until2p29(s57)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10648, 10644])).
% 1.37/1.56 tff(10650,plain,
% 1.37/1.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s56, s57)) | until2p29(s57) | (~xuntil2p30(s56)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s56, s57)) | until2p29(s57) | (~xuntil2p30(s56)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10651,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s56, s57)) | until2p29(s57) | (~xuntil2p30(s56)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10652,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s56, s57)) | until2p29(s57) | (~xuntil2p30(s56))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10651, 10650])).
% 1.37/1.56 tff(10653,plain,
% 1.37/1.56 (until2p29(s57) | (~xuntil2p30(s56))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10652, 4943, 10229])).
% 1.37/1.56 tff(10654,plain,
% 1.37/1.56 (~xuntil2p30(s56)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10653, 10649])).
% 1.37/1.56 tff(10655,plain,
% 1.37/1.56 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s56) | xuntil2p30(s56) | (~until2p29(s56)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s56) | xuntil2p30(s56) | (~until2p29(s56)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10656,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s56) | xuntil2p30(s56) | (~until2p29(s56)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10657,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s56) | xuntil2p30(s56) | (~until2p29(s56))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10656, 10655])).
% 1.37/1.56 tff(10658,plain,
% 1.37/1.56 (xuntil2p30(s56) | (~until2p29(s56))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10657, 10214, 9592])).
% 1.37/1.56 tff(10659,plain,
% 1.37/1.56 (~until2p29(s56)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10658, 10654])).
% 1.37/1.56 tff(10660,plain,
% 1.37/1.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s55, s56)) | until2p29(s56) | (~xuntil2p30(s55)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s55, s56)) | until2p29(s56) | (~xuntil2p30(s55)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10661,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s55, s56)) | until2p29(s56) | (~xuntil2p30(s55)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10662,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s55, s56)) | until2p29(s56) | (~xuntil2p30(s55))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10661, 10660])).
% 1.37/1.56 tff(10663,plain,
% 1.37/1.56 (until2p29(s56) | (~xuntil2p30(s55))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10662, 4882, 10229])).
% 1.37/1.56 tff(10664,plain,
% 1.37/1.56 (~xuntil2p30(s55)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10663, 10659])).
% 1.37/1.56 tff(10665,plain,
% 1.37/1.56 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s55) | xuntil2p30(s55) | (~until2p29(s55)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s55) | xuntil2p30(s55) | (~until2p29(s55)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10666,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s55) | xuntil2p30(s55) | (~until2p29(s55)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10667,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s55) | xuntil2p30(s55) | (~until2p29(s55))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10666, 10665])).
% 1.37/1.56 tff(10668,plain,
% 1.37/1.56 (xuntil2p30(s55) | (~until2p29(s55))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10667, 10214, 8420])).
% 1.37/1.56 tff(10669,plain,
% 1.37/1.56 (~until2p29(s55)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10668, 10664])).
% 1.37/1.56 tff(10670,plain,
% 1.37/1.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s54, s55)) | until2p29(s55) | (~xuntil2p30(s54)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s54, s55)) | until2p29(s55) | (~xuntil2p30(s54)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10671,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s54, s55)) | until2p29(s55) | (~xuntil2p30(s54)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10672,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s54, s55)) | until2p29(s55) | (~xuntil2p30(s54))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10671, 10670])).
% 1.37/1.56 tff(10673,plain,
% 1.37/1.56 (until2p29(s55) | (~xuntil2p30(s54))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10672, 4804, 10229])).
% 1.37/1.56 tff(10674,plain,
% 1.37/1.56 (~xuntil2p30(s54)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10673, 10669])).
% 1.37/1.56 tff(10675,plain,
% 1.37/1.56 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s54) | xuntil2p30(s54) | (~until2p29(s54)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s54) | xuntil2p30(s54) | (~until2p29(s54)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10676,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s54) | xuntil2p30(s54) | (~until2p29(s54)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10677,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s54) | xuntil2p30(s54) | (~until2p29(s54))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10676, 10675])).
% 1.37/1.56 tff(10678,plain,
% 1.37/1.56 (xuntil2p30(s54) | (~until2p29(s54))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10677, 10214, 8429])).
% 1.37/1.56 tff(10679,plain,
% 1.37/1.56 (~until2p29(s54)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10678, 10674])).
% 1.37/1.56 tff(10680,plain,
% 1.37/1.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s53, s54)) | until2p29(s54) | (~xuntil2p30(s53)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s53, s54)) | until2p29(s54) | (~xuntil2p30(s53)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10681,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s53, s54)) | until2p29(s54) | (~xuntil2p30(s53)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10682,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s53, s54)) | until2p29(s54) | (~xuntil2p30(s53))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10681, 10680])).
% 1.37/1.56 tff(10683,plain,
% 1.37/1.56 (until2p29(s54) | (~xuntil2p30(s53))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10682, 4705, 10229])).
% 1.37/1.56 tff(10684,plain,
% 1.37/1.56 (~xuntil2p30(s53)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10683, 10679])).
% 1.37/1.56 tff(10685,plain,
% 1.37/1.56 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s53) | xuntil2p30(s53) | (~until2p29(s53)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s53) | xuntil2p30(s53) | (~until2p29(s53)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10686,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s53) | xuntil2p30(s53) | (~until2p29(s53)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10687,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s53) | xuntil2p30(s53) | (~until2p29(s53))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10686, 10685])).
% 1.37/1.56 tff(10688,plain,
% 1.37/1.56 (xuntil2p30(s53) | (~until2p29(s53))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10687, 10214, 8433])).
% 1.37/1.56 tff(10689,plain,
% 1.37/1.56 (~until2p29(s53)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10688, 10684])).
% 1.37/1.56 tff(10690,plain,
% 1.37/1.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s52, s53)) | until2p29(s53) | (~xuntil2p30(s52)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s52, s53)) | until2p29(s53) | (~xuntil2p30(s52)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10691,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s52, s53)) | until2p29(s53) | (~xuntil2p30(s52)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10692,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s52, s53)) | until2p29(s53) | (~xuntil2p30(s52))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10691, 10690])).
% 1.37/1.56 tff(10693,plain,
% 1.37/1.56 (until2p29(s53) | (~xuntil2p30(s52))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10692, 4638, 10229])).
% 1.37/1.56 tff(10694,plain,
% 1.37/1.56 (~xuntil2p30(s52)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10693, 10689])).
% 1.37/1.56 tff(10695,plain,
% 1.37/1.56 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s52) | xuntil2p30(s52) | (~until2p29(s52)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s52) | xuntil2p30(s52) | (~until2p29(s52)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10696,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s52) | xuntil2p30(s52) | (~until2p29(s52)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10697,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s52) | xuntil2p30(s52) | (~until2p29(s52))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10696, 10695])).
% 1.37/1.56 tff(10698,plain,
% 1.37/1.56 (xuntil2p30(s52) | (~until2p29(s52))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10697, 10214, 9538])).
% 1.37/1.56 tff(10699,plain,
% 1.37/1.56 (~until2p29(s52)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10698, 10694])).
% 1.37/1.56 tff(10700,plain,
% 1.37/1.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s51, s52)) | until2p29(s52) | (~xuntil2p30(s51)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s51, s52)) | until2p29(s52) | (~xuntil2p30(s51)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10701,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s51, s52)) | until2p29(s52) | (~xuntil2p30(s51)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10702,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s51, s52)) | until2p29(s52) | (~xuntil2p30(s51))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10701, 10700])).
% 1.37/1.56 tff(10703,plain,
% 1.37/1.56 (until2p29(s52) | (~xuntil2p30(s51))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10702, 4549, 10229])).
% 1.37/1.56 tff(10704,plain,
% 1.37/1.56 (~xuntil2p30(s51)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10703, 10699])).
% 1.37/1.56 tff(10705,plain,
% 1.37/1.56 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s51) | xuntil2p30(s51) | (~until2p29(s51)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s51) | xuntil2p30(s51) | (~until2p29(s51)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10706,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s51) | xuntil2p30(s51) | (~until2p29(s51)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10707,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s51) | xuntil2p30(s51) | (~until2p29(s51))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10706, 10705])).
% 1.37/1.56 tff(10708,plain,
% 1.37/1.56 (xuntil2p30(s51) | (~until2p29(s51))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10707, 10214, 8449])).
% 1.37/1.56 tff(10709,plain,
% 1.37/1.56 (~until2p29(s51)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10708, 10704])).
% 1.37/1.56 tff(10710,plain,
% 1.37/1.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s50, s51)) | until2p29(s51) | (~xuntil2p30(s50)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s50, s51)) | until2p29(s51) | (~xuntil2p30(s50)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10711,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s50, s51)) | until2p29(s51) | (~xuntil2p30(s50)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10712,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s50, s51)) | until2p29(s51) | (~xuntil2p30(s50))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10711, 10710])).
% 1.37/1.56 tff(10713,plain,
% 1.37/1.56 (until2p29(s51) | (~xuntil2p30(s50))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10712, 4474, 10229])).
% 1.37/1.56 tff(10714,plain,
% 1.37/1.56 (~xuntil2p30(s50)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10713, 10709])).
% 1.37/1.56 tff(10715,plain,
% 1.37/1.56 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s50) | xuntil2p30(s50) | (~until2p29(s50)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s50) | xuntil2p30(s50) | (~until2p29(s50)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10716,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s50) | xuntil2p30(s50) | (~until2p29(s50)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10717,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s50) | xuntil2p30(s50) | (~until2p29(s50))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10716, 10715])).
% 1.37/1.56 tff(10718,plain,
% 1.37/1.56 (xuntil2p30(s50) | (~until2p29(s50))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10717, 10214, 8458])).
% 1.37/1.56 tff(10719,plain,
% 1.37/1.56 (~until2p29(s50)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10718, 10714])).
% 1.37/1.56 tff(10720,plain,
% 1.37/1.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s49, s50)) | until2p29(s50) | (~xuntil2p30(s49)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s49, s50)) | until2p29(s50) | (~xuntil2p30(s49)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10721,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s49, s50)) | until2p29(s50) | (~xuntil2p30(s49)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10722,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s49, s50)) | until2p29(s50) | (~xuntil2p30(s49))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10721, 10720])).
% 1.37/1.56 tff(10723,plain,
% 1.37/1.56 (until2p29(s50) | (~xuntil2p30(s49))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10722, 4410, 10229])).
% 1.37/1.56 tff(10724,plain,
% 1.37/1.56 (~xuntil2p30(s49)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10723, 10719])).
% 1.37/1.56 tff(10725,plain,
% 1.37/1.56 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s49) | xuntil2p30(s49) | (~until2p29(s49)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s49) | xuntil2p30(s49) | (~until2p29(s49)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10726,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s49) | xuntil2p30(s49) | (~until2p29(s49)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10727,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s49) | xuntil2p30(s49) | (~until2p29(s49))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10726, 10725])).
% 1.37/1.56 tff(10728,plain,
% 1.37/1.56 (xuntil2p30(s49) | (~until2p29(s49))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10727, 10214, 8462])).
% 1.37/1.56 tff(10729,plain,
% 1.37/1.56 (~until2p29(s49)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10728, 10724])).
% 1.37/1.56 tff(10730,plain,
% 1.37/1.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s48, s49)) | until2p29(s49) | (~xuntil2p30(s48)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s48, s49)) | until2p29(s49) | (~xuntil2p30(s48)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10731,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s48, s49)) | until2p29(s49) | (~xuntil2p30(s48)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10732,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s48, s49)) | until2p29(s49) | (~xuntil2p30(s48))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10731, 10730])).
% 1.37/1.56 tff(10733,plain,
% 1.37/1.56 (until2p29(s49) | (~xuntil2p30(s48))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10732, 4315, 10229])).
% 1.37/1.56 tff(10734,plain,
% 1.37/1.56 (~xuntil2p30(s48)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10733, 10729])).
% 1.37/1.56 tff(10735,plain,
% 1.37/1.56 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s48) | xuntil2p30(s48) | (~until2p29(s48)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s48) | xuntil2p30(s48) | (~until2p29(s48)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10736,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s48) | xuntil2p30(s48) | (~until2p29(s48)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10737,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s48) | xuntil2p30(s48) | (~until2p29(s48))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10736, 10735])).
% 1.37/1.56 tff(10738,plain,
% 1.37/1.56 (xuntil2p30(s48) | (~until2p29(s48))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10737, 10214, 9484])).
% 1.37/1.56 tff(10739,plain,
% 1.37/1.56 (~until2p29(s48)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10738, 10734])).
% 1.37/1.56 tff(10740,plain,
% 1.37/1.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s47, s48)) | until2p29(s48) | (~xuntil2p30(s47)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s47, s48)) | until2p29(s48) | (~xuntil2p30(s47)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10741,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s47, s48)) | until2p29(s48) | (~xuntil2p30(s47)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10742,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s47, s48)) | until2p29(s48) | (~xuntil2p30(s47))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10741, 10740])).
% 1.37/1.56 tff(10743,plain,
% 1.37/1.56 (until2p29(s48) | (~xuntil2p30(s47))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10742, 4254, 10229])).
% 1.37/1.56 tff(10744,plain,
% 1.37/1.56 (~xuntil2p30(s47)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10743, 10739])).
% 1.37/1.56 tff(10745,plain,
% 1.37/1.56 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s47) | xuntil2p30(s47) | (~until2p29(s47)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s47) | xuntil2p30(s47) | (~until2p29(s47)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10746,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s47) | xuntil2p30(s47) | (~until2p29(s47)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10747,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s47) | xuntil2p30(s47) | (~until2p29(s47))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10746, 10745])).
% 1.37/1.56 tff(10748,plain,
% 1.37/1.56 (xuntil2p30(s47) | (~until2p29(s47))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10747, 10214, 8478])).
% 1.37/1.56 tff(10749,plain,
% 1.37/1.56 (~until2p29(s47)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10748, 10744])).
% 1.37/1.56 tff(10750,plain,
% 1.37/1.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s46, s47)) | until2p29(s47) | (~xuntil2p30(s46)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s46, s47)) | until2p29(s47) | (~xuntil2p30(s46)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10751,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s46, s47)) | until2p29(s47) | (~xuntil2p30(s46)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10752,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s46, s47)) | until2p29(s47) | (~xuntil2p30(s46))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10751, 10750])).
% 1.37/1.56 tff(10753,plain,
% 1.37/1.56 (until2p29(s47) | (~xuntil2p30(s46))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10752, 4176, 10229])).
% 1.37/1.56 tff(10754,plain,
% 1.37/1.56 (~xuntil2p30(s46)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10753, 10749])).
% 1.37/1.56 tff(10755,plain,
% 1.37/1.56 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s46) | xuntil2p30(s46) | (~until2p29(s46)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s46) | xuntil2p30(s46) | (~until2p29(s46)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10756,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s46) | xuntil2p30(s46) | (~until2p29(s46)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10757,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s46) | xuntil2p30(s46) | (~until2p29(s46))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10756, 10755])).
% 1.37/1.56 tff(10758,plain,
% 1.37/1.56 (xuntil2p30(s46) | (~until2p29(s46))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10757, 10214, 8487])).
% 1.37/1.56 tff(10759,plain,
% 1.37/1.56 (~until2p29(s46)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10758, 10754])).
% 1.37/1.56 tff(10760,plain,
% 1.37/1.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s45, s46)) | until2p29(s46) | (~xuntil2p30(s45)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s45, s46)) | until2p29(s46) | (~xuntil2p30(s45)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10761,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s45, s46)) | until2p29(s46) | (~xuntil2p30(s45)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10762,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s45, s46)) | until2p29(s46) | (~xuntil2p30(s45))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10761, 10760])).
% 1.37/1.56 tff(10763,plain,
% 1.37/1.56 (until2p29(s46) | (~xuntil2p30(s45))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10762, 4077, 10229])).
% 1.37/1.56 tff(10764,plain,
% 1.37/1.56 (~xuntil2p30(s45)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10763, 10759])).
% 1.37/1.56 tff(10765,plain,
% 1.37/1.56 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s45) | xuntil2p30(s45) | (~until2p29(s45)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s45) | xuntil2p30(s45) | (~until2p29(s45)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10766,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s45) | xuntil2p30(s45) | (~until2p29(s45)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10767,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s45) | xuntil2p30(s45) | (~until2p29(s45))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10766, 10765])).
% 1.37/1.56 tff(10768,plain,
% 1.37/1.56 (xuntil2p30(s45) | (~until2p29(s45))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10767, 10214, 8491])).
% 1.37/1.56 tff(10769,plain,
% 1.37/1.56 (~until2p29(s45)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10768, 10764])).
% 1.37/1.56 tff(10770,plain,
% 1.37/1.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s44, s45)) | until2p29(s45) | (~xuntil2p30(s44)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s44, s45)) | until2p29(s45) | (~xuntil2p30(s44)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10771,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s44, s45)) | until2p29(s45) | (~xuntil2p30(s44)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10772,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s44, s45)) | until2p29(s45) | (~xuntil2p30(s44))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10771, 10770])).
% 1.37/1.56 tff(10773,plain,
% 1.37/1.56 (until2p29(s45) | (~xuntil2p30(s44))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10772, 4010, 10229])).
% 1.37/1.56 tff(10774,plain,
% 1.37/1.56 (~xuntil2p30(s44)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10773, 10769])).
% 1.37/1.56 tff(10775,plain,
% 1.37/1.56 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s44) | xuntil2p30(s44) | (~until2p29(s44)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s44) | xuntil2p30(s44) | (~until2p29(s44)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10776,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s44) | xuntil2p30(s44) | (~until2p29(s44)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10777,plain,
% 1.37/1.56 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s44) | xuntil2p30(s44) | (~until2p29(s44))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10776, 10775])).
% 1.37/1.56 tff(10778,plain,
% 1.37/1.56 (xuntil2p30(s44) | (~until2p29(s44))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10777, 10214, 9430])).
% 1.37/1.56 tff(10779,plain,
% 1.37/1.56 (~until2p29(s44)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10778, 10774])).
% 1.37/1.56 tff(10780,plain,
% 1.37/1.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s43, s44)) | until2p29(s44) | (~xuntil2p30(s43)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s43, s44)) | until2p29(s44) | (~xuntil2p30(s43)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(10781,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s43, s44)) | until2p29(s44) | (~xuntil2p30(s43)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(10782,plain,
% 1.37/1.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s43, s44)) | until2p29(s44) | (~xuntil2p30(s43))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[10781, 10780])).
% 1.37/1.56 tff(10783,plain,
% 1.37/1.56 (until2p29(s44) | (~xuntil2p30(s43))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10782, 3888, 10229])).
% 1.37/1.56 tff(10784,plain,
% 1.37/1.56 (~xuntil2p30(s43)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[10783, 10779])).
% 1.37/1.56 tff(10785,plain,
% 1.37/1.56 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s43) | xuntil2p30(s43) | (~until2p29(s43)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s43) | xuntil2p30(s43) | (~until2p29(s43)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(10786,plain,
% 1.37/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s43) | xuntil2p30(s43) | (~until2p29(s43)))),
% 1.37/1.57 inference(quant_inst,[status(thm)],[])).
% 1.37/1.57 tff(10787,plain,
% 1.37/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s43) | xuntil2p30(s43) | (~until2p29(s43))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[10786, 10785])).
% 1.37/1.57 tff(10788,plain,
% 1.37/1.57 (xuntil2p30(s43) | (~until2p29(s43))),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[10787, 10214, 8500])).
% 1.37/1.57 tff(10789,plain,
% 1.37/1.57 (~until2p29(s43)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[10788, 10784])).
% 1.37/1.57 tff(10790,plain,
% 1.37/1.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s42, s43)) | until2p29(s43) | (~xuntil2p30(s42)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s42, s43)) | until2p29(s43) | (~xuntil2p30(s42)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(10791,plain,
% 1.37/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s42, s43)) | until2p29(s43) | (~xuntil2p30(s42)))),
% 1.37/1.57 inference(quant_inst,[status(thm)],[])).
% 1.37/1.57 tff(10792,plain,
% 1.37/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s42, s43)) | until2p29(s43) | (~xuntil2p30(s42))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[10791, 10790])).
% 1.37/1.57 tff(10793,plain,
% 1.37/1.57 (until2p29(s43) | (~xuntil2p30(s42))),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[10792, 3810, 10229])).
% 1.37/1.57 tff(10794,plain,
% 1.37/1.57 (~xuntil2p30(s42)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[10793, 10789])).
% 1.37/1.57 tff(10795,plain,
% 1.37/1.57 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s42) | xuntil2p30(s42) | (~until2p29(s42)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s42) | xuntil2p30(s42) | (~until2p29(s42)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(10796,plain,
% 1.37/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s42) | xuntil2p30(s42) | (~until2p29(s42)))),
% 1.37/1.57 inference(quant_inst,[status(thm)],[])).
% 1.37/1.57 tff(10797,plain,
% 1.37/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s42) | xuntil2p30(s42) | (~until2p29(s42))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[10796, 10795])).
% 1.37/1.57 tff(10798,plain,
% 1.37/1.57 (xuntil2p30(s42) | (~until2p29(s42))),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[10797, 10214, 8509])).
% 1.37/1.57 tff(10799,plain,
% 1.37/1.57 (~until2p29(s42)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[10798, 10794])).
% 1.37/1.57 tff(10800,plain,
% 1.37/1.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s41, s42)) | until2p29(s42) | (~xuntil2p30(s41)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s41, s42)) | until2p29(s42) | (~xuntil2p30(s41)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(10801,plain,
% 1.37/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s41, s42)) | until2p29(s42) | (~xuntil2p30(s41)))),
% 1.37/1.57 inference(quant_inst,[status(thm)],[])).
% 1.37/1.57 tff(10802,plain,
% 1.37/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s41, s42)) | until2p29(s42) | (~xuntil2p30(s41))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[10801, 10800])).
% 1.37/1.57 tff(10803,plain,
% 1.37/1.57 (until2p29(s42) | (~xuntil2p30(s41))),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[10802, 3711, 10229])).
% 1.37/1.57 tff(10804,plain,
% 1.37/1.57 (~xuntil2p30(s41)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[10803, 10799])).
% 1.37/1.57 tff(10805,plain,
% 1.37/1.57 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s41) | xuntil2p30(s41) | (~until2p29(s41)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s41) | xuntil2p30(s41) | (~until2p29(s41)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(10806,plain,
% 1.37/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s41) | xuntil2p30(s41) | (~until2p29(s41)))),
% 1.37/1.57 inference(quant_inst,[status(thm)],[])).
% 1.37/1.57 tff(10807,plain,
% 1.37/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s41) | xuntil2p30(s41) | (~until2p29(s41))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[10806, 10805])).
% 1.37/1.57 tff(10808,plain,
% 1.37/1.57 (xuntil2p30(s41) | (~until2p29(s41))),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[10807, 10214, 8513])).
% 1.37/1.57 tff(10809,plain,
% 1.37/1.57 (~until2p29(s41)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[10808, 10804])).
% 1.37/1.57 tff(10810,plain,
% 1.37/1.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s40, s41)) | until2p29(s41) | (~xuntil2p30(s40)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s40, s41)) | until2p29(s41) | (~xuntil2p30(s40)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(10811,plain,
% 1.37/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s40, s41)) | until2p29(s41) | (~xuntil2p30(s40)))),
% 1.37/1.57 inference(quant_inst,[status(thm)],[])).
% 1.37/1.57 tff(10812,plain,
% 1.37/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s40, s41)) | until2p29(s41) | (~xuntil2p30(s40))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[10811, 10810])).
% 1.37/1.57 tff(10813,plain,
% 1.37/1.57 (until2p29(s41) | (~xuntil2p30(s40))),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[10812, 3644, 10229])).
% 1.37/1.57 tff(10814,plain,
% 1.37/1.57 (~xuntil2p30(s40)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[10813, 10809])).
% 1.37/1.57 tff(10815,plain,
% 1.37/1.57 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s40) | xuntil2p30(s40) | (~until2p29(s40)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s40) | xuntil2p30(s40) | (~until2p29(s40)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(10816,plain,
% 1.37/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s40) | xuntil2p30(s40) | (~until2p29(s40)))),
% 1.37/1.57 inference(quant_inst,[status(thm)],[])).
% 1.37/1.57 tff(10817,plain,
% 1.37/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s40) | xuntil2p30(s40) | (~until2p29(s40))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[10816, 10815])).
% 1.37/1.57 tff(10818,plain,
% 1.37/1.57 (xuntil2p30(s40) | (~until2p29(s40))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10817, 10214, 9376])).
% 1.40/1.57 tff(10819,plain,
% 1.40/1.57 (~until2p29(s40)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10818, 10814])).
% 1.40/1.57 tff(10820,plain,
% 1.40/1.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s39, s40)) | until2p29(s40) | (~xuntil2p30(s39)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s39, s40)) | until2p29(s40) | (~xuntil2p30(s39)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10821,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s39, s40)) | until2p29(s40) | (~xuntil2p30(s39)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10822,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s39, s40)) | until2p29(s40) | (~xuntil2p30(s39))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10821, 10820])).
% 1.40/1.57 tff(10823,plain,
% 1.40/1.57 (until2p29(s40) | (~xuntil2p30(s39))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10822, 3555, 10229])).
% 1.40/1.57 tff(10824,plain,
% 1.40/1.57 (~xuntil2p30(s39)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10823, 10819])).
% 1.40/1.57 tff(10825,plain,
% 1.40/1.57 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s39) | xuntil2p30(s39) | (~until2p29(s39)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s39) | xuntil2p30(s39) | (~until2p29(s39)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10826,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s39) | xuntil2p30(s39) | (~until2p29(s39)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10827,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s39) | xuntil2p30(s39) | (~until2p29(s39))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10826, 10825])).
% 1.40/1.57 tff(10828,plain,
% 1.40/1.57 (xuntil2p30(s39) | (~until2p29(s39))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10827, 10214, 8529])).
% 1.40/1.57 tff(10829,plain,
% 1.40/1.57 (~until2p29(s39)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10828, 10824])).
% 1.40/1.57 tff(10830,plain,
% 1.40/1.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s38, s39)) | until2p29(s39) | (~xuntil2p30(s38)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s38, s39)) | until2p29(s39) | (~xuntil2p30(s38)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10831,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s38, s39)) | until2p29(s39) | (~xuntil2p30(s38)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10832,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s38, s39)) | until2p29(s39) | (~xuntil2p30(s38))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10831, 10830])).
% 1.40/1.57 tff(10833,plain,
% 1.40/1.57 (until2p29(s39) | (~xuntil2p30(s38))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10832, 3480, 10229])).
% 1.40/1.57 tff(10834,plain,
% 1.40/1.57 (~xuntil2p30(s38)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10833, 10829])).
% 1.40/1.57 tff(10835,plain,
% 1.40/1.57 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s38) | xuntil2p30(s38) | (~until2p29(s38)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s38) | xuntil2p30(s38) | (~until2p29(s38)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10836,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s38) | xuntil2p30(s38) | (~until2p29(s38)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10837,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s38) | xuntil2p30(s38) | (~until2p29(s38))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10836, 10835])).
% 1.40/1.57 tff(10838,plain,
% 1.40/1.57 (xuntil2p30(s38) | (~until2p29(s38))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10837, 10214, 8538])).
% 1.40/1.57 tff(10839,plain,
% 1.40/1.57 (~until2p29(s38)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10838, 10834])).
% 1.40/1.57 tff(10840,plain,
% 1.40/1.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s37, s38)) | until2p29(s38) | (~xuntil2p30(s37)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s37, s38)) | until2p29(s38) | (~xuntil2p30(s37)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10841,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s37, s38)) | until2p29(s38) | (~xuntil2p30(s37)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10842,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s37, s38)) | until2p29(s38) | (~xuntil2p30(s37))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10841, 10840])).
% 1.40/1.57 tff(10843,plain,
% 1.40/1.57 (until2p29(s38) | (~xuntil2p30(s37))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10842, 3416, 10229])).
% 1.40/1.57 tff(10844,plain,
% 1.40/1.57 (~xuntil2p30(s37)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10843, 10839])).
% 1.40/1.57 tff(10845,plain,
% 1.40/1.57 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s37) | xuntil2p30(s37) | (~until2p29(s37)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s37) | xuntil2p30(s37) | (~until2p29(s37)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10846,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s37) | xuntil2p30(s37) | (~until2p29(s37)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10847,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s37) | xuntil2p30(s37) | (~until2p29(s37))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10846, 10845])).
% 1.40/1.57 tff(10848,plain,
% 1.40/1.57 (xuntil2p30(s37) | (~until2p29(s37))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10847, 10214, 8542])).
% 1.40/1.57 tff(10849,plain,
% 1.40/1.57 (~until2p29(s37)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10848, 10844])).
% 1.40/1.57 tff(10850,plain,
% 1.40/1.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s36, s37)) | until2p29(s37) | (~xuntil2p30(s36)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s36, s37)) | until2p29(s37) | (~xuntil2p30(s36)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10851,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s36, s37)) | until2p29(s37) | (~xuntil2p30(s36)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10852,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s36, s37)) | until2p29(s37) | (~xuntil2p30(s36))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10851, 10850])).
% 1.40/1.57 tff(10853,plain,
% 1.40/1.57 (until2p29(s37) | (~xuntil2p30(s36))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10852, 3321, 10229])).
% 1.40/1.57 tff(10854,plain,
% 1.40/1.57 (~xuntil2p30(s36)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10853, 10849])).
% 1.40/1.57 tff(10855,plain,
% 1.40/1.57 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s36) | xuntil2p30(s36) | (~until2p29(s36)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s36) | xuntil2p30(s36) | (~until2p29(s36)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10856,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s36) | xuntil2p30(s36) | (~until2p29(s36)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10857,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s36) | xuntil2p30(s36) | (~until2p29(s36))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10856, 10855])).
% 1.40/1.57 tff(10858,plain,
% 1.40/1.57 (xuntil2p30(s36) | (~until2p29(s36))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10857, 10214, 9322])).
% 1.40/1.57 tff(10859,plain,
% 1.40/1.57 (~until2p29(s36)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10858, 10854])).
% 1.40/1.57 tff(10860,plain,
% 1.40/1.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s35, s36)) | until2p29(s36) | (~xuntil2p30(s35)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s35, s36)) | until2p29(s36) | (~xuntil2p30(s35)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10861,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s35, s36)) | until2p29(s36) | (~xuntil2p30(s35)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10862,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s35, s36)) | until2p29(s36) | (~xuntil2p30(s35))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10861, 10860])).
% 1.40/1.57 tff(10863,plain,
% 1.40/1.57 (until2p29(s36) | (~xuntil2p30(s35))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10862, 3260, 10229])).
% 1.40/1.57 tff(10864,plain,
% 1.40/1.57 (~xuntil2p30(s35)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10863, 10859])).
% 1.40/1.57 tff(10865,plain,
% 1.40/1.57 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s35) | xuntil2p30(s35) | (~until2p29(s35)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s35) | xuntil2p30(s35) | (~until2p29(s35)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10866,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s35) | xuntil2p30(s35) | (~until2p29(s35)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10867,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s35) | xuntil2p30(s35) | (~until2p29(s35))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10866, 10865])).
% 1.40/1.57 tff(10868,plain,
% 1.40/1.57 (xuntil2p30(s35) | (~until2p29(s35))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10867, 10214, 8558])).
% 1.40/1.57 tff(10869,plain,
% 1.40/1.57 (~until2p29(s35)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10868, 10864])).
% 1.40/1.57 tff(10870,plain,
% 1.40/1.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s34, s35)) | until2p29(s35) | (~xuntil2p30(s34)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s34, s35)) | until2p29(s35) | (~xuntil2p30(s34)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10871,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s34, s35)) | until2p29(s35) | (~xuntil2p30(s34)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10872,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s34, s35)) | until2p29(s35) | (~xuntil2p30(s34))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10871, 10870])).
% 1.40/1.57 tff(10873,plain,
% 1.40/1.57 (until2p29(s35) | (~xuntil2p30(s34))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10872, 3182, 10229])).
% 1.40/1.57 tff(10874,plain,
% 1.40/1.57 (~xuntil2p30(s34)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10873, 10869])).
% 1.40/1.57 tff(10875,plain,
% 1.40/1.57 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s34) | xuntil2p30(s34) | (~until2p29(s34)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s34) | xuntil2p30(s34) | (~until2p29(s34)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10876,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s34) | xuntil2p30(s34) | (~until2p29(s34)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10877,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s34) | xuntil2p30(s34) | (~until2p29(s34))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10876, 10875])).
% 1.40/1.57 tff(10878,plain,
% 1.40/1.57 (xuntil2p30(s34) | (~until2p29(s34))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10877, 10214, 8567])).
% 1.40/1.57 tff(10879,plain,
% 1.40/1.57 (~until2p29(s34)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10878, 10874])).
% 1.40/1.57 tff(10880,plain,
% 1.40/1.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s33, s34)) | until2p29(s34) | (~xuntil2p30(s33)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s33, s34)) | until2p29(s34) | (~xuntil2p30(s33)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10881,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s33, s34)) | until2p29(s34) | (~xuntil2p30(s33)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10882,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s33, s34)) | until2p29(s34) | (~xuntil2p30(s33))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10881, 10880])).
% 1.40/1.57 tff(10883,plain,
% 1.40/1.57 (until2p29(s34) | (~xuntil2p30(s33))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10882, 3083, 10229])).
% 1.40/1.57 tff(10884,plain,
% 1.40/1.57 (~xuntil2p30(s33)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10883, 10879])).
% 1.40/1.57 tff(10885,plain,
% 1.40/1.57 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s33) | xuntil2p30(s33) | (~until2p29(s33)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s33) | xuntil2p30(s33) | (~until2p29(s33)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10886,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s33) | xuntil2p30(s33) | (~until2p29(s33)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10887,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s33) | xuntil2p30(s33) | (~until2p29(s33))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10886, 10885])).
% 1.40/1.57 tff(10888,plain,
% 1.40/1.57 (xuntil2p30(s33) | (~until2p29(s33))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10887, 10214, 8571])).
% 1.40/1.57 tff(10889,plain,
% 1.40/1.57 (~until2p29(s33)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10888, 10884])).
% 1.40/1.57 tff(10890,plain,
% 1.40/1.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s32, s33)) | until2p29(s33) | (~xuntil2p30(s32)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s32, s33)) | until2p29(s33) | (~xuntil2p30(s32)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10891,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s32, s33)) | until2p29(s33) | (~xuntil2p30(s32)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10892,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s32, s33)) | until2p29(s33) | (~xuntil2p30(s32))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10891, 10890])).
% 1.40/1.57 tff(10893,plain,
% 1.40/1.57 (until2p29(s33) | (~xuntil2p30(s32))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10892, 3016, 10229])).
% 1.40/1.57 tff(10894,plain,
% 1.40/1.57 (~xuntil2p30(s32)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10893, 10889])).
% 1.40/1.57 tff(10895,plain,
% 1.40/1.57 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s32) | xuntil2p30(s32) | (~until2p29(s32)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s32) | xuntil2p30(s32) | (~until2p29(s32)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10896,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s32) | xuntil2p30(s32) | (~until2p29(s32)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10897,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s32) | xuntil2p30(s32) | (~until2p29(s32))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10896, 10895])).
% 1.40/1.57 tff(10898,plain,
% 1.40/1.57 (xuntil2p30(s32) | (~until2p29(s32))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10897, 10214, 9268])).
% 1.40/1.57 tff(10899,plain,
% 1.40/1.57 (~until2p29(s32)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10898, 10894])).
% 1.40/1.57 tff(10900,plain,
% 1.40/1.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s31, s32)) | until2p29(s32) | (~xuntil2p30(s31)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s31, s32)) | until2p29(s32) | (~xuntil2p30(s31)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10901,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s31, s32)) | until2p29(s32) | (~xuntil2p30(s31)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10902,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s31, s32)) | until2p29(s32) | (~xuntil2p30(s31))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10901, 10900])).
% 1.40/1.57 tff(10903,plain,
% 1.40/1.57 (until2p29(s32) | (~xuntil2p30(s31))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10902, 2927, 10229])).
% 1.40/1.57 tff(10904,plain,
% 1.40/1.57 (~xuntil2p30(s31)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10903, 10899])).
% 1.40/1.57 tff(10905,plain,
% 1.40/1.57 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s31) | xuntil2p30(s31) | (~until2p29(s31)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s31) | xuntil2p30(s31) | (~until2p29(s31)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10906,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s31) | xuntil2p30(s31) | (~until2p29(s31)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10907,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s31) | xuntil2p30(s31) | (~until2p29(s31))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10906, 10905])).
% 1.40/1.57 tff(10908,plain,
% 1.40/1.57 (xuntil2p30(s31) | (~until2p29(s31))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10907, 10214, 8587])).
% 1.40/1.57 tff(10909,plain,
% 1.40/1.57 (~until2p29(s31)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10908, 10904])).
% 1.40/1.57 tff(10910,plain,
% 1.40/1.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s30, s31)) | until2p29(s31) | (~xuntil2p30(s30)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s30, s31)) | until2p29(s31) | (~xuntil2p30(s30)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10911,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s30, s31)) | until2p29(s31) | (~xuntil2p30(s30)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10912,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s30, s31)) | until2p29(s31) | (~xuntil2p30(s30))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10911, 10910])).
% 1.40/1.57 tff(10913,plain,
% 1.40/1.57 (until2p29(s31) | (~xuntil2p30(s30))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10912, 2852, 10229])).
% 1.40/1.57 tff(10914,plain,
% 1.40/1.57 (~xuntil2p30(s30)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10913, 10909])).
% 1.40/1.57 tff(10915,plain,
% 1.40/1.57 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s30) | xuntil2p30(s30) | (~until2p29(s30)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s30) | xuntil2p30(s30) | (~until2p29(s30)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10916,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s30) | xuntil2p30(s30) | (~until2p29(s30)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10917,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s30) | xuntil2p30(s30) | (~until2p29(s30))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10916, 10915])).
% 1.40/1.57 tff(10918,plain,
% 1.40/1.57 (xuntil2p30(s30) | (~until2p29(s30))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10917, 10214, 8596])).
% 1.40/1.57 tff(10919,plain,
% 1.40/1.57 (~until2p29(s30)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10918, 10914])).
% 1.40/1.57 tff(10920,plain,
% 1.40/1.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s29, s30)) | until2p29(s30) | (~xuntil2p30(s29)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s29, s30)) | until2p29(s30) | (~xuntil2p30(s29)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10921,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s29, s30)) | until2p29(s30) | (~xuntil2p30(s29)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10922,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s29, s30)) | until2p29(s30) | (~xuntil2p30(s29))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10921, 10920])).
% 1.40/1.57 tff(10923,plain,
% 1.40/1.57 (until2p29(s30) | (~xuntil2p30(s29))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10922, 2788, 10229])).
% 1.40/1.57 tff(10924,plain,
% 1.40/1.57 (~xuntil2p30(s29)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10923, 10919])).
% 1.40/1.57 tff(10925,plain,
% 1.40/1.57 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s29) | xuntil2p30(s29) | (~until2p29(s29)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s29) | xuntil2p30(s29) | (~until2p29(s29)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10926,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s29) | xuntil2p30(s29) | (~until2p29(s29)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10927,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s29) | xuntil2p30(s29) | (~until2p29(s29))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10926, 10925])).
% 1.40/1.57 tff(10928,plain,
% 1.40/1.57 (xuntil2p30(s29) | (~until2p29(s29))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10927, 10214, 8600])).
% 1.40/1.57 tff(10929,plain,
% 1.40/1.57 (~until2p29(s29)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10928, 10924])).
% 1.40/1.57 tff(10930,plain,
% 1.40/1.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s28, s29)) | until2p29(s29) | (~xuntil2p30(s28)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s28, s29)) | until2p29(s29) | (~xuntil2p30(s28)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10931,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s28, s29)) | until2p29(s29) | (~xuntil2p30(s28)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10932,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s28, s29)) | until2p29(s29) | (~xuntil2p30(s28))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10931, 10930])).
% 1.40/1.57 tff(10933,plain,
% 1.40/1.57 (until2p29(s29) | (~xuntil2p30(s28))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10932, 2693, 10229])).
% 1.40/1.57 tff(10934,plain,
% 1.40/1.57 (~xuntil2p30(s28)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10933, 10929])).
% 1.40/1.57 tff(10935,plain,
% 1.40/1.57 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s28) | xuntil2p30(s28) | (~until2p29(s28)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s28) | xuntil2p30(s28) | (~until2p29(s28)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10936,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s28) | xuntil2p30(s28) | (~until2p29(s28)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10937,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s28) | xuntil2p30(s28) | (~until2p29(s28))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10936, 10935])).
% 1.40/1.57 tff(10938,plain,
% 1.40/1.57 (xuntil2p30(s28) | (~until2p29(s28))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10937, 10214, 9214])).
% 1.40/1.57 tff(10939,plain,
% 1.40/1.57 (~until2p29(s28)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10938, 10934])).
% 1.40/1.57 tff(10940,plain,
% 1.40/1.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s27, s28)) | until2p29(s28) | (~xuntil2p30(s27)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s27, s28)) | until2p29(s28) | (~xuntil2p30(s27)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10941,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s27, s28)) | until2p29(s28) | (~xuntil2p30(s27)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10942,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s27, s28)) | until2p29(s28) | (~xuntil2p30(s27))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10941, 10940])).
% 1.40/1.57 tff(10943,plain,
% 1.40/1.57 (until2p29(s28) | (~xuntil2p30(s27))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10942, 2632, 10229])).
% 1.40/1.57 tff(10944,plain,
% 1.40/1.57 (~xuntil2p30(s27)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10943, 10939])).
% 1.40/1.57 tff(10945,plain,
% 1.40/1.57 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s27) | xuntil2p30(s27) | (~until2p29(s27)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s27) | xuntil2p30(s27) | (~until2p29(s27)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10946,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s27) | xuntil2p30(s27) | (~until2p29(s27)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10947,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s27) | xuntil2p30(s27) | (~until2p29(s27))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10946, 10945])).
% 1.40/1.57 tff(10948,plain,
% 1.40/1.57 (xuntil2p30(s27) | (~until2p29(s27))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10947, 10214, 8616])).
% 1.40/1.57 tff(10949,plain,
% 1.40/1.57 (~until2p29(s27)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10948, 10944])).
% 1.40/1.57 tff(10950,plain,
% 1.40/1.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s26, s27)) | until2p29(s27) | (~xuntil2p30(s26)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s26, s27)) | until2p29(s27) | (~xuntil2p30(s26)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10951,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s26, s27)) | until2p29(s27) | (~xuntil2p30(s26)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10952,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s26, s27)) | until2p29(s27) | (~xuntil2p30(s26))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10951, 10950])).
% 1.40/1.57 tff(10953,plain,
% 1.40/1.57 (until2p29(s27) | (~xuntil2p30(s26))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10952, 2554, 10229])).
% 1.40/1.57 tff(10954,plain,
% 1.40/1.57 (~xuntil2p30(s26)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10953, 10949])).
% 1.40/1.57 tff(10955,plain,
% 1.40/1.57 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s26) | xuntil2p30(s26) | (~until2p29(s26)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s26) | xuntil2p30(s26) | (~until2p29(s26)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10956,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s26) | xuntil2p30(s26) | (~until2p29(s26)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10957,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s26) | xuntil2p30(s26) | (~until2p29(s26))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10956, 10955])).
% 1.40/1.57 tff(10958,plain,
% 1.40/1.57 (xuntil2p30(s26) | (~until2p29(s26))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10957, 10214, 8625])).
% 1.40/1.57 tff(10959,plain,
% 1.40/1.57 (~until2p29(s26)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10958, 10954])).
% 1.40/1.57 tff(10960,plain,
% 1.40/1.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s25, s26)) | until2p29(s26) | (~xuntil2p30(s25)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s25, s26)) | until2p29(s26) | (~xuntil2p30(s25)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10961,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s25, s26)) | until2p29(s26) | (~xuntil2p30(s25)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10962,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s25, s26)) | until2p29(s26) | (~xuntil2p30(s25))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10961, 10960])).
% 1.40/1.57 tff(10963,plain,
% 1.40/1.57 (until2p29(s26) | (~xuntil2p30(s25))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10962, 2455, 10229])).
% 1.40/1.57 tff(10964,plain,
% 1.40/1.57 (~xuntil2p30(s25)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10963, 10959])).
% 1.40/1.57 tff(10965,plain,
% 1.40/1.57 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s25) | xuntil2p30(s25) | (~until2p29(s25)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s25) | xuntil2p30(s25) | (~until2p29(s25)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10966,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s25) | xuntil2p30(s25) | (~until2p29(s25)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10967,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s25) | xuntil2p30(s25) | (~until2p29(s25))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10966, 10965])).
% 1.40/1.57 tff(10968,plain,
% 1.40/1.57 (xuntil2p30(s25) | (~until2p29(s25))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10967, 10214, 8629])).
% 1.40/1.57 tff(10969,plain,
% 1.40/1.57 (~until2p29(s25)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10968, 10964])).
% 1.40/1.57 tff(10970,plain,
% 1.40/1.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s24, s25)) | until2p29(s25) | (~xuntil2p30(s24)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s24, s25)) | until2p29(s25) | (~xuntil2p30(s24)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10971,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s24, s25)) | until2p29(s25) | (~xuntil2p30(s24)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10972,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s24, s25)) | until2p29(s25) | (~xuntil2p30(s24))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10971, 10970])).
% 1.40/1.57 tff(10973,plain,
% 1.40/1.57 (until2p29(s25) | (~xuntil2p30(s24))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10972, 2388, 10229])).
% 1.40/1.57 tff(10974,plain,
% 1.40/1.57 (~xuntil2p30(s24)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10973, 10969])).
% 1.40/1.57 tff(10975,plain,
% 1.40/1.57 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s24) | xuntil2p30(s24) | (~until2p29(s24)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s24) | xuntil2p30(s24) | (~until2p29(s24)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10976,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s24) | xuntil2p30(s24) | (~until2p29(s24)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(10977,plain,
% 1.40/1.57 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s24) | xuntil2p30(s24) | (~until2p29(s24))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[10976, 10975])).
% 1.40/1.57 tff(10978,plain,
% 1.40/1.57 (xuntil2p30(s24) | (~until2p29(s24))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10977, 10214, 9160])).
% 1.40/1.57 tff(10979,plain,
% 1.40/1.57 (~until2p29(s24)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[10978, 10974])).
% 1.40/1.57 tff(10980,plain,
% 1.40/1.57 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s23, s24)) | until2p29(s24) | (~xuntil2p30(s23)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s23, s24)) | until2p29(s24) | (~xuntil2p30(s23)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(10981,plain,
% 1.40/1.57 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s23, s24)) | until2p29(s24) | (~xuntil2p30(s23)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(10982,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s23, s24)) | until2p29(s24) | (~xuntil2p30(s23))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[10981, 10980])).
% 1.40/1.58 tff(10983,plain,
% 1.40/1.58 (until2p29(s24) | (~xuntil2p30(s23))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[10982, 2299, 10229])).
% 1.40/1.58 tff(10984,plain,
% 1.40/1.58 (~xuntil2p30(s23)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[10983, 10979])).
% 1.40/1.58 tff(10985,plain,
% 1.40/1.58 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s23) | xuntil2p30(s23) | (~until2p29(s23)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s23) | xuntil2p30(s23) | (~until2p29(s23)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(10986,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s23) | xuntil2p30(s23) | (~until2p29(s23)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(10987,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s23) | xuntil2p30(s23) | (~until2p29(s23))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[10986, 10985])).
% 1.40/1.58 tff(10988,plain,
% 1.40/1.58 (xuntil2p30(s23) | (~until2p29(s23))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[10987, 10214, 8645])).
% 1.40/1.58 tff(10989,plain,
% 1.40/1.58 (~until2p29(s23)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[10988, 10984])).
% 1.40/1.58 tff(10990,plain,
% 1.40/1.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s22, s23)) | until2p29(s23) | (~xuntil2p30(s22)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s22, s23)) | until2p29(s23) | (~xuntil2p30(s22)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(10991,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s22, s23)) | until2p29(s23) | (~xuntil2p30(s22)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(10992,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s22, s23)) | until2p29(s23) | (~xuntil2p30(s22))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[10991, 10990])).
% 1.40/1.58 tff(10993,plain,
% 1.40/1.58 (until2p29(s23) | (~xuntil2p30(s22))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[10992, 2224, 10229])).
% 1.40/1.58 tff(10994,plain,
% 1.40/1.58 (~xuntil2p30(s22)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[10993, 10989])).
% 1.40/1.58 tff(10995,plain,
% 1.40/1.58 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s22) | xuntil2p30(s22) | (~until2p29(s22)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s22) | xuntil2p30(s22) | (~until2p29(s22)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(10996,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s22) | xuntil2p30(s22) | (~until2p29(s22)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(10997,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s22) | xuntil2p30(s22) | (~until2p29(s22))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[10996, 10995])).
% 1.40/1.58 tff(10998,plain,
% 1.40/1.58 (xuntil2p30(s22) | (~until2p29(s22))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[10997, 10214, 8654])).
% 1.40/1.58 tff(10999,plain,
% 1.40/1.58 (~until2p29(s22)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[10998, 10994])).
% 1.40/1.58 tff(11000,plain,
% 1.40/1.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s21, s22)) | until2p29(s22) | (~xuntil2p30(s21)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s21, s22)) | until2p29(s22) | (~xuntil2p30(s21)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11001,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s21, s22)) | until2p29(s22) | (~xuntil2p30(s21)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11002,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s21, s22)) | until2p29(s22) | (~xuntil2p30(s21))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11001, 11000])).
% 1.40/1.58 tff(11003,plain,
% 1.40/1.58 (until2p29(s22) | (~xuntil2p30(s21))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11002, 2160, 10229])).
% 1.40/1.58 tff(11004,plain,
% 1.40/1.58 (~xuntil2p30(s21)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11003, 10999])).
% 1.40/1.58 tff(11005,plain,
% 1.40/1.58 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s21) | xuntil2p30(s21) | (~until2p29(s21)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s21) | xuntil2p30(s21) | (~until2p29(s21)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11006,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s21) | xuntil2p30(s21) | (~until2p29(s21)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11007,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s21) | xuntil2p30(s21) | (~until2p29(s21))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11006, 11005])).
% 1.40/1.58 tff(11008,plain,
% 1.40/1.58 (xuntil2p30(s21) | (~until2p29(s21))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11007, 10214, 8658])).
% 1.40/1.58 tff(11009,plain,
% 1.40/1.58 (~until2p29(s21)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11008, 11004])).
% 1.40/1.58 tff(11010,plain,
% 1.40/1.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s20, s21)) | until2p29(s21) | (~xuntil2p30(s20)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s20, s21)) | until2p29(s21) | (~xuntil2p30(s20)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11011,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s20, s21)) | until2p29(s21) | (~xuntil2p30(s20)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11012,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s20, s21)) | until2p29(s21) | (~xuntil2p30(s20))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11011, 11010])).
% 1.40/1.58 tff(11013,plain,
% 1.40/1.58 (until2p29(s21) | (~xuntil2p30(s20))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11012, 2065, 10229])).
% 1.40/1.58 tff(11014,plain,
% 1.40/1.58 (~xuntil2p30(s20)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11013, 11009])).
% 1.40/1.58 tff(11015,plain,
% 1.40/1.58 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s20) | xuntil2p30(s20) | (~until2p29(s20)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s20) | xuntil2p30(s20) | (~until2p29(s20)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11016,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s20) | xuntil2p30(s20) | (~until2p29(s20)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11017,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s20) | xuntil2p30(s20) | (~until2p29(s20))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11016, 11015])).
% 1.40/1.58 tff(11018,plain,
% 1.40/1.58 (xuntil2p30(s20) | (~until2p29(s20))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11017, 10214, 9106])).
% 1.40/1.58 tff(11019,plain,
% 1.40/1.58 (~until2p29(s20)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11018, 11014])).
% 1.40/1.58 tff(11020,plain,
% 1.40/1.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s19, s20)) | until2p29(s20) | (~xuntil2p30(s19)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s19, s20)) | until2p29(s20) | (~xuntil2p30(s19)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11021,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s19, s20)) | until2p29(s20) | (~xuntil2p30(s19)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11022,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s19, s20)) | until2p29(s20) | (~xuntil2p30(s19))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11021, 11020])).
% 1.40/1.58 tff(11023,plain,
% 1.40/1.58 (until2p29(s20) | (~xuntil2p30(s19))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11022, 2004, 10229])).
% 1.40/1.58 tff(11024,plain,
% 1.40/1.58 (~xuntil2p30(s19)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11023, 11019])).
% 1.40/1.58 tff(11025,plain,
% 1.40/1.58 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s19) | xuntil2p30(s19) | (~until2p29(s19)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s19) | xuntil2p30(s19) | (~until2p29(s19)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11026,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s19) | xuntil2p30(s19) | (~until2p29(s19)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11027,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s19) | xuntil2p30(s19) | (~until2p29(s19))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11026, 11025])).
% 1.40/1.58 tff(11028,plain,
% 1.40/1.58 (xuntil2p30(s19) | (~until2p29(s19))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11027, 10214, 8674])).
% 1.40/1.58 tff(11029,plain,
% 1.40/1.58 (~until2p29(s19)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11028, 11024])).
% 1.40/1.58 tff(11030,plain,
% 1.40/1.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s18, s19)) | until2p29(s19) | (~xuntil2p30(s18)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s18, s19)) | until2p29(s19) | (~xuntil2p30(s18)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11031,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s18, s19)) | until2p29(s19) | (~xuntil2p30(s18)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11032,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s18, s19)) | until2p29(s19) | (~xuntil2p30(s18))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11031, 11030])).
% 1.40/1.58 tff(11033,plain,
% 1.40/1.58 (until2p29(s19) | (~xuntil2p30(s18))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11032, 1926, 10229])).
% 1.40/1.58 tff(11034,plain,
% 1.40/1.58 (~xuntil2p30(s18)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11033, 11029])).
% 1.40/1.58 tff(11035,plain,
% 1.40/1.58 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s18) | xuntil2p30(s18) | (~until2p29(s18)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s18) | xuntil2p30(s18) | (~until2p29(s18)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11036,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s18) | xuntil2p30(s18) | (~until2p29(s18)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11037,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s18) | xuntil2p30(s18) | (~until2p29(s18))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11036, 11035])).
% 1.40/1.58 tff(11038,plain,
% 1.40/1.58 (xuntil2p30(s18) | (~until2p29(s18))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11037, 10214, 8683])).
% 1.40/1.58 tff(11039,plain,
% 1.40/1.58 (~until2p29(s18)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11038, 11034])).
% 1.40/1.58 tff(11040,plain,
% 1.40/1.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s17, s18)) | until2p29(s18) | (~xuntil2p30(s17)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s17, s18)) | until2p29(s18) | (~xuntil2p30(s17)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11041,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s17, s18)) | until2p29(s18) | (~xuntil2p30(s17)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11042,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s17, s18)) | until2p29(s18) | (~xuntil2p30(s17))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11041, 11040])).
% 1.40/1.58 tff(11043,plain,
% 1.40/1.58 (until2p29(s18) | (~xuntil2p30(s17))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11042, 1827, 10229])).
% 1.40/1.58 tff(11044,plain,
% 1.40/1.58 (~xuntil2p30(s17)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11043, 11039])).
% 1.40/1.58 tff(11045,plain,
% 1.40/1.58 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s17) | xuntil2p30(s17) | (~until2p29(s17)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s17) | xuntil2p30(s17) | (~until2p29(s17)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11046,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s17) | xuntil2p30(s17) | (~until2p29(s17)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11047,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s17) | xuntil2p30(s17) | (~until2p29(s17))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11046, 11045])).
% 1.40/1.58 tff(11048,plain,
% 1.40/1.58 (xuntil2p30(s17) | (~until2p29(s17))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11047, 10214, 8687])).
% 1.40/1.58 tff(11049,plain,
% 1.40/1.58 (~until2p29(s17)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11048, 11044])).
% 1.40/1.58 tff(11050,plain,
% 1.40/1.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s16, s17)) | until2p29(s17) | (~xuntil2p30(s16)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s16, s17)) | until2p29(s17) | (~xuntil2p30(s16)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11051,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s16, s17)) | until2p29(s17) | (~xuntil2p30(s16)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11052,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s16, s17)) | until2p29(s17) | (~xuntil2p30(s16))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11051, 11050])).
% 1.40/1.58 tff(11053,plain,
% 1.40/1.58 (until2p29(s17) | (~xuntil2p30(s16))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11052, 1760, 10229])).
% 1.40/1.58 tff(11054,plain,
% 1.40/1.58 (~xuntil2p30(s16)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11053, 11049])).
% 1.40/1.58 tff(11055,plain,
% 1.40/1.58 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s16) | xuntil2p30(s16) | (~until2p29(s16)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s16) | xuntil2p30(s16) | (~until2p29(s16)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11056,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s16) | xuntil2p30(s16) | (~until2p29(s16)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11057,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s16) | xuntil2p30(s16) | (~until2p29(s16))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11056, 11055])).
% 1.40/1.58 tff(11058,plain,
% 1.40/1.58 (xuntil2p30(s16) | (~until2p29(s16))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11057, 10214, 9052])).
% 1.40/1.58 tff(11059,plain,
% 1.40/1.58 (~until2p29(s16)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11058, 11054])).
% 1.40/1.58 tff(11060,plain,
% 1.40/1.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s15, s16)) | until2p29(s16) | (~xuntil2p30(s15)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s15, s16)) | until2p29(s16) | (~xuntil2p30(s15)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11061,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s15, s16)) | until2p29(s16) | (~xuntil2p30(s15)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11062,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s15, s16)) | until2p29(s16) | (~xuntil2p30(s15))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11061, 11060])).
% 1.40/1.58 tff(11063,plain,
% 1.40/1.58 (until2p29(s16) | (~xuntil2p30(s15))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11062, 1671, 10229])).
% 1.40/1.58 tff(11064,plain,
% 1.40/1.58 (~xuntil2p30(s15)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11063, 11059])).
% 1.40/1.58 tff(11065,plain,
% 1.40/1.58 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s15) | xuntil2p30(s15) | (~until2p29(s15)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s15) | xuntil2p30(s15) | (~until2p29(s15)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11066,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s15) | xuntil2p30(s15) | (~until2p29(s15)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11067,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s15) | xuntil2p30(s15) | (~until2p29(s15))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11066, 11065])).
% 1.40/1.58 tff(11068,plain,
% 1.40/1.58 (xuntil2p30(s15) | (~until2p29(s15))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11067, 10214, 8703])).
% 1.40/1.58 tff(11069,plain,
% 1.40/1.58 (~until2p29(s15)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11068, 11064])).
% 1.40/1.58 tff(11070,plain,
% 1.40/1.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s14, s15)) | until2p29(s15) | (~xuntil2p30(s14)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s14, s15)) | until2p29(s15) | (~xuntil2p30(s14)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11071,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s14, s15)) | until2p29(s15) | (~xuntil2p30(s14)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11072,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s14, s15)) | until2p29(s15) | (~xuntil2p30(s14))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11071, 11070])).
% 1.40/1.58 tff(11073,plain,
% 1.40/1.58 (until2p29(s15) | (~xuntil2p30(s14))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11072, 1596, 10229])).
% 1.40/1.58 tff(11074,plain,
% 1.40/1.58 (~xuntil2p30(s14)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11073, 11069])).
% 1.40/1.58 tff(11075,plain,
% 1.40/1.58 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s14) | xuntil2p30(s14) | (~until2p29(s14)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s14) | xuntil2p30(s14) | (~until2p29(s14)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11076,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s14) | xuntil2p30(s14) | (~until2p29(s14)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11077,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s14) | xuntil2p30(s14) | (~until2p29(s14))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11076, 11075])).
% 1.40/1.58 tff(11078,plain,
% 1.40/1.58 (xuntil2p30(s14) | (~until2p29(s14))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11077, 10214, 8712])).
% 1.40/1.58 tff(11079,plain,
% 1.40/1.58 (~until2p29(s14)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11078, 11074])).
% 1.40/1.58 tff(11080,plain,
% 1.40/1.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s13, s14)) | until2p29(s14) | (~xuntil2p30(s13)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s13, s14)) | until2p29(s14) | (~xuntil2p30(s13)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11081,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s13, s14)) | until2p29(s14) | (~xuntil2p30(s13)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11082,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s13, s14)) | until2p29(s14) | (~xuntil2p30(s13))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11081, 11080])).
% 1.40/1.58 tff(11083,plain,
% 1.40/1.58 (until2p29(s14) | (~xuntil2p30(s13))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11082, 1532, 10229])).
% 1.40/1.58 tff(11084,plain,
% 1.40/1.58 (~xuntil2p30(s13)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11083, 11079])).
% 1.40/1.58 tff(11085,plain,
% 1.40/1.58 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s13) | xuntil2p30(s13) | (~until2p29(s13)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s13) | xuntil2p30(s13) | (~until2p29(s13)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11086,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s13) | xuntil2p30(s13) | (~until2p29(s13)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11087,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s13) | xuntil2p30(s13) | (~until2p29(s13))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11086, 11085])).
% 1.40/1.58 tff(11088,plain,
% 1.40/1.58 (xuntil2p30(s13) | (~until2p29(s13))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11087, 10214, 8716])).
% 1.40/1.58 tff(11089,plain,
% 1.40/1.58 (~until2p29(s13)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11088, 11084])).
% 1.40/1.58 tff(11090,plain,
% 1.40/1.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s12, s13)) | until2p29(s13) | (~xuntil2p30(s12)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s12, s13)) | until2p29(s13) | (~xuntil2p30(s12)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11091,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s12, s13)) | until2p29(s13) | (~xuntil2p30(s12)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11092,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s12, s13)) | until2p29(s13) | (~xuntil2p30(s12))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11091, 11090])).
% 1.40/1.58 tff(11093,plain,
% 1.40/1.58 (until2p29(s13) | (~xuntil2p30(s12))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11092, 1437, 10229])).
% 1.40/1.58 tff(11094,plain,
% 1.40/1.58 (~xuntil2p30(s12)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11093, 11089])).
% 1.40/1.58 tff(11095,plain,
% 1.40/1.58 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s12) | xuntil2p30(s12) | (~until2p29(s12)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s12) | xuntil2p30(s12) | (~until2p29(s12)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11096,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s12) | xuntil2p30(s12) | (~until2p29(s12)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11097,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s12) | xuntil2p30(s12) | (~until2p29(s12))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11096, 11095])).
% 1.40/1.58 tff(11098,plain,
% 1.40/1.58 (xuntil2p30(s12) | (~until2p29(s12))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11097, 10214, 8998])).
% 1.40/1.58 tff(11099,plain,
% 1.40/1.58 (~until2p29(s12)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11098, 11094])).
% 1.40/1.58 tff(11100,plain,
% 1.40/1.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s11, s12)) | until2p29(s12) | (~xuntil2p30(s11)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s11, s12)) | until2p29(s12) | (~xuntil2p30(s11)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11101,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s11, s12)) | until2p29(s12) | (~xuntil2p30(s11)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11102,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s11, s12)) | until2p29(s12) | (~xuntil2p30(s11))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11101, 11100])).
% 1.40/1.58 tff(11103,plain,
% 1.40/1.58 (until2p29(s12) | (~xuntil2p30(s11))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11102, 1376, 10229])).
% 1.40/1.58 tff(11104,plain,
% 1.40/1.58 (~xuntil2p30(s11)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11103, 11099])).
% 1.40/1.58 tff(11105,plain,
% 1.40/1.58 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s11) | xuntil2p30(s11) | (~until2p29(s11)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s11) | xuntil2p30(s11) | (~until2p29(s11)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11106,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s11) | xuntil2p30(s11) | (~until2p29(s11)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11107,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s11) | xuntil2p30(s11) | (~until2p29(s11))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11106, 11105])).
% 1.40/1.58 tff(11108,plain,
% 1.40/1.58 (xuntil2p30(s11) | (~until2p29(s11))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11107, 10214, 8732])).
% 1.40/1.58 tff(11109,plain,
% 1.40/1.58 (~until2p29(s11)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11108, 11104])).
% 1.40/1.58 tff(11110,plain,
% 1.40/1.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s10, s11)) | until2p29(s11) | (~xuntil2p30(s10)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s10, s11)) | until2p29(s11) | (~xuntil2p30(s10)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11111,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s10, s11)) | until2p29(s11) | (~xuntil2p30(s10)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11112,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s10, s11)) | until2p29(s11) | (~xuntil2p30(s10))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11111, 11110])).
% 1.40/1.58 tff(11113,plain,
% 1.40/1.58 (until2p29(s11) | (~xuntil2p30(s10))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11112, 1298, 10229])).
% 1.40/1.58 tff(11114,plain,
% 1.40/1.58 (~xuntil2p30(s10)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11113, 11109])).
% 1.40/1.58 tff(11115,plain,
% 1.40/1.58 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s10) | xuntil2p30(s10) | (~until2p29(s10)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s10) | xuntil2p30(s10) | (~until2p29(s10)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11116,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s10) | xuntil2p30(s10) | (~until2p29(s10)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11117,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s10) | xuntil2p30(s10) | (~until2p29(s10))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11116, 11115])).
% 1.40/1.58 tff(11118,plain,
% 1.40/1.58 (xuntil2p30(s10) | (~until2p29(s10))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11117, 10214, 8741])).
% 1.40/1.58 tff(11119,plain,
% 1.40/1.58 (~until2p29(s10)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11118, 11114])).
% 1.40/1.58 tff(11120,plain,
% 1.40/1.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s9, s10)) | until2p29(s10) | (~xuntil2p30(s9)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s9, s10)) | until2p29(s10) | (~xuntil2p30(s9)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11121,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s9, s10)) | until2p29(s10) | (~xuntil2p30(s9)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11122,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s9, s10)) | until2p29(s10) | (~xuntil2p30(s9))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11121, 11120])).
% 1.40/1.58 tff(11123,plain,
% 1.40/1.58 (until2p29(s10) | (~xuntil2p30(s9))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11122, 1199, 10229])).
% 1.40/1.58 tff(11124,plain,
% 1.40/1.58 (~xuntil2p30(s9)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11123, 11119])).
% 1.40/1.58 tff(11125,plain,
% 1.40/1.58 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s9) | xuntil2p30(s9) | (~until2p29(s9)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s9) | xuntil2p30(s9) | (~until2p29(s9)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11126,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s9) | xuntil2p30(s9) | (~until2p29(s9)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11127,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s9) | xuntil2p30(s9) | (~until2p29(s9))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11126, 11125])).
% 1.40/1.58 tff(11128,plain,
% 1.40/1.58 (xuntil2p30(s9) | (~until2p29(s9))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11127, 10214, 8745])).
% 1.40/1.58 tff(11129,plain,
% 1.40/1.58 (~until2p29(s9)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11128, 11124])).
% 1.40/1.58 tff(11130,plain,
% 1.40/1.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s8, s9)) | until2p29(s9) | (~xuntil2p30(s8)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s8, s9)) | until2p29(s9) | (~xuntil2p30(s8)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11131,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s8, s9)) | until2p29(s9) | (~xuntil2p30(s8)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11132,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s8, s9)) | until2p29(s9) | (~xuntil2p30(s8))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11131, 11130])).
% 1.40/1.58 tff(11133,plain,
% 1.40/1.58 (until2p29(s9) | (~xuntil2p30(s8))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11132, 1132, 10229])).
% 1.40/1.58 tff(11134,plain,
% 1.40/1.58 (~xuntil2p30(s8)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11133, 11129])).
% 1.40/1.58 tff(11135,plain,
% 1.40/1.58 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s8) | xuntil2p30(s8) | (~until2p29(s8)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s8) | xuntil2p30(s8) | (~until2p29(s8)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11136,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s8) | xuntil2p30(s8) | (~until2p29(s8)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11137,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s8) | xuntil2p30(s8) | (~until2p29(s8))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11136, 11135])).
% 1.40/1.58 tff(11138,plain,
% 1.40/1.58 (xuntil2p30(s8) | (~until2p29(s8))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11137, 10214, 8944])).
% 1.40/1.58 tff(11139,plain,
% 1.40/1.58 (~until2p29(s8)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11138, 11134])).
% 1.40/1.58 tff(11140,plain,
% 1.40/1.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s7, s8)) | until2p29(s8) | (~xuntil2p30(s7)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s7, s8)) | until2p29(s8) | (~xuntil2p30(s7)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11141,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s7, s8)) | until2p29(s8) | (~xuntil2p30(s7)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11142,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s7, s8)) | until2p29(s8) | (~xuntil2p30(s7))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11141, 11140])).
% 1.40/1.58 tff(11143,plain,
% 1.40/1.58 (until2p29(s8) | (~xuntil2p30(s7))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11142, 1043, 10229])).
% 1.40/1.58 tff(11144,plain,
% 1.40/1.58 (~xuntil2p30(s7)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11143, 11139])).
% 1.40/1.58 tff(11145,plain,
% 1.40/1.58 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s7) | xuntil2p30(s7) | (~until2p29(s7)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s7) | xuntil2p30(s7) | (~until2p29(s7)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11146,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s7) | xuntil2p30(s7) | (~until2p29(s7)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11147,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s7) | xuntil2p30(s7) | (~until2p29(s7))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11146, 11145])).
% 1.40/1.58 tff(11148,plain,
% 1.40/1.58 (xuntil2p30(s7) | (~until2p29(s7))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11147, 10214, 8761])).
% 1.40/1.58 tff(11149,plain,
% 1.40/1.58 (~until2p29(s7)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11148, 11144])).
% 1.40/1.58 tff(11150,plain,
% 1.40/1.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s6, s7)) | until2p29(s7) | (~xuntil2p30(s6)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s6, s7)) | until2p29(s7) | (~xuntil2p30(s6)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11151,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s6, s7)) | until2p29(s7) | (~xuntil2p30(s6)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11152,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s6, s7)) | until2p29(s7) | (~xuntil2p30(s6))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11151, 11150])).
% 1.40/1.58 tff(11153,plain,
% 1.40/1.58 (until2p29(s7) | (~xuntil2p30(s6))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11152, 958, 10229])).
% 1.40/1.58 tff(11154,plain,
% 1.40/1.58 (~xuntil2p30(s6)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11153, 11149])).
% 1.40/1.58 tff(11155,plain,
% 1.40/1.58 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s6) | xuntil2p30(s6) | (~until2p29(s6)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s6) | xuntil2p30(s6) | (~until2p29(s6)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11156,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s6) | xuntil2p30(s6) | (~until2p29(s6)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11157,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s6) | xuntil2p30(s6) | (~until2p29(s6))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11156, 11155])).
% 1.40/1.58 tff(11158,plain,
% 1.40/1.58 (xuntil2p30(s6) | (~until2p29(s6))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11157, 10214, 8770])).
% 1.40/1.58 tff(11159,plain,
% 1.40/1.58 (~until2p29(s6)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11158, 11154])).
% 1.40/1.58 tff(11160,plain,
% 1.40/1.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s5, s6)) | until2p29(s6) | (~xuntil2p30(s5)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s5, s6)) | until2p29(s6) | (~xuntil2p30(s5)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11161,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s5, s6)) | until2p29(s6) | (~xuntil2p30(s5)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11162,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s5, s6)) | until2p29(s6) | (~xuntil2p30(s5))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11161, 11160])).
% 1.40/1.58 tff(11163,plain,
% 1.40/1.58 (until2p29(s6) | (~xuntil2p30(s5))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11162, 874, 10229])).
% 1.40/1.58 tff(11164,plain,
% 1.40/1.58 (~xuntil2p30(s5)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11163, 11159])).
% 1.40/1.58 tff(11165,plain,
% 1.40/1.58 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s5) | xuntil2p30(s5) | (~until2p29(s5)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s5) | xuntil2p30(s5) | (~until2p29(s5)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11166,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s5) | xuntil2p30(s5) | (~until2p29(s5)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11167,plain,
% 1.40/1.58 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s5) | xuntil2p30(s5) | (~until2p29(s5))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[11166, 11165])).
% 1.40/1.58 tff(11168,plain,
% 1.40/1.58 (xuntil2p30(s5) | (~until2p29(s5))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11167, 10214, 8774])).
% 1.40/1.58 tff(11169,plain,
% 1.40/1.58 (~until2p29(s5)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[11168, 11164])).
% 1.40/1.58 tff(11170,plain,
% 1.40/1.58 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s4, s5)) | until2p29(s5) | (~xuntil2p30(s4)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s4, s5)) | until2p29(s5) | (~xuntil2p30(s4)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(11171,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s4, s5)) | until2p29(s5) | (~xuntil2p30(s4)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(11172,plain,
% 1.40/1.58 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s4, s5)) | until2p29(s5) | (~xuntil2p30(s4))),
% 1.40/1.59 inference(modus_ponens,[status(thm)],[11171, 11170])).
% 1.40/1.59 tff(11173,plain,
% 1.40/1.59 (until2p29(s5) | (~xuntil2p30(s4))),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11172, 708, 10229])).
% 1.40/1.59 tff(11174,plain,
% 1.40/1.59 (~xuntil2p30(s4)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11173, 11169])).
% 1.40/1.59 tff(11175,plain,
% 1.40/1.59 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s4) | xuntil2p30(s4) | (~until2p29(s4)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s4) | xuntil2p30(s4) | (~until2p29(s4)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(11176,plain,
% 1.40/1.59 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s4) | xuntil2p30(s4) | (~until2p29(s4)))),
% 1.40/1.59 inference(quant_inst,[status(thm)],[])).
% 1.40/1.59 tff(11177,plain,
% 1.40/1.59 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s4) | xuntil2p30(s4) | (~until2p29(s4))),
% 1.40/1.59 inference(modus_ponens,[status(thm)],[11176, 11175])).
% 1.40/1.59 tff(11178,plain,
% 1.40/1.59 (xuntil2p30(s4) | (~until2p29(s4))),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11177, 10214, 8890])).
% 1.40/1.59 tff(11179,plain,
% 1.40/1.59 (~until2p29(s4)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11178, 11174])).
% 1.40/1.59 tff(11180,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s3, s4)) | until2p29(s4) | (~xuntil2p30(s3)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s3, s4)) | until2p29(s4) | (~xuntil2p30(s3)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(11181,plain,
% 1.40/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s3, s4)) | until2p29(s4) | (~xuntil2p30(s3)))),
% 1.40/1.59 inference(quant_inst,[status(thm)],[])).
% 1.40/1.59 tff(11182,plain,
% 1.40/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s3, s4)) | until2p29(s4) | (~xuntil2p30(s3))),
% 1.40/1.59 inference(modus_ponens,[status(thm)],[11181, 11180])).
% 1.40/1.59 tff(11183,plain,
% 1.40/1.59 (until2p29(s4) | (~xuntil2p30(s3))),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11182, 599, 10229])).
% 1.40/1.59 tff(11184,plain,
% 1.40/1.59 (~xuntil2p30(s3)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11183, 11179])).
% 1.40/1.59 tff(11185,plain,
% 1.40/1.59 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s3) | xuntil2p30(s3) | (~until2p29(s3)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s3) | xuntil2p30(s3) | (~until2p29(s3)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(11186,plain,
% 1.40/1.59 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s3) | xuntil2p30(s3) | (~until2p29(s3)))),
% 1.40/1.59 inference(quant_inst,[status(thm)],[])).
% 1.40/1.59 tff(11187,plain,
% 1.40/1.59 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s3) | xuntil2p30(s3) | (~until2p29(s3))),
% 1.40/1.59 inference(modus_ponens,[status(thm)],[11186, 11185])).
% 1.40/1.59 tff(11188,plain,
% 1.40/1.59 (xuntil2p30(s3) | (~until2p29(s3))),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11187, 10214, 8873])).
% 1.40/1.59 tff(11189,plain,
% 1.40/1.59 (~until2p29(s3)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11188, 11184])).
% 1.40/1.59 tff(11190,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s2, s3)) | until2p29(s3) | (~xuntil2p30(s2)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s2, s3)) | until2p29(s3) | (~xuntil2p30(s2)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(11191,plain,
% 1.40/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s2, s3)) | until2p29(s3) | (~xuntil2p30(s2)))),
% 1.40/1.59 inference(quant_inst,[status(thm)],[])).
% 1.40/1.59 tff(11192,plain,
% 1.40/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s2, s3)) | until2p29(s3) | (~xuntil2p30(s2))),
% 1.40/1.59 inference(modus_ponens,[status(thm)],[11191, 11190])).
% 1.40/1.59 tff(11193,plain,
% 1.40/1.59 (until2p29(s3) | (~xuntil2p30(s2))),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11192, 480, 10229])).
% 1.40/1.59 tff(11194,plain,
% 1.40/1.59 (~xuntil2p30(s2)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11193, 11189])).
% 1.40/1.59 tff(11195,plain,
% 1.40/1.59 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s2) | xuntil2p30(s2) | (~until2p29(s2)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s2) | xuntil2p30(s2) | (~until2p29(s2)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(11196,plain,
% 1.40/1.59 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s2) | xuntil2p30(s2) | (~until2p29(s2)))),
% 1.40/1.59 inference(quant_inst,[status(thm)],[])).
% 1.40/1.59 tff(11197,plain,
% 1.40/1.59 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s2) | xuntil2p30(s2) | (~until2p29(s2))),
% 1.40/1.59 inference(modus_ponens,[status(thm)],[11196, 11195])).
% 1.40/1.59 tff(11198,plain,
% 1.40/1.59 (xuntil2p30(s2) | (~until2p29(s2))),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11197, 10214, 8795])).
% 1.40/1.59 tff(11199,plain,
% 1.40/1.59 (~until2p29(s2)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11198, 11194])).
% 1.40/1.59 tff(11200,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s1, s2)) | until2p29(s2) | (~xuntil2p30(s1)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s1, s2)) | until2p29(s2) | (~xuntil2p30(s1)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(11201,plain,
% 1.40/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s1, s2)) | until2p29(s2) | (~xuntil2p30(s1)))),
% 1.40/1.59 inference(quant_inst,[status(thm)],[])).
% 1.40/1.59 tff(11202,plain,
% 1.40/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s1, s2)) | until2p29(s2) | (~xuntil2p30(s1))),
% 1.40/1.59 inference(modus_ponens,[status(thm)],[11201, 11200])).
% 1.40/1.59 tff(11203,plain,
% 1.40/1.59 (until2p29(s2) | (~xuntil2p30(s1))),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11202, 278, 10229])).
% 1.40/1.59 tff(11204,plain,
% 1.40/1.59 (~xuntil2p30(s1)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11203, 11199])).
% 1.40/1.59 tff(11205,plain,
% 1.40/1.59 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s1) | xuntil2p30(s1) | (~until2p29(s1)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s1) | xuntil2p30(s1) | (~until2p29(s1)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(11206,plain,
% 1.40/1.59 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s1) | xuntil2p30(s1) | (~until2p29(s1)))),
% 1.40/1.59 inference(quant_inst,[status(thm)],[])).
% 1.40/1.59 tff(11207,plain,
% 1.40/1.59 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s1) | xuntil2p30(s1) | (~until2p29(s1))),
% 1.40/1.59 inference(modus_ponens,[status(thm)],[11206, 11205])).
% 1.40/1.59 tff(11208,plain,
% 1.40/1.59 (xuntil2p30(s1) | (~until2p29(s1))),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11207, 10214, 8804])).
% 1.40/1.59 tff(11209,plain,
% 1.40/1.59 (~until2p29(s1)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11208, 11204])).
% 1.40/1.59 tff(11210,plain,
% 1.40/1.59 (^[Y: $i, X: $i] : refl(((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y)) <=> ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y)))),
% 1.40/1.59 inference(bind,[status(th)],[])).
% 1.40/1.59 tff(11211,plain,
% 1.40/1.59 (![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y)) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))),
% 1.40/1.59 inference(quant_intro,[status(thm)],[11210])).
% 1.40/1.59 tff(11212,plain,
% 1.40/1.59 (![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y)) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(11213,plain,
% 1.40/1.59 (^[Y: $i, X: $i] : trans(monotonicity(rewrite(((until2p29(Y) | (~trans(X, Y))) | (~last(X))) <=> ((~trans(X, Y)) | (~last(X)) | until2p29(Y))), ((((until2p29(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil28(X))) <=> (((~trans(X, Y)) | (~last(X)) | until2p29(Y)) | (~xuntil28(X))))), rewrite((((~trans(X, Y)) | (~last(X)) | until2p29(Y)) | (~xuntil28(X))) <=> ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))), ((((until2p29(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil28(X))) <=> ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))))),
% 1.40/1.59 inference(bind,[status(th)],[])).
% 1.40/1.59 tff(11214,plain,
% 1.40/1.59 (![Y: $i, X: $i] : (((until2p29(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil28(X))) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))),
% 1.40/1.59 inference(quant_intro,[status(thm)],[11213])).
% 1.40/1.59 tff(11215,axiom,(![Y: $i, X: $i] : (((until2p29(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil28(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty22')).
% 1.40/1.59 tff(11216,plain,
% 1.40/1.59 (![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))),
% 1.40/1.59 inference(modus_ponens,[status(thm)],[11215, 11214])).
% 1.40/1.59 tff(11217,plain,
% 1.40/1.59 (![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))),
% 1.40/1.59 inference(modus_ponens,[status(thm)],[11216, 11212])).
% 1.40/1.59 tff(11218,plain,(
% 1.40/1.59 ![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))),
% 1.40/1.59 inference(skolemize,[status(sab)],[11217])).
% 1.40/1.59 tff(11219,plain,
% 1.40/1.59 (![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))),
% 1.40/1.59 inference(modus_ponens,[status(thm)],[11218, 11211])).
% 1.40/1.59 tff(11220,assumption,(xuntil28(s99)), introduced(assumption)).
% 1.40/1.59 tff(11221,assumption,(~until2p29(s72)), introduced(assumption)).
% 1.40/1.59 tff(11222,assumption,(trans(s99, s72)), introduced(assumption)).
% 1.40/1.59 tff(11223,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s72) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s72)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s72) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s72)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(11224,plain,
% 1.40/1.59 (((~trans(s99, s72)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s72)) <=> (until2p29(s72) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s72)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(11225,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s72)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s72))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s72) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s72))))),
% 1.40/1.59 inference(monotonicity,[status(thm)],[11224])).
% 1.40/1.59 tff(11226,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s72)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s72))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s72) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s72)))),
% 1.40/1.59 inference(transitivity,[status(thm)],[11225, 11223])).
% 1.40/1.59 tff(11227,plain,
% 1.40/1.59 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s72)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s72))),
% 1.40/1.59 inference(quant_inst,[status(thm)],[])).
% 1.40/1.59 tff(11228,plain,
% 1.40/1.59 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s72) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s72))),
% 1.40/1.59 inference(modus_ponens,[status(thm)],[11227, 11226])).
% 1.40/1.59 tff(11229,plain,
% 1.40/1.59 ($false),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11228, 10200, 11222, 11219, 11221, 11220])).
% 1.40/1.59 tff(11230,plain,((~trans(s99, s72)) | until2p29(s72) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.59 tff(11231,plain,
% 1.40/1.59 (~trans(s99, s72)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11230, 10499, 10186])).
% 1.40/1.59 tff(11232,assumption,(~until2p29(s65)), introduced(assumption)).
% 1.40/1.59 tff(11233,assumption,(trans(s99, s65)), introduced(assumption)).
% 1.40/1.59 tff(11234,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s65) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s65)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s65) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s65)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(11235,plain,
% 1.40/1.59 (((~trans(s99, s65)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s65)) <=> (until2p29(s65) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s65)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(11236,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s65)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s65))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s65) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s65))))),
% 1.40/1.59 inference(monotonicity,[status(thm)],[11235])).
% 1.40/1.59 tff(11237,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s65)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s65))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s65) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s65)))),
% 1.40/1.59 inference(transitivity,[status(thm)],[11236, 11234])).
% 1.40/1.59 tff(11238,plain,
% 1.40/1.59 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s65)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s65))),
% 1.40/1.59 inference(quant_inst,[status(thm)],[])).
% 1.40/1.59 tff(11239,plain,
% 1.40/1.59 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s65) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s65))),
% 1.40/1.59 inference(modus_ponens,[status(thm)],[11238, 11237])).
% 1.40/1.59 tff(11240,plain,
% 1.40/1.59 ($false),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11239, 10200, 11233, 11219, 11232, 11220])).
% 1.40/1.59 tff(11241,plain,((~trans(s99, s65)) | until2p29(s65) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.59 tff(11242,plain,
% 1.40/1.59 (~trans(s99, s65)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11241, 10569, 10186])).
% 1.40/1.59 tff(11243,assumption,(~until2p29(s91)), introduced(assumption)).
% 1.40/1.59 tff(11244,assumption,(trans(s99, s91)), introduced(assumption)).
% 1.40/1.59 tff(11245,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s91) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s91)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s91) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s91)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(11246,plain,
% 1.40/1.59 (((~trans(s99, s91)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s91)) <=> (until2p29(s91) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s91)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(11247,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s91)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s91))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s91) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s91))))),
% 1.40/1.59 inference(monotonicity,[status(thm)],[11246])).
% 1.40/1.59 tff(11248,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s91)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s91))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s91) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s91)))),
% 1.40/1.59 inference(transitivity,[status(thm)],[11247, 11245])).
% 1.40/1.59 tff(11249,plain,
% 1.40/1.59 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s91)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s91))),
% 1.40/1.59 inference(quant_inst,[status(thm)],[])).
% 1.40/1.59 tff(11250,plain,
% 1.40/1.59 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s91) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s91))),
% 1.40/1.59 inference(modus_ponens,[status(thm)],[11249, 11248])).
% 1.40/1.59 tff(11251,plain,
% 1.40/1.59 ($false),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11250, 10200, 11244, 11219, 11243, 11220])).
% 1.40/1.59 tff(11252,plain,((~trans(s99, s91)) | until2p29(s91) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.59 tff(11253,plain,
% 1.40/1.59 (~trans(s99, s91)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11252, 10309, 10186])).
% 1.40/1.59 tff(11254,assumption,(~until2p29(s75)), introduced(assumption)).
% 1.40/1.59 tff(11255,assumption,(trans(s99, s75)), introduced(assumption)).
% 1.40/1.59 tff(11256,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s75) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s75)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s75) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s75)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(11257,plain,
% 1.40/1.59 (((~trans(s99, s75)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s75)) <=> (until2p29(s75) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s75)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(11258,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s75)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s75))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s75) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s75))))),
% 1.40/1.59 inference(monotonicity,[status(thm)],[11257])).
% 1.40/1.59 tff(11259,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s75)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s75))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s75) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s75)))),
% 1.40/1.59 inference(transitivity,[status(thm)],[11258, 11256])).
% 1.40/1.59 tff(11260,plain,
% 1.40/1.59 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s75)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s75))),
% 1.40/1.59 inference(quant_inst,[status(thm)],[])).
% 1.40/1.59 tff(11261,plain,
% 1.40/1.59 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s75) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s75))),
% 1.40/1.59 inference(modus_ponens,[status(thm)],[11260, 11259])).
% 1.40/1.59 tff(11262,plain,
% 1.40/1.59 ($false),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11261, 10200, 11255, 11219, 11254, 11220])).
% 1.40/1.59 tff(11263,plain,((~trans(s99, s75)) | until2p29(s75) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.59 tff(11264,plain,
% 1.40/1.59 (~trans(s99, s75)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11263, 10469, 10186])).
% 1.40/1.59 tff(11265,assumption,(~until2p29(s76)), introduced(assumption)).
% 1.40/1.59 tff(11266,assumption,(trans(s99, s76)), introduced(assumption)).
% 1.40/1.59 tff(11267,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s76) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s76)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s76) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s76)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(11268,plain,
% 1.40/1.59 (((~trans(s99, s76)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s76)) <=> (until2p29(s76) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s76)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(11269,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s76)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s76))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s76) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s76))))),
% 1.40/1.59 inference(monotonicity,[status(thm)],[11268])).
% 1.40/1.59 tff(11270,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s76)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s76))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s76) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s76)))),
% 1.40/1.59 inference(transitivity,[status(thm)],[11269, 11267])).
% 1.40/1.59 tff(11271,plain,
% 1.40/1.59 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s76)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s76))),
% 1.40/1.59 inference(quant_inst,[status(thm)],[])).
% 1.40/1.59 tff(11272,plain,
% 1.40/1.59 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s76) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s76))),
% 1.40/1.59 inference(modus_ponens,[status(thm)],[11271, 11270])).
% 1.40/1.59 tff(11273,plain,
% 1.40/1.59 ($false),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11272, 10200, 11266, 11219, 11265, 11220])).
% 1.40/1.59 tff(11274,plain,((~trans(s99, s76)) | until2p29(s76) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.59 tff(11275,plain,
% 1.40/1.59 (~trans(s99, s76)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11274, 10459, 10186])).
% 1.40/1.59 tff(11276,assumption,(~until2p29(s78)), introduced(assumption)).
% 1.40/1.59 tff(11277,assumption,(trans(s99, s78)), introduced(assumption)).
% 1.40/1.59 tff(11278,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s78) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s78)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s78) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s78)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(11279,plain,
% 1.40/1.59 (((~trans(s99, s78)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s78)) <=> (until2p29(s78) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s78)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(11280,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s78)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s78))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s78) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s78))))),
% 1.40/1.59 inference(monotonicity,[status(thm)],[11279])).
% 1.40/1.59 tff(11281,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s78)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s78))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s78) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s78)))),
% 1.40/1.59 inference(transitivity,[status(thm)],[11280, 11278])).
% 1.40/1.59 tff(11282,plain,
% 1.40/1.59 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s78)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s78))),
% 1.40/1.59 inference(quant_inst,[status(thm)],[])).
% 1.40/1.59 tff(11283,plain,
% 1.40/1.59 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s78) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s78))),
% 1.40/1.59 inference(modus_ponens,[status(thm)],[11282, 11281])).
% 1.40/1.59 tff(11284,plain,
% 1.40/1.59 ($false),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11283, 10200, 11277, 11219, 11276, 11220])).
% 1.40/1.59 tff(11285,plain,((~trans(s99, s78)) | until2p29(s78) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.59 tff(11286,plain,
% 1.40/1.59 (~trans(s99, s78)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11285, 10439, 10186])).
% 1.40/1.59 tff(11287,assumption,(~until2p29(s74)), introduced(assumption)).
% 1.40/1.59 tff(11288,assumption,(trans(s99, s74)), introduced(assumption)).
% 1.40/1.59 tff(11289,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s74) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s74)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s74) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s74)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(11290,plain,
% 1.40/1.59 (((~trans(s99, s74)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s74)) <=> (until2p29(s74) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s74)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(11291,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s74)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s74))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s74) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s74))))),
% 1.40/1.59 inference(monotonicity,[status(thm)],[11290])).
% 1.40/1.59 tff(11292,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s74)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s74))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s74) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s74)))),
% 1.40/1.59 inference(transitivity,[status(thm)],[11291, 11289])).
% 1.40/1.59 tff(11293,plain,
% 1.40/1.59 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s74)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s74))),
% 1.40/1.59 inference(quant_inst,[status(thm)],[])).
% 1.40/1.59 tff(11294,plain,
% 1.40/1.59 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s74) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s74))),
% 1.40/1.59 inference(modus_ponens,[status(thm)],[11293, 11292])).
% 1.40/1.59 tff(11295,plain,
% 1.40/1.59 ($false),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11294, 10200, 11288, 11219, 11287, 11220])).
% 1.40/1.59 tff(11296,plain,((~trans(s99, s74)) | until2p29(s74) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.59 tff(11297,plain,
% 1.40/1.59 (~trans(s99, s74)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11296, 10479, 10186])).
% 1.40/1.59 tff(11298,assumption,(~until2p29(s45)), introduced(assumption)).
% 1.40/1.59 tff(11299,assumption,(trans(s99, s45)), introduced(assumption)).
% 1.40/1.59 tff(11300,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s45) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s45)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s45) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s45)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(11301,plain,
% 1.40/1.59 (((~trans(s99, s45)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s45)) <=> (until2p29(s45) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s45)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(11302,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s45)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s45))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s45) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s45))))),
% 1.40/1.59 inference(monotonicity,[status(thm)],[11301])).
% 1.40/1.59 tff(11303,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s45)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s45))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s45) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s45)))),
% 1.40/1.59 inference(transitivity,[status(thm)],[11302, 11300])).
% 1.40/1.59 tff(11304,plain,
% 1.40/1.59 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s45)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s45))),
% 1.40/1.59 inference(quant_inst,[status(thm)],[])).
% 1.40/1.59 tff(11305,plain,
% 1.40/1.59 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s45) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s45))),
% 1.40/1.59 inference(modus_ponens,[status(thm)],[11304, 11303])).
% 1.40/1.59 tff(11306,plain,
% 1.40/1.59 ($false),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11305, 10200, 11299, 11219, 11298, 11220])).
% 1.40/1.59 tff(11307,plain,((~trans(s99, s45)) | until2p29(s45) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.59 tff(11308,plain,
% 1.40/1.59 (~trans(s99, s45)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11307, 10769, 10186])).
% 1.40/1.59 tff(11309,assumption,(~until2p29(s90)), introduced(assumption)).
% 1.40/1.59 tff(11310,assumption,(trans(s99, s90)), introduced(assumption)).
% 1.40/1.59 tff(11311,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s90) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s90)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s90) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s90)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(11312,plain,
% 1.40/1.59 (((~trans(s99, s90)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s90)) <=> (until2p29(s90) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s90)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(11313,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s90)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s90))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s90) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s90))))),
% 1.40/1.59 inference(monotonicity,[status(thm)],[11312])).
% 1.40/1.59 tff(11314,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s90)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s90))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s90) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s90)))),
% 1.40/1.59 inference(transitivity,[status(thm)],[11313, 11311])).
% 1.40/1.59 tff(11315,plain,
% 1.40/1.59 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s90)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s90))),
% 1.40/1.59 inference(quant_inst,[status(thm)],[])).
% 1.40/1.59 tff(11316,plain,
% 1.40/1.59 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s90) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s90))),
% 1.40/1.59 inference(modus_ponens,[status(thm)],[11315, 11314])).
% 1.40/1.59 tff(11317,plain,
% 1.40/1.59 ($false),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11316, 10200, 11310, 11219, 11309, 11220])).
% 1.40/1.59 tff(11318,plain,((~trans(s99, s90)) | until2p29(s90) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.59 tff(11319,plain,
% 1.40/1.59 (~trans(s99, s90)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11318, 10319, 10186])).
% 1.40/1.59 tff(11320,assumption,(~until2p29(s81)), introduced(assumption)).
% 1.40/1.59 tff(11321,assumption,(trans(s99, s81)), introduced(assumption)).
% 1.40/1.59 tff(11322,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s81) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s81)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s81) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s81)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(11323,plain,
% 1.40/1.59 (((~trans(s99, s81)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s81)) <=> (until2p29(s81) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s81)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(11324,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s81)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s81))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s81) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s81))))),
% 1.40/1.59 inference(monotonicity,[status(thm)],[11323])).
% 1.40/1.59 tff(11325,plain,
% 1.40/1.59 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s81)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s81))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s81) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s81)))),
% 1.40/1.59 inference(transitivity,[status(thm)],[11324, 11322])).
% 1.40/1.59 tff(11326,plain,
% 1.40/1.59 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s81)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s81))),
% 1.40/1.59 inference(quant_inst,[status(thm)],[])).
% 1.40/1.59 tff(11327,plain,
% 1.40/1.59 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s81) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s81))),
% 1.40/1.59 inference(modus_ponens,[status(thm)],[11326, 11325])).
% 1.40/1.59 tff(11328,plain,
% 1.40/1.59 ($false),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11327, 10200, 11321, 11219, 11320, 11220])).
% 1.40/1.59 tff(11329,plain,((~trans(s99, s81)) | until2p29(s81) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.59 tff(11330,plain,
% 1.40/1.59 (~trans(s99, s81)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[11329, 10409, 10186])).
% 1.40/1.59 tff(11331,assumption,(~until2p29(s68)), introduced(assumption)).
% 1.40/1.59 tff(11332,assumption,(trans(s99, s68)), introduced(assumption)).
% 1.40/1.60 tff(11333,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s68) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s68)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s68) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s68)))),
% 1.40/1.60 inference(rewrite,[status(thm)],[])).
% 1.40/1.60 tff(11334,plain,
% 1.40/1.60 (((~trans(s99, s68)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s68)) <=> (until2p29(s68) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s68)))),
% 1.40/1.60 inference(rewrite,[status(thm)],[])).
% 1.40/1.60 tff(11335,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s68)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s68))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s68) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s68))))),
% 1.40/1.60 inference(monotonicity,[status(thm)],[11334])).
% 1.40/1.60 tff(11336,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s68)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s68))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s68) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s68)))),
% 1.40/1.60 inference(transitivity,[status(thm)],[11335, 11333])).
% 1.40/1.60 tff(11337,plain,
% 1.40/1.60 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s68)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s68))),
% 1.40/1.60 inference(quant_inst,[status(thm)],[])).
% 1.40/1.60 tff(11338,plain,
% 1.40/1.60 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s68) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s68))),
% 1.40/1.60 inference(modus_ponens,[status(thm)],[11337, 11336])).
% 1.40/1.60 tff(11339,plain,
% 1.40/1.60 ($false),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[11338, 10200, 11332, 11219, 11331, 11220])).
% 1.40/1.60 tff(11340,plain,((~trans(s99, s68)) | until2p29(s68) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.60 tff(11341,plain,
% 1.40/1.60 (~trans(s99, s68)),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[11340, 10539, 10186])).
% 1.40/1.60 tff(11342,assumption,(~until2p29(s10)), introduced(assumption)).
% 1.40/1.60 tff(11343,assumption,(trans(s99, s10)), introduced(assumption)).
% 1.40/1.60 tff(11344,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s10) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s10)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s10) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s10)))),
% 1.40/1.60 inference(rewrite,[status(thm)],[])).
% 1.40/1.60 tff(11345,plain,
% 1.40/1.60 (((~trans(s99, s10)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s10)) <=> (until2p29(s10) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s10)))),
% 1.40/1.60 inference(rewrite,[status(thm)],[])).
% 1.40/1.60 tff(11346,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s10)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s10))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s10) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s10))))),
% 1.40/1.60 inference(monotonicity,[status(thm)],[11345])).
% 1.40/1.60 tff(11347,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s10)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s10))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s10) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s10)))),
% 1.40/1.60 inference(transitivity,[status(thm)],[11346, 11344])).
% 1.40/1.60 tff(11348,plain,
% 1.40/1.60 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s10)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s10))),
% 1.40/1.60 inference(quant_inst,[status(thm)],[])).
% 1.40/1.60 tff(11349,plain,
% 1.40/1.60 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s10) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s10))),
% 1.40/1.60 inference(modus_ponens,[status(thm)],[11348, 11347])).
% 1.40/1.60 tff(11350,plain,
% 1.40/1.60 ($false),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[11349, 10200, 11343, 11219, 11342, 11220])).
% 1.40/1.60 tff(11351,plain,((~trans(s99, s10)) | until2p29(s10) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.60 tff(11352,plain,
% 1.40/1.60 (~trans(s99, s10)),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[11351, 11119, 10186])).
% 1.40/1.60 tff(11353,assumption,(~until2p29(s82)), introduced(assumption)).
% 1.40/1.60 tff(11354,assumption,(trans(s99, s82)), introduced(assumption)).
% 1.40/1.60 tff(11355,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s82) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s82)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s82) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s82)))),
% 1.40/1.60 inference(rewrite,[status(thm)],[])).
% 1.40/1.60 tff(11356,plain,
% 1.40/1.60 (((~trans(s99, s82)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s82)) <=> (until2p29(s82) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s82)))),
% 1.40/1.60 inference(rewrite,[status(thm)],[])).
% 1.40/1.60 tff(11357,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s82)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s82))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s82) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s82))))),
% 1.40/1.60 inference(monotonicity,[status(thm)],[11356])).
% 1.40/1.60 tff(11358,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s82)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s82))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s82) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s82)))),
% 1.40/1.60 inference(transitivity,[status(thm)],[11357, 11355])).
% 1.40/1.60 tff(11359,plain,
% 1.40/1.60 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s82)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s82))),
% 1.40/1.60 inference(quant_inst,[status(thm)],[])).
% 1.40/1.60 tff(11360,plain,
% 1.40/1.60 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s82) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s82))),
% 1.40/1.60 inference(modus_ponens,[status(thm)],[11359, 11358])).
% 1.40/1.60 tff(11361,plain,
% 1.40/1.60 ($false),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[11360, 10200, 11354, 11219, 11353, 11220])).
% 1.40/1.60 tff(11362,plain,((~trans(s99, s82)) | until2p29(s82) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.60 tff(11363,plain,
% 1.40/1.60 (~trans(s99, s82)),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[11362, 10399, 10186])).
% 1.40/1.60 tff(11364,assumption,(~until2p29(s35)), introduced(assumption)).
% 1.40/1.60 tff(11365,assumption,(trans(s99, s35)), introduced(assumption)).
% 1.40/1.60 tff(11366,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s35) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s35)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s35) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s35)))),
% 1.40/1.60 inference(rewrite,[status(thm)],[])).
% 1.40/1.60 tff(11367,plain,
% 1.40/1.60 (((~trans(s99, s35)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s35)) <=> (until2p29(s35) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s35)))),
% 1.40/1.60 inference(rewrite,[status(thm)],[])).
% 1.40/1.60 tff(11368,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s35)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s35))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s35) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s35))))),
% 1.40/1.60 inference(monotonicity,[status(thm)],[11367])).
% 1.40/1.60 tff(11369,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s35)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s35))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s35) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s35)))),
% 1.40/1.60 inference(transitivity,[status(thm)],[11368, 11366])).
% 1.40/1.60 tff(11370,plain,
% 1.40/1.60 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s35)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s35))),
% 1.40/1.60 inference(quant_inst,[status(thm)],[])).
% 1.40/1.60 tff(11371,plain,
% 1.40/1.60 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s35) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s35))),
% 1.40/1.60 inference(modus_ponens,[status(thm)],[11370, 11369])).
% 1.40/1.60 tff(11372,plain,
% 1.40/1.60 ($false),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[11371, 10200, 11365, 11219, 11364, 11220])).
% 1.40/1.60 tff(11373,plain,((~trans(s99, s35)) | until2p29(s35) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.60 tff(11374,plain,
% 1.40/1.60 (~trans(s99, s35)),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[11373, 10869, 10186])).
% 1.40/1.60 tff(11375,assumption,(~until2p29(s37)), introduced(assumption)).
% 1.40/1.60 tff(11376,assumption,(trans(s99, s37)), introduced(assumption)).
% 1.40/1.60 tff(11377,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s37) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s37)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s37) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s37)))),
% 1.40/1.60 inference(rewrite,[status(thm)],[])).
% 1.40/1.60 tff(11378,plain,
% 1.40/1.60 (((~trans(s99, s37)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s37)) <=> (until2p29(s37) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s37)))),
% 1.40/1.60 inference(rewrite,[status(thm)],[])).
% 1.40/1.60 tff(11379,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s37)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s37))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s37) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s37))))),
% 1.40/1.60 inference(monotonicity,[status(thm)],[11378])).
% 1.40/1.60 tff(11380,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s37)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s37))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s37) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s37)))),
% 1.40/1.60 inference(transitivity,[status(thm)],[11379, 11377])).
% 1.40/1.60 tff(11381,plain,
% 1.40/1.60 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s37)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s37))),
% 1.40/1.60 inference(quant_inst,[status(thm)],[])).
% 1.40/1.60 tff(11382,plain,
% 1.40/1.60 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s37) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s37))),
% 1.40/1.60 inference(modus_ponens,[status(thm)],[11381, 11380])).
% 1.40/1.60 tff(11383,plain,
% 1.40/1.60 ($false),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[11382, 10200, 11376, 11219, 11375, 11220])).
% 1.40/1.60 tff(11384,plain,((~trans(s99, s37)) | until2p29(s37) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.60 tff(11385,plain,
% 1.40/1.60 (~trans(s99, s37)),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[11384, 10849, 10186])).
% 1.40/1.60 tff(11386,assumption,(~until2p29(s2)), introduced(assumption)).
% 1.40/1.60 tff(11387,assumption,(trans(s99, s2)), introduced(assumption)).
% 1.40/1.60 tff(11388,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s2) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s2)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s2) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s2)))),
% 1.40/1.60 inference(rewrite,[status(thm)],[])).
% 1.40/1.60 tff(11389,plain,
% 1.40/1.60 (((~trans(s99, s2)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s2)) <=> (until2p29(s2) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s2)))),
% 1.40/1.60 inference(rewrite,[status(thm)],[])).
% 1.40/1.60 tff(11390,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s2)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s2))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s2) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s2))))),
% 1.40/1.60 inference(monotonicity,[status(thm)],[11389])).
% 1.40/1.60 tff(11391,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s2)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s2))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s2) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s2)))),
% 1.40/1.60 inference(transitivity,[status(thm)],[11390, 11388])).
% 1.40/1.60 tff(11392,plain,
% 1.40/1.60 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s2)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s2))),
% 1.40/1.60 inference(quant_inst,[status(thm)],[])).
% 1.40/1.60 tff(11393,plain,
% 1.40/1.60 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s2) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s2))),
% 1.40/1.60 inference(modus_ponens,[status(thm)],[11392, 11391])).
% 1.40/1.60 tff(11394,plain,
% 1.40/1.60 ($false),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[11393, 10200, 11387, 11219, 11386, 11220])).
% 1.40/1.60 tff(11395,plain,((~trans(s99, s2)) | until2p29(s2) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.60 tff(11396,plain,
% 1.40/1.60 (~trans(s99, s2)),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[11395, 11199, 10186])).
% 1.40/1.60 tff(11397,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s0, s1)) | until2p29(s1) | (~xuntil2p30(s0)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s0, s1)) | until2p29(s1) | (~xuntil2p30(s0)))),
% 1.40/1.60 inference(rewrite,[status(thm)],[])).
% 1.40/1.60 tff(11398,plain,
% 1.40/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s0, s1)) | until2p29(s1) | (~xuntil2p30(s0)))),
% 1.40/1.60 inference(quant_inst,[status(thm)],[])).
% 1.40/1.60 tff(11399,plain,
% 1.40/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s0, s1)) | until2p29(s1) | (~xuntil2p30(s0))),
% 1.40/1.60 inference(modus_ponens,[status(thm)],[11398, 11397])).
% 1.40/1.60 tff(11400,plain,
% 1.40/1.60 (until2p29(s1) | (~xuntil2p30(s0))),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[11399, 35, 10229])).
% 1.40/1.60 tff(11401,plain,
% 1.40/1.60 (~xuntil2p30(s0)),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[11400, 11209])).
% 1.40/1.60 tff(11402,plain,
% 1.40/1.60 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s0) | xuntil2p30(s0) | (~until2p29(s0)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s0) | xuntil2p30(s0) | (~until2p29(s0)))),
% 1.40/1.60 inference(rewrite,[status(thm)],[])).
% 1.40/1.60 tff(11403,plain,
% 1.40/1.60 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s0) | xuntil2p30(s0) | (~until2p29(s0)))),
% 1.40/1.60 inference(quant_inst,[status(thm)],[])).
% 1.40/1.60 tff(11404,plain,
% 1.40/1.60 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s0) | xuntil2p30(s0) | (~until2p29(s0))),
% 1.40/1.60 inference(modus_ponens,[status(thm)],[11403, 11402])).
% 1.40/1.60 tff(11405,plain,
% 1.40/1.60 (xuntil2p30(s0) | (~until2p29(s0))),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[11404, 10214, 8808])).
% 1.40/1.60 tff(11406,plain,
% 1.40/1.60 (~until2p29(s0)),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[11405, 11401])).
% 1.40/1.60 tff(11407,assumption,(~until2p29(s0)), introduced(assumption)).
% 1.40/1.60 tff(11408,assumption,(trans(s99, s0)), introduced(assumption)).
% 1.40/1.60 tff(11409,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~last(s99)) | (~xuntil28(s99)) | until2p29(s0) | (~trans(s99, s0)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s0) | (~trans(s99, s0)))),
% 1.40/1.60 inference(rewrite,[status(thm)],[])).
% 1.40/1.60 tff(11410,plain,
% 1.40/1.60 (((~trans(s99, s0)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s0)) <=> ((~last(s99)) | (~xuntil28(s99)) | until2p29(s0) | (~trans(s99, s0)))),
% 1.40/1.60 inference(rewrite,[status(thm)],[])).
% 1.40/1.60 tff(11411,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s0)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s0))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~last(s99)) | (~xuntil28(s99)) | until2p29(s0) | (~trans(s99, s0))))),
% 1.40/1.60 inference(monotonicity,[status(thm)],[11410])).
% 1.40/1.60 tff(11412,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s0)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s0))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s0) | (~trans(s99, s0)))),
% 1.40/1.60 inference(transitivity,[status(thm)],[11411, 11409])).
% 1.40/1.60 tff(11413,plain,
% 1.40/1.60 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s0)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s0))),
% 1.40/1.60 inference(quant_inst,[status(thm)],[])).
% 1.40/1.60 tff(11414,plain,
% 1.40/1.60 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s0) | (~trans(s99, s0))),
% 1.40/1.60 inference(modus_ponens,[status(thm)],[11413, 11412])).
% 1.40/1.60 tff(11415,plain,
% 1.40/1.60 ($false),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[11414, 10200, 11408, 11219, 11220, 11407])).
% 1.40/1.60 tff(11416,plain,((~trans(s99, s0)) | (~xuntil28(s99)) | until2p29(s0)), inference(lemma,lemma(discharge,[]))).
% 1.40/1.60 tff(11417,plain,
% 1.40/1.60 (~trans(s99, s0)),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[11416, 11406, 10186])).
% 1.40/1.60 tff(11418,assumption,(~until2p29(s84)), introduced(assumption)).
% 1.40/1.60 tff(11419,assumption,(trans(s99, s84)), introduced(assumption)).
% 1.40/1.60 tff(11420,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s84) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s84)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s84) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s84)))),
% 1.40/1.60 inference(rewrite,[status(thm)],[])).
% 1.40/1.60 tff(11421,plain,
% 1.40/1.60 (((~trans(s99, s84)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s84)) <=> (until2p29(s84) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s84)))),
% 1.40/1.60 inference(rewrite,[status(thm)],[])).
% 1.40/1.60 tff(11422,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s84)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s84))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s84) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s84))))),
% 1.40/1.60 inference(monotonicity,[status(thm)],[11421])).
% 1.40/1.60 tff(11423,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s84)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s84))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s84) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s84)))),
% 1.40/1.60 inference(transitivity,[status(thm)],[11422, 11420])).
% 1.40/1.60 tff(11424,plain,
% 1.40/1.60 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s84)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s84))),
% 1.40/1.60 inference(quant_inst,[status(thm)],[])).
% 1.40/1.60 tff(11425,plain,
% 1.40/1.60 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s84) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s84))),
% 1.40/1.60 inference(modus_ponens,[status(thm)],[11424, 11423])).
% 1.40/1.60 tff(11426,plain,
% 1.40/1.60 ($false),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[11425, 10200, 11419, 11219, 11418, 11220])).
% 1.40/1.60 tff(11427,plain,((~trans(s99, s84)) | until2p29(s84) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.60 tff(11428,plain,
% 1.40/1.60 (~trans(s99, s84)),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[11427, 10379, 10186])).
% 1.40/1.60 tff(11429,assumption,(~until2p29(s73)), introduced(assumption)).
% 1.40/1.60 tff(11430,assumption,(trans(s99, s73)), introduced(assumption)).
% 1.40/1.60 tff(11431,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s73) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s73)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s73) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s73)))),
% 1.40/1.60 inference(rewrite,[status(thm)],[])).
% 1.40/1.60 tff(11432,plain,
% 1.40/1.60 (((~trans(s99, s73)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s73)) <=> (until2p29(s73) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s73)))),
% 1.40/1.60 inference(rewrite,[status(thm)],[])).
% 1.40/1.60 tff(11433,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s73)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s73))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s73) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s73))))),
% 1.40/1.60 inference(monotonicity,[status(thm)],[11432])).
% 1.40/1.60 tff(11434,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s73)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s73))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s73) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s73)))),
% 1.40/1.60 inference(transitivity,[status(thm)],[11433, 11431])).
% 1.40/1.60 tff(11435,plain,
% 1.40/1.60 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s73)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s73))),
% 1.40/1.60 inference(quant_inst,[status(thm)],[])).
% 1.40/1.60 tff(11436,plain,
% 1.40/1.60 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s73) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s73))),
% 1.40/1.60 inference(modus_ponens,[status(thm)],[11435, 11434])).
% 1.40/1.60 tff(11437,plain,
% 1.40/1.60 ($false),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[11436, 10200, 11430, 11219, 11429, 11220])).
% 1.40/1.60 tff(11438,plain,((~trans(s99, s73)) | until2p29(s73) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.60 tff(11439,plain,
% 1.40/1.60 (~trans(s99, s73)),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[11438, 10489, 10186])).
% 1.40/1.60 tff(11440,assumption,(~until2p29(s41)), introduced(assumption)).
% 1.40/1.60 tff(11441,assumption,(trans(s99, s41)), introduced(assumption)).
% 1.40/1.60 tff(11442,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s41) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s41)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s41) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s41)))),
% 1.40/1.60 inference(rewrite,[status(thm)],[])).
% 1.40/1.60 tff(11443,plain,
% 1.40/1.60 (((~trans(s99, s41)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s41)) <=> (until2p29(s41) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s41)))),
% 1.40/1.60 inference(rewrite,[status(thm)],[])).
% 1.40/1.60 tff(11444,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s41)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s41))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s41) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s41))))),
% 1.40/1.60 inference(monotonicity,[status(thm)],[11443])).
% 1.40/1.60 tff(11445,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s41)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s41))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s41) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s41)))),
% 1.40/1.60 inference(transitivity,[status(thm)],[11444, 11442])).
% 1.40/1.60 tff(11446,plain,
% 1.40/1.60 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s41)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s41))),
% 1.40/1.60 inference(quant_inst,[status(thm)],[])).
% 1.40/1.60 tff(11447,plain,
% 1.40/1.60 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s41) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s41))),
% 1.40/1.60 inference(modus_ponens,[status(thm)],[11446, 11445])).
% 1.40/1.60 tff(11448,plain,
% 1.40/1.60 ($false),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[11447, 10200, 11441, 11219, 11440, 11220])).
% 1.40/1.60 tff(11449,plain,((~trans(s99, s41)) | until2p29(s41) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.60 tff(11450,plain,
% 1.40/1.60 (~trans(s99, s41)),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[11449, 10809, 10186])).
% 1.40/1.60 tff(11451,assumption,(~until2p29(s12)), introduced(assumption)).
% 1.40/1.60 tff(11452,assumption,(trans(s99, s12)), introduced(assumption)).
% 1.40/1.60 tff(11453,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s12) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s12)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s12) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s12)))),
% 1.40/1.60 inference(rewrite,[status(thm)],[])).
% 1.40/1.60 tff(11454,plain,
% 1.40/1.60 (((~trans(s99, s12)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s12)) <=> (until2p29(s12) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s12)))),
% 1.40/1.60 inference(rewrite,[status(thm)],[])).
% 1.40/1.60 tff(11455,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s12)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s12))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s12) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s12))))),
% 1.40/1.60 inference(monotonicity,[status(thm)],[11454])).
% 1.40/1.60 tff(11456,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s12)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s12))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s12) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s12)))),
% 1.40/1.60 inference(transitivity,[status(thm)],[11455, 11453])).
% 1.40/1.60 tff(11457,plain,
% 1.40/1.60 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s12)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s12))),
% 1.40/1.60 inference(quant_inst,[status(thm)],[])).
% 1.40/1.60 tff(11458,plain,
% 1.40/1.60 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s12) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s12))),
% 1.40/1.60 inference(modus_ponens,[status(thm)],[11457, 11456])).
% 1.40/1.60 tff(11459,plain,
% 1.40/1.60 ($false),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[11458, 10200, 11452, 11219, 11451, 11220])).
% 1.40/1.60 tff(11460,plain,((~trans(s99, s12)) | until2p29(s12) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.60 tff(11461,plain,
% 1.40/1.60 (~trans(s99, s12)),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[11460, 11099, 10186])).
% 1.40/1.60 tff(11462,assumption,(~until2p29(s55)), introduced(assumption)).
% 1.40/1.60 tff(11463,assumption,(trans(s99, s55)), introduced(assumption)).
% 1.40/1.60 tff(11464,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s55) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s55)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s55) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s55)))),
% 1.40/1.60 inference(rewrite,[status(thm)],[])).
% 1.40/1.60 tff(11465,plain,
% 1.40/1.60 (((~trans(s99, s55)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s55)) <=> (until2p29(s55) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s55)))),
% 1.40/1.60 inference(rewrite,[status(thm)],[])).
% 1.40/1.60 tff(11466,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s55)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s55))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s55) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s55))))),
% 1.40/1.60 inference(monotonicity,[status(thm)],[11465])).
% 1.40/1.60 tff(11467,plain,
% 1.40/1.60 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s55)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s55))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s55) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s55)))),
% 1.40/1.60 inference(transitivity,[status(thm)],[11466, 11464])).
% 1.40/1.60 tff(11468,plain,
% 1.40/1.60 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s55)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s55))),
% 1.40/1.60 inference(quant_inst,[status(thm)],[])).
% 1.40/1.60 tff(11469,plain,
% 1.40/1.60 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s55) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s55))),
% 1.40/1.60 inference(modus_ponens,[status(thm)],[11468, 11467])).
% 1.40/1.60 tff(11470,plain,
% 1.40/1.60 ($false),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[11469, 10200, 11463, 11219, 11462, 11220])).
% 1.40/1.60 tff(11471,plain,((~trans(s99, s55)) | until2p29(s55) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.60 tff(11472,plain,
% 1.40/1.60 (~trans(s99, s55)),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[11471, 10669, 10186])).
% 1.40/1.61 tff(11473,assumption,(~until2p29(s56)), introduced(assumption)).
% 1.40/1.61 tff(11474,assumption,(trans(s99, s56)), introduced(assumption)).
% 1.40/1.61 tff(11475,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s56) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s56)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s56) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s56)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(11476,plain,
% 1.40/1.61 (((~trans(s99, s56)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s56)) <=> (until2p29(s56) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s56)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(11477,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s56)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s56))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s56) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s56))))),
% 1.40/1.61 inference(monotonicity,[status(thm)],[11476])).
% 1.40/1.61 tff(11478,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s56)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s56))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s56) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s56)))),
% 1.40/1.61 inference(transitivity,[status(thm)],[11477, 11475])).
% 1.40/1.61 tff(11479,plain,
% 1.40/1.61 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s56)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s56))),
% 1.40/1.61 inference(quant_inst,[status(thm)],[])).
% 1.40/1.61 tff(11480,plain,
% 1.40/1.61 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s56) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s56))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[11479, 11478])).
% 1.40/1.61 tff(11481,plain,
% 1.40/1.61 ($false),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[11480, 10200, 11474, 11219, 11473, 11220])).
% 1.40/1.61 tff(11482,plain,((~trans(s99, s56)) | until2p29(s56) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.61 tff(11483,plain,
% 1.40/1.61 (~trans(s99, s56)),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[11482, 10659, 10186])).
% 1.40/1.61 tff(11484,assumption,(~until2p29(s86)), introduced(assumption)).
% 1.40/1.61 tff(11485,assumption,(trans(s99, s86)), introduced(assumption)).
% 1.40/1.61 tff(11486,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s86) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s86)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s86) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s86)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(11487,plain,
% 1.40/1.61 (((~trans(s99, s86)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s86)) <=> (until2p29(s86) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s86)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(11488,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s86)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s86))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s86) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s86))))),
% 1.40/1.61 inference(monotonicity,[status(thm)],[11487])).
% 1.40/1.61 tff(11489,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s86)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s86))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s86) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s86)))),
% 1.40/1.61 inference(transitivity,[status(thm)],[11488, 11486])).
% 1.40/1.61 tff(11490,plain,
% 1.40/1.61 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s86)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s86))),
% 1.40/1.61 inference(quant_inst,[status(thm)],[])).
% 1.40/1.61 tff(11491,plain,
% 1.40/1.61 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s86) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s86))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[11490, 11489])).
% 1.40/1.61 tff(11492,plain,
% 1.40/1.61 ($false),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[11491, 10200, 11485, 11219, 11484, 11220])).
% 1.40/1.61 tff(11493,plain,((~trans(s99, s86)) | until2p29(s86) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.61 tff(11494,plain,
% 1.40/1.61 (~trans(s99, s86)),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[11493, 10359, 10186])).
% 1.40/1.61 tff(11495,assumption,(~until2p29(s62)), introduced(assumption)).
% 1.40/1.61 tff(11496,assumption,(trans(s99, s62)), introduced(assumption)).
% 1.40/1.61 tff(11497,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s62) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s62)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s62) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s62)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(11498,plain,
% 1.40/1.61 (((~trans(s99, s62)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s62)) <=> (until2p29(s62) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s62)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(11499,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s62)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s62))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s62) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s62))))),
% 1.40/1.61 inference(monotonicity,[status(thm)],[11498])).
% 1.40/1.61 tff(11500,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s62)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s62))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s62) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s62)))),
% 1.40/1.61 inference(transitivity,[status(thm)],[11499, 11497])).
% 1.40/1.61 tff(11501,plain,
% 1.40/1.61 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s62)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s62))),
% 1.40/1.61 inference(quant_inst,[status(thm)],[])).
% 1.40/1.61 tff(11502,plain,
% 1.40/1.61 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s62) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s62))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[11501, 11500])).
% 1.40/1.61 tff(11503,plain,
% 1.40/1.61 ($false),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[11502, 10200, 11496, 11219, 11495, 11220])).
% 1.40/1.61 tff(11504,plain,((~trans(s99, s62)) | until2p29(s62) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.61 tff(11505,plain,
% 1.40/1.61 (~trans(s99, s62)),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[11504, 10599, 10186])).
% 1.40/1.61 tff(11506,assumption,(~until2p29(s11)), introduced(assumption)).
% 1.40/1.61 tff(11507,assumption,(trans(s99, s11)), introduced(assumption)).
% 1.40/1.61 tff(11508,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s11) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s11)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s11) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s11)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(11509,plain,
% 1.40/1.61 (((~trans(s99, s11)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s11)) <=> (until2p29(s11) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s11)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(11510,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s11)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s11))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s11) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s11))))),
% 1.40/1.61 inference(monotonicity,[status(thm)],[11509])).
% 1.40/1.61 tff(11511,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s11)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s11))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s11) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s11)))),
% 1.40/1.61 inference(transitivity,[status(thm)],[11510, 11508])).
% 1.40/1.61 tff(11512,plain,
% 1.40/1.61 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s11)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s11))),
% 1.40/1.61 inference(quant_inst,[status(thm)],[])).
% 1.40/1.61 tff(11513,plain,
% 1.40/1.61 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s11) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s11))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[11512, 11511])).
% 1.40/1.61 tff(11514,plain,
% 1.40/1.61 ($false),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[11513, 10200, 11507, 11219, 11506, 11220])).
% 1.40/1.61 tff(11515,plain,((~trans(s99, s11)) | until2p29(s11) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.61 tff(11516,plain,
% 1.40/1.61 (~trans(s99, s11)),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[11515, 11109, 10186])).
% 1.40/1.61 tff(11517,assumption,(~until2p29(s40)), introduced(assumption)).
% 1.40/1.61 tff(11518,assumption,(trans(s99, s40)), introduced(assumption)).
% 1.40/1.61 tff(11519,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s40) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s40)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s40) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s40)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(11520,plain,
% 1.40/1.61 (((~trans(s99, s40)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s40)) <=> (until2p29(s40) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s40)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(11521,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s40)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s40))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s40) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s40))))),
% 1.40/1.61 inference(monotonicity,[status(thm)],[11520])).
% 1.40/1.61 tff(11522,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s40)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s40))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s40) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s40)))),
% 1.40/1.61 inference(transitivity,[status(thm)],[11521, 11519])).
% 1.40/1.61 tff(11523,plain,
% 1.40/1.61 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s40)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s40))),
% 1.40/1.61 inference(quant_inst,[status(thm)],[])).
% 1.40/1.61 tff(11524,plain,
% 1.40/1.61 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s40) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s40))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[11523, 11522])).
% 1.40/1.61 tff(11525,plain,
% 1.40/1.61 ($false),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[11524, 10200, 11518, 11219, 11517, 11220])).
% 1.40/1.61 tff(11526,plain,((~trans(s99, s40)) | until2p29(s40) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.61 tff(11527,plain,
% 1.40/1.61 (~trans(s99, s40)),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[11526, 10819, 10186])).
% 1.40/1.61 tff(11528,assumption,(~until2p29(s57)), introduced(assumption)).
% 1.40/1.61 tff(11529,assumption,(trans(s99, s57)), introduced(assumption)).
% 1.40/1.61 tff(11530,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s57) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s57)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s57) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s57)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(11531,plain,
% 1.40/1.61 (((~trans(s99, s57)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s57)) <=> (until2p29(s57) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s57)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(11532,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s57)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s57))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s57) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s57))))),
% 1.40/1.61 inference(monotonicity,[status(thm)],[11531])).
% 1.40/1.61 tff(11533,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s57)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s57))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s57) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s57)))),
% 1.40/1.61 inference(transitivity,[status(thm)],[11532, 11530])).
% 1.40/1.61 tff(11534,plain,
% 1.40/1.61 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s57)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s57))),
% 1.40/1.61 inference(quant_inst,[status(thm)],[])).
% 1.40/1.61 tff(11535,plain,
% 1.40/1.61 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s57) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s57))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[11534, 11533])).
% 1.40/1.61 tff(11536,plain,
% 1.40/1.61 ($false),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[11535, 10200, 11529, 11219, 11528, 11220])).
% 1.40/1.61 tff(11537,plain,((~trans(s99, s57)) | until2p29(s57) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.61 tff(11538,plain,
% 1.40/1.61 (~trans(s99, s57)),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[11537, 10649, 10186])).
% 1.40/1.61 tff(11539,assumption,(~until2p29(s54)), introduced(assumption)).
% 1.40/1.61 tff(11540,assumption,(trans(s99, s54)), introduced(assumption)).
% 1.40/1.61 tff(11541,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s54) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s54)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s54) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s54)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(11542,plain,
% 1.40/1.61 (((~trans(s99, s54)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s54)) <=> (until2p29(s54) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s54)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(11543,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s54)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s54))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s54) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s54))))),
% 1.40/1.61 inference(monotonicity,[status(thm)],[11542])).
% 1.40/1.61 tff(11544,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s54)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s54))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s54) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s54)))),
% 1.40/1.61 inference(transitivity,[status(thm)],[11543, 11541])).
% 1.40/1.61 tff(11545,plain,
% 1.40/1.61 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s54)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s54))),
% 1.40/1.61 inference(quant_inst,[status(thm)],[])).
% 1.40/1.61 tff(11546,plain,
% 1.40/1.61 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s54) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s54))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[11545, 11544])).
% 1.40/1.61 tff(11547,plain,
% 1.40/1.61 ($false),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[11546, 10200, 11540, 11219, 11539, 11220])).
% 1.40/1.61 tff(11548,plain,((~trans(s99, s54)) | until2p29(s54) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.61 tff(11549,plain,
% 1.40/1.61 (~trans(s99, s54)),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[11548, 10679, 10186])).
% 1.40/1.61 tff(11550,assumption,(~until2p29(s51)), introduced(assumption)).
% 1.40/1.61 tff(11551,assumption,(trans(s99, s51)), introduced(assumption)).
% 1.40/1.61 tff(11552,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s51) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s51)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s51) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s51)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(11553,plain,
% 1.40/1.61 (((~trans(s99, s51)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s51)) <=> (until2p29(s51) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s51)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(11554,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s51)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s51))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s51) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s51))))),
% 1.40/1.61 inference(monotonicity,[status(thm)],[11553])).
% 1.40/1.61 tff(11555,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s51)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s51))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s51) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s51)))),
% 1.40/1.61 inference(transitivity,[status(thm)],[11554, 11552])).
% 1.40/1.61 tff(11556,plain,
% 1.40/1.61 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s51)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s51))),
% 1.40/1.61 inference(quant_inst,[status(thm)],[])).
% 1.40/1.61 tff(11557,plain,
% 1.40/1.61 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s51) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s51))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[11556, 11555])).
% 1.40/1.61 tff(11558,plain,
% 1.40/1.61 ($false),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[11557, 10200, 11551, 11219, 11550, 11220])).
% 1.40/1.61 tff(11559,plain,((~trans(s99, s51)) | until2p29(s51) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.61 tff(11560,plain,
% 1.40/1.61 (~trans(s99, s51)),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[11559, 10709, 10186])).
% 1.40/1.61 tff(11561,assumption,(~until2p29(s44)), introduced(assumption)).
% 1.40/1.61 tff(11562,assumption,(trans(s99, s44)), introduced(assumption)).
% 1.40/1.61 tff(11563,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s44) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s44)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s44) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s44)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(11564,plain,
% 1.40/1.61 (((~trans(s99, s44)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s44)) <=> (until2p29(s44) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s44)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(11565,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s44)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s44))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s44) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s44))))),
% 1.40/1.61 inference(monotonicity,[status(thm)],[11564])).
% 1.40/1.61 tff(11566,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s44)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s44))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s44) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s44)))),
% 1.40/1.61 inference(transitivity,[status(thm)],[11565, 11563])).
% 1.40/1.61 tff(11567,plain,
% 1.40/1.61 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s44)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s44))),
% 1.40/1.61 inference(quant_inst,[status(thm)],[])).
% 1.40/1.61 tff(11568,plain,
% 1.40/1.61 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s44) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s44))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[11567, 11566])).
% 1.40/1.61 tff(11569,plain,
% 1.40/1.61 ($false),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[11568, 10200, 11562, 11219, 11561, 11220])).
% 1.40/1.61 tff(11570,plain,((~trans(s99, s44)) | until2p29(s44) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.61 tff(11571,plain,
% 1.40/1.61 (~trans(s99, s44)),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[11570, 10779, 10186])).
% 1.40/1.61 tff(11572,assumption,(~until2p29(s4)), introduced(assumption)).
% 1.40/1.61 tff(11573,assumption,(trans(s99, s4)), introduced(assumption)).
% 1.40/1.61 tff(11574,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s4) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s4)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s4) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s4)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(11575,plain,
% 1.40/1.61 (((~trans(s99, s4)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s4)) <=> (until2p29(s4) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s4)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(11576,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s4)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s4))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s4) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s4))))),
% 1.40/1.61 inference(monotonicity,[status(thm)],[11575])).
% 1.40/1.61 tff(11577,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s4)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s4))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s4) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s4)))),
% 1.40/1.61 inference(transitivity,[status(thm)],[11576, 11574])).
% 1.40/1.61 tff(11578,plain,
% 1.40/1.61 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s4)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s4))),
% 1.40/1.61 inference(quant_inst,[status(thm)],[])).
% 1.40/1.61 tff(11579,plain,
% 1.40/1.61 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s4) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s4))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[11578, 11577])).
% 1.40/1.61 tff(11580,plain,
% 1.40/1.61 ($false),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[11579, 10200, 11573, 11219, 11572, 11220])).
% 1.40/1.61 tff(11581,plain,((~trans(s99, s4)) | until2p29(s4) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.61 tff(11582,plain,
% 1.40/1.61 (~trans(s99, s4)),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[11581, 11179, 10186])).
% 1.40/1.61 tff(11583,assumption,(~until2p29(s94)), introduced(assumption)).
% 1.40/1.61 tff(11584,assumption,(trans(s99, s94)), introduced(assumption)).
% 1.40/1.61 tff(11585,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s94) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s94)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s94) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s94)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(11586,plain,
% 1.40/1.61 (((~trans(s99, s94)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s94)) <=> (until2p29(s94) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s94)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(11587,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s94)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s94))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s94) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s94))))),
% 1.40/1.61 inference(monotonicity,[status(thm)],[11586])).
% 1.40/1.61 tff(11588,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s94)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s94))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s94) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s94)))),
% 1.40/1.61 inference(transitivity,[status(thm)],[11587, 11585])).
% 1.40/1.61 tff(11589,plain,
% 1.40/1.61 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s94)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s94))),
% 1.40/1.61 inference(quant_inst,[status(thm)],[])).
% 1.40/1.61 tff(11590,plain,
% 1.40/1.61 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s94) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s94))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[11589, 11588])).
% 1.40/1.61 tff(11591,plain,
% 1.40/1.61 ($false),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[11590, 10200, 11584, 11219, 11583, 11220])).
% 1.40/1.61 tff(11592,plain,((~trans(s99, s94)) | until2p29(s94) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.61 tff(11593,plain,
% 1.40/1.61 (~trans(s99, s94)),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[11592, 10279, 10186])).
% 1.40/1.61 tff(11594,assumption,(~until2p29(s59)), introduced(assumption)).
% 1.40/1.61 tff(11595,assumption,(trans(s99, s59)), introduced(assumption)).
% 1.40/1.61 tff(11596,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s59) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s59)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s59) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s59)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(11597,plain,
% 1.40/1.61 (((~trans(s99, s59)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s59)) <=> (until2p29(s59) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s59)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(11598,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s59)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s59))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s59) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s59))))),
% 1.40/1.61 inference(monotonicity,[status(thm)],[11597])).
% 1.40/1.61 tff(11599,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s59)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s59))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s59) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s59)))),
% 1.40/1.61 inference(transitivity,[status(thm)],[11598, 11596])).
% 1.40/1.61 tff(11600,plain,
% 1.40/1.61 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s59)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s59))),
% 1.40/1.61 inference(quant_inst,[status(thm)],[])).
% 1.40/1.61 tff(11601,plain,
% 1.40/1.61 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s59) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s59))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[11600, 11599])).
% 1.40/1.61 tff(11602,plain,
% 1.40/1.61 ($false),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[11601, 10200, 11595, 11219, 11594, 11220])).
% 1.40/1.61 tff(11603,plain,((~trans(s99, s59)) | until2p29(s59) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.61 tff(11604,plain,
% 1.40/1.61 (~trans(s99, s59)),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[11603, 10629, 10186])).
% 1.40/1.61 tff(11605,assumption,(~until2p29(s53)), introduced(assumption)).
% 1.40/1.61 tff(11606,assumption,(trans(s99, s53)), introduced(assumption)).
% 1.40/1.61 tff(11607,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s53) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s53)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s53) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s53)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(11608,plain,
% 1.40/1.61 (((~trans(s99, s53)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s53)) <=> (until2p29(s53) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s53)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(11609,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s53)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s53))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s53) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s53))))),
% 1.40/1.61 inference(monotonicity,[status(thm)],[11608])).
% 1.40/1.61 tff(11610,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s53)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s53))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s53) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s53)))),
% 1.40/1.61 inference(transitivity,[status(thm)],[11609, 11607])).
% 1.40/1.61 tff(11611,plain,
% 1.40/1.61 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s53)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s53))),
% 1.40/1.61 inference(quant_inst,[status(thm)],[])).
% 1.40/1.61 tff(11612,plain,
% 1.40/1.61 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s53) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s53))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[11611, 11610])).
% 1.40/1.61 tff(11613,plain,
% 1.40/1.61 ($false),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[11612, 10200, 11606, 11219, 11605, 11220])).
% 1.40/1.61 tff(11614,plain,((~trans(s99, s53)) | until2p29(s53) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.61 tff(11615,plain,
% 1.40/1.61 (~trans(s99, s53)),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[11614, 10689, 10186])).
% 1.40/1.61 tff(11616,assumption,(~until2p29(s18)), introduced(assumption)).
% 1.40/1.61 tff(11617,assumption,(trans(s99, s18)), introduced(assumption)).
% 1.40/1.61 tff(11618,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s18) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s18)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s18) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s18)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(11619,plain,
% 1.40/1.61 (((~trans(s99, s18)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s18)) <=> (until2p29(s18) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s18)))),
% 1.40/1.61 inference(rewrite,[status(thm)],[])).
% 1.40/1.61 tff(11620,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s18)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s18))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s18) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s18))))),
% 1.40/1.61 inference(monotonicity,[status(thm)],[11619])).
% 1.40/1.61 tff(11621,plain,
% 1.40/1.61 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s18)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s18))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s18) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s18)))),
% 1.40/1.61 inference(transitivity,[status(thm)],[11620, 11618])).
% 1.40/1.61 tff(11622,plain,
% 1.40/1.61 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s18)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s18))),
% 1.40/1.61 inference(quant_inst,[status(thm)],[])).
% 1.40/1.61 tff(11623,plain,
% 1.40/1.61 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s18) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s18))),
% 1.40/1.61 inference(modus_ponens,[status(thm)],[11622, 11621])).
% 1.40/1.61 tff(11624,plain,
% 1.40/1.61 ($false),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[11623, 10200, 11617, 11219, 11616, 11220])).
% 1.40/1.61 tff(11625,plain,((~trans(s99, s18)) | until2p29(s18) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.61 tff(11626,plain,
% 1.40/1.61 (~trans(s99, s18)),
% 1.40/1.61 inference(unit_resolution,[status(thm)],[11625, 11039, 10186])).
% 1.40/1.62 tff(11627,assumption,(~until2p29(s69)), introduced(assumption)).
% 1.40/1.62 tff(11628,assumption,(trans(s99, s69)), introduced(assumption)).
% 1.40/1.62 tff(11629,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s69) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s69)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s69) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s69)))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(11630,plain,
% 1.40/1.62 (((~trans(s99, s69)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s69)) <=> (until2p29(s69) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s69)))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(11631,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s69)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s69))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s69) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s69))))),
% 1.40/1.62 inference(monotonicity,[status(thm)],[11630])).
% 1.40/1.62 tff(11632,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s69)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s69))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s69) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s69)))),
% 1.40/1.62 inference(transitivity,[status(thm)],[11631, 11629])).
% 1.40/1.62 tff(11633,plain,
% 1.40/1.62 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s69)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s69))),
% 1.40/1.62 inference(quant_inst,[status(thm)],[])).
% 1.40/1.62 tff(11634,plain,
% 1.40/1.62 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s69) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s69))),
% 1.40/1.62 inference(modus_ponens,[status(thm)],[11633, 11632])).
% 1.40/1.62 tff(11635,plain,
% 1.40/1.62 ($false),
% 1.40/1.62 inference(unit_resolution,[status(thm)],[11634, 10200, 11628, 11219, 11627, 11220])).
% 1.40/1.62 tff(11636,plain,((~trans(s99, s69)) | until2p29(s69) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.62 tff(11637,plain,
% 1.40/1.62 (~trans(s99, s69)),
% 1.40/1.62 inference(unit_resolution,[status(thm)],[11636, 10529, 10186])).
% 1.40/1.62 tff(11638,assumption,(~until2p29(s93)), introduced(assumption)).
% 1.40/1.62 tff(11639,assumption,(trans(s99, s93)), introduced(assumption)).
% 1.40/1.62 tff(11640,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s93) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s93)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s93) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s93)))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(11641,plain,
% 1.40/1.62 (((~trans(s99, s93)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s93)) <=> (until2p29(s93) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s93)))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(11642,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s93)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s93))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s93) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s93))))),
% 1.40/1.62 inference(monotonicity,[status(thm)],[11641])).
% 1.40/1.62 tff(11643,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s93)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s93))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s93) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s93)))),
% 1.40/1.62 inference(transitivity,[status(thm)],[11642, 11640])).
% 1.40/1.62 tff(11644,plain,
% 1.40/1.62 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s93)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s93))),
% 1.40/1.62 inference(quant_inst,[status(thm)],[])).
% 1.40/1.62 tff(11645,plain,
% 1.40/1.62 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s93) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s93))),
% 1.40/1.62 inference(modus_ponens,[status(thm)],[11644, 11643])).
% 1.40/1.62 tff(11646,plain,
% 1.40/1.62 ($false),
% 1.40/1.62 inference(unit_resolution,[status(thm)],[11645, 10200, 11639, 11219, 11638, 11220])).
% 1.40/1.62 tff(11647,plain,((~trans(s99, s93)) | until2p29(s93) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.62 tff(11648,plain,
% 1.40/1.62 (~trans(s99, s93)),
% 1.40/1.62 inference(unit_resolution,[status(thm)],[11647, 10289, 10186])).
% 1.40/1.62 tff(11649,assumption,(~until2p29(s61)), introduced(assumption)).
% 1.40/1.62 tff(11650,assumption,(trans(s99, s61)), introduced(assumption)).
% 1.40/1.62 tff(11651,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s61) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s61)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s61) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s61)))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(11652,plain,
% 1.40/1.62 (((~trans(s99, s61)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s61)) <=> (until2p29(s61) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s61)))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(11653,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s61)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s61))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s61) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s61))))),
% 1.40/1.62 inference(monotonicity,[status(thm)],[11652])).
% 1.40/1.62 tff(11654,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s61)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s61))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s61) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s61)))),
% 1.40/1.62 inference(transitivity,[status(thm)],[11653, 11651])).
% 1.40/1.62 tff(11655,plain,
% 1.40/1.62 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s61)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s61))),
% 1.40/1.62 inference(quant_inst,[status(thm)],[])).
% 1.40/1.62 tff(11656,plain,
% 1.40/1.62 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s61) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s61))),
% 1.40/1.62 inference(modus_ponens,[status(thm)],[11655, 11654])).
% 1.40/1.62 tff(11657,plain,
% 1.40/1.62 ($false),
% 1.40/1.62 inference(unit_resolution,[status(thm)],[11656, 10200, 11650, 11219, 11649, 11220])).
% 1.40/1.62 tff(11658,plain,((~trans(s99, s61)) | until2p29(s61) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.62 tff(11659,plain,
% 1.40/1.62 (~trans(s99, s61)),
% 1.40/1.62 inference(unit_resolution,[status(thm)],[11658, 10609, 10186])).
% 1.40/1.62 tff(11660,assumption,(~until2p29(s30)), introduced(assumption)).
% 1.40/1.62 tff(11661,assumption,(trans(s99, s30)), introduced(assumption)).
% 1.40/1.62 tff(11662,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s30) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s30)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s30) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s30)))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(11663,plain,
% 1.40/1.62 (((~trans(s99, s30)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s30)) <=> (until2p29(s30) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s30)))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(11664,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s30)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s30))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s30) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s30))))),
% 1.40/1.62 inference(monotonicity,[status(thm)],[11663])).
% 1.40/1.62 tff(11665,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s30)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s30))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s30) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s30)))),
% 1.40/1.62 inference(transitivity,[status(thm)],[11664, 11662])).
% 1.40/1.62 tff(11666,plain,
% 1.40/1.62 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s30)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s30))),
% 1.40/1.62 inference(quant_inst,[status(thm)],[])).
% 1.40/1.62 tff(11667,plain,
% 1.40/1.62 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s30) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s30))),
% 1.40/1.62 inference(modus_ponens,[status(thm)],[11666, 11665])).
% 1.40/1.62 tff(11668,plain,
% 1.40/1.62 ($false),
% 1.40/1.62 inference(unit_resolution,[status(thm)],[11667, 10200, 11661, 11219, 11660, 11220])).
% 1.40/1.62 tff(11669,plain,((~trans(s99, s30)) | until2p29(s30) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.62 tff(11670,plain,
% 1.40/1.62 (~trans(s99, s30)),
% 1.40/1.62 inference(unit_resolution,[status(thm)],[11669, 10919, 10186])).
% 1.40/1.62 tff(11671,assumption,(~until2p29(s36)), introduced(assumption)).
% 1.40/1.62 tff(11672,assumption,(trans(s99, s36)), introduced(assumption)).
% 1.40/1.62 tff(11673,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s36) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s36)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s36) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s36)))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(11674,plain,
% 1.40/1.62 (((~trans(s99, s36)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s36)) <=> (until2p29(s36) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s36)))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(11675,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s36)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s36))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s36) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s36))))),
% 1.40/1.62 inference(monotonicity,[status(thm)],[11674])).
% 1.40/1.62 tff(11676,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s36)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s36))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s36) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s36)))),
% 1.40/1.62 inference(transitivity,[status(thm)],[11675, 11673])).
% 1.40/1.62 tff(11677,plain,
% 1.40/1.62 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s36)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s36))),
% 1.40/1.62 inference(quant_inst,[status(thm)],[])).
% 1.40/1.62 tff(11678,plain,
% 1.40/1.62 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s36) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s36))),
% 1.40/1.62 inference(modus_ponens,[status(thm)],[11677, 11676])).
% 1.40/1.62 tff(11679,plain,
% 1.40/1.62 ($false),
% 1.40/1.62 inference(unit_resolution,[status(thm)],[11678, 10200, 11672, 11219, 11671, 11220])).
% 1.40/1.62 tff(11680,plain,((~trans(s99, s36)) | until2p29(s36) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.62 tff(11681,plain,
% 1.40/1.62 (~trans(s99, s36)),
% 1.40/1.62 inference(unit_resolution,[status(thm)],[11680, 10859, 10186])).
% 1.40/1.62 tff(11682,assumption,(~until2p29(s26)), introduced(assumption)).
% 1.40/1.62 tff(11683,assumption,(trans(s99, s26)), introduced(assumption)).
% 1.40/1.62 tff(11684,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s26) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s26)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s26) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s26)))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(11685,plain,
% 1.40/1.62 (((~trans(s99, s26)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s26)) <=> (until2p29(s26) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s26)))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(11686,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s26)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s26))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s26) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s26))))),
% 1.40/1.62 inference(monotonicity,[status(thm)],[11685])).
% 1.40/1.62 tff(11687,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s26)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s26))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s26) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s26)))),
% 1.40/1.62 inference(transitivity,[status(thm)],[11686, 11684])).
% 1.40/1.62 tff(11688,plain,
% 1.40/1.62 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s26)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s26))),
% 1.40/1.62 inference(quant_inst,[status(thm)],[])).
% 1.40/1.62 tff(11689,plain,
% 1.40/1.62 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s26) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s26))),
% 1.40/1.62 inference(modus_ponens,[status(thm)],[11688, 11687])).
% 1.40/1.62 tff(11690,plain,
% 1.40/1.62 ($false),
% 1.40/1.62 inference(unit_resolution,[status(thm)],[11689, 10200, 11683, 11219, 11682, 11220])).
% 1.40/1.62 tff(11691,plain,((~trans(s99, s26)) | until2p29(s26) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.62 tff(11692,plain,
% 1.40/1.62 (~trans(s99, s26)),
% 1.40/1.62 inference(unit_resolution,[status(thm)],[11691, 10959, 10186])).
% 1.40/1.62 tff(11693,assumption,(~until2p29(s70)), introduced(assumption)).
% 1.40/1.62 tff(11694,assumption,(trans(s99, s70)), introduced(assumption)).
% 1.40/1.62 tff(11695,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s70) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s70)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s70) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s70)))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(11696,plain,
% 1.40/1.62 (((~trans(s99, s70)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s70)) <=> (until2p29(s70) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s70)))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(11697,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s70)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s70))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s70) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s70))))),
% 1.40/1.62 inference(monotonicity,[status(thm)],[11696])).
% 1.40/1.62 tff(11698,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s70)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s70))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s70) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s70)))),
% 1.40/1.62 inference(transitivity,[status(thm)],[11697, 11695])).
% 1.40/1.62 tff(11699,plain,
% 1.40/1.62 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s70)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s70))),
% 1.40/1.62 inference(quant_inst,[status(thm)],[])).
% 1.40/1.62 tff(11700,plain,
% 1.40/1.62 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s70) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s70))),
% 1.40/1.62 inference(modus_ponens,[status(thm)],[11699, 11698])).
% 1.40/1.62 tff(11701,plain,
% 1.40/1.62 ($false),
% 1.40/1.62 inference(unit_resolution,[status(thm)],[11700, 10200, 11694, 11219, 11693, 11220])).
% 1.40/1.62 tff(11702,plain,((~trans(s99, s70)) | until2p29(s70) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.62 tff(11703,plain,
% 1.40/1.62 (~trans(s99, s70)),
% 1.40/1.62 inference(unit_resolution,[status(thm)],[11702, 10519, 10186])).
% 1.40/1.62 tff(11704,assumption,(~until2p29(s19)), introduced(assumption)).
% 1.40/1.62 tff(11705,assumption,(trans(s99, s19)), introduced(assumption)).
% 1.40/1.62 tff(11706,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s19) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s19)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s19) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s19)))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(11707,plain,
% 1.40/1.62 (((~trans(s99, s19)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s19)) <=> (until2p29(s19) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s19)))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(11708,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s19)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s19))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s19) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s19))))),
% 1.40/1.62 inference(monotonicity,[status(thm)],[11707])).
% 1.40/1.62 tff(11709,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s19)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s19))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s19) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s19)))),
% 1.40/1.62 inference(transitivity,[status(thm)],[11708, 11706])).
% 1.40/1.62 tff(11710,plain,
% 1.40/1.62 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s19)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s19))),
% 1.40/1.62 inference(quant_inst,[status(thm)],[])).
% 1.40/1.62 tff(11711,plain,
% 1.40/1.62 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s19) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s19))),
% 1.40/1.62 inference(modus_ponens,[status(thm)],[11710, 11709])).
% 1.40/1.62 tff(11712,plain,
% 1.40/1.62 ($false),
% 1.40/1.62 inference(unit_resolution,[status(thm)],[11711, 10200, 11705, 11219, 11704, 11220])).
% 1.40/1.62 tff(11713,plain,((~trans(s99, s19)) | until2p29(s19) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.62 tff(11714,plain,
% 1.40/1.62 (~trans(s99, s19)),
% 1.40/1.62 inference(unit_resolution,[status(thm)],[11713, 11029, 10186])).
% 1.40/1.62 tff(11715,assumption,(~until2p29(s63)), introduced(assumption)).
% 1.40/1.62 tff(11716,assumption,(trans(s99, s63)), introduced(assumption)).
% 1.40/1.62 tff(11717,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s63) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s63)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s63) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s63)))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(11718,plain,
% 1.40/1.62 (((~trans(s99, s63)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s63)) <=> (until2p29(s63) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s63)))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(11719,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s63)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s63))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s63) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s63))))),
% 1.40/1.62 inference(monotonicity,[status(thm)],[11718])).
% 1.40/1.62 tff(11720,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s63)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s63))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s63) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s63)))),
% 1.40/1.62 inference(transitivity,[status(thm)],[11719, 11717])).
% 1.40/1.62 tff(11721,plain,
% 1.40/1.62 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s63)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s63))),
% 1.40/1.62 inference(quant_inst,[status(thm)],[])).
% 1.40/1.62 tff(11722,plain,
% 1.40/1.62 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s63) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s63))),
% 1.40/1.62 inference(modus_ponens,[status(thm)],[11721, 11720])).
% 1.40/1.62 tff(11723,plain,
% 1.40/1.62 ($false),
% 1.40/1.62 inference(unit_resolution,[status(thm)],[11722, 10200, 11716, 11219, 11715, 11220])).
% 1.40/1.62 tff(11724,plain,((~trans(s99, s63)) | until2p29(s63) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.62 tff(11725,plain,
% 1.40/1.62 (~trans(s99, s63)),
% 1.40/1.62 inference(unit_resolution,[status(thm)],[11724, 10589, 10186])).
% 1.40/1.62 tff(11726,assumption,(~until2p29(s50)), introduced(assumption)).
% 1.40/1.62 tff(11727,assumption,(trans(s99, s50)), introduced(assumption)).
% 1.40/1.62 tff(11728,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s50) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s50)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s50) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s50)))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(11729,plain,
% 1.40/1.62 (((~trans(s99, s50)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s50)) <=> (until2p29(s50) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s50)))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(11730,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s50)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s50))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s50) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s50))))),
% 1.40/1.62 inference(monotonicity,[status(thm)],[11729])).
% 1.40/1.62 tff(11731,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s50)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s50))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s50) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s50)))),
% 1.40/1.62 inference(transitivity,[status(thm)],[11730, 11728])).
% 1.40/1.62 tff(11732,plain,
% 1.40/1.62 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s50)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s50))),
% 1.40/1.62 inference(quant_inst,[status(thm)],[])).
% 1.40/1.62 tff(11733,plain,
% 1.40/1.62 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s50) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s50))),
% 1.40/1.62 inference(modus_ponens,[status(thm)],[11732, 11731])).
% 1.40/1.62 tff(11734,plain,
% 1.40/1.62 ($false),
% 1.40/1.62 inference(unit_resolution,[status(thm)],[11733, 10200, 11727, 11219, 11726, 11220])).
% 1.40/1.62 tff(11735,plain,((~trans(s99, s50)) | until2p29(s50) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.62 tff(11736,plain,
% 1.40/1.62 (~trans(s99, s50)),
% 1.40/1.62 inference(unit_resolution,[status(thm)],[11735, 10719, 10186])).
% 1.40/1.62 tff(11737,assumption,(~until2p29(s66)), introduced(assumption)).
% 1.40/1.62 tff(11738,assumption,(trans(s99, s66)), introduced(assumption)).
% 1.40/1.62 tff(11739,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s66) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s66)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s66) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s66)))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(11740,plain,
% 1.40/1.62 (((~trans(s99, s66)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s66)) <=> (until2p29(s66) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s66)))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(11741,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s66)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s66))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s66) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s66))))),
% 1.40/1.62 inference(monotonicity,[status(thm)],[11740])).
% 1.40/1.62 tff(11742,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s66)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s66))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s66) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s66)))),
% 1.40/1.62 inference(transitivity,[status(thm)],[11741, 11739])).
% 1.40/1.62 tff(11743,plain,
% 1.40/1.62 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s66)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s66))),
% 1.40/1.62 inference(quant_inst,[status(thm)],[])).
% 1.40/1.62 tff(11744,plain,
% 1.40/1.62 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s66) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s66))),
% 1.40/1.62 inference(modus_ponens,[status(thm)],[11743, 11742])).
% 1.40/1.62 tff(11745,plain,
% 1.40/1.62 ($false),
% 1.40/1.62 inference(unit_resolution,[status(thm)],[11744, 10200, 11738, 11219, 11737, 11220])).
% 1.40/1.62 tff(11746,plain,((~trans(s99, s66)) | until2p29(s66) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.62 tff(11747,plain,
% 1.40/1.62 (~trans(s99, s66)),
% 1.40/1.62 inference(unit_resolution,[status(thm)],[11746, 10559, 10186])).
% 1.40/1.62 tff(11748,assumption,(~until2p29(s58)), introduced(assumption)).
% 1.40/1.62 tff(11749,assumption,(trans(s99, s58)), introduced(assumption)).
% 1.40/1.62 tff(11750,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s58) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s58)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s58) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s58)))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(11751,plain,
% 1.40/1.62 (((~trans(s99, s58)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s58)) <=> (until2p29(s58) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s58)))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(11752,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s58)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s58))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s58) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s58))))),
% 1.40/1.62 inference(monotonicity,[status(thm)],[11751])).
% 1.40/1.62 tff(11753,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s58)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s58))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s58) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s58)))),
% 1.40/1.62 inference(transitivity,[status(thm)],[11752, 11750])).
% 1.40/1.62 tff(11754,plain,
% 1.40/1.62 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s58)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s58))),
% 1.40/1.62 inference(quant_inst,[status(thm)],[])).
% 1.40/1.62 tff(11755,plain,
% 1.40/1.62 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s58) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s58))),
% 1.40/1.62 inference(modus_ponens,[status(thm)],[11754, 11753])).
% 1.40/1.62 tff(11756,plain,
% 1.40/1.62 ($false),
% 1.40/1.62 inference(unit_resolution,[status(thm)],[11755, 10200, 11749, 11219, 11748, 11220])).
% 1.40/1.62 tff(11757,plain,((~trans(s99, s58)) | until2p29(s58) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.62 tff(11758,plain,
% 1.40/1.62 (~trans(s99, s58)),
% 1.40/1.62 inference(unit_resolution,[status(thm)],[11757, 10639, 10186])).
% 1.40/1.62 tff(11759,assumption,(~until2p29(s87)), introduced(assumption)).
% 1.40/1.62 tff(11760,assumption,(trans(s99, s87)), introduced(assumption)).
% 1.40/1.62 tff(11761,plain,
% 1.40/1.62 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s87) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s87)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s87) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s87)))),
% 1.40/1.62 inference(rewrite,[status(thm)],[])).
% 1.40/1.62 tff(11762,plain,
% 1.40/1.62 (((~trans(s99, s87)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s87)) <=> (until2p29(s87) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s87)))),
% 1.40/1.63 inference(rewrite,[status(thm)],[])).
% 1.40/1.63 tff(11763,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s87)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s87))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s87) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s87))))),
% 1.40/1.63 inference(monotonicity,[status(thm)],[11762])).
% 1.40/1.63 tff(11764,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s87)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s87))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s87) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s87)))),
% 1.40/1.63 inference(transitivity,[status(thm)],[11763, 11761])).
% 1.40/1.63 tff(11765,plain,
% 1.40/1.63 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s87)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s87))),
% 1.40/1.63 inference(quant_inst,[status(thm)],[])).
% 1.40/1.63 tff(11766,plain,
% 1.40/1.63 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s87) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s87))),
% 1.40/1.63 inference(modus_ponens,[status(thm)],[11765, 11764])).
% 1.40/1.63 tff(11767,plain,
% 1.40/1.63 ($false),
% 1.40/1.63 inference(unit_resolution,[status(thm)],[11766, 10200, 11760, 11219, 11759, 11220])).
% 1.40/1.63 tff(11768,plain,((~trans(s99, s87)) | until2p29(s87) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.63 tff(11769,plain,
% 1.40/1.63 (~trans(s99, s87)),
% 1.40/1.63 inference(unit_resolution,[status(thm)],[11768, 10349, 10186])).
% 1.40/1.63 tff(11770,assumption,(~until2p29(s80)), introduced(assumption)).
% 1.40/1.63 tff(11771,assumption,(trans(s99, s80)), introduced(assumption)).
% 1.40/1.63 tff(11772,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s80) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s80)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s80) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s80)))),
% 1.40/1.63 inference(rewrite,[status(thm)],[])).
% 1.40/1.63 tff(11773,plain,
% 1.40/1.63 (((~trans(s99, s80)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s80)) <=> (until2p29(s80) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s80)))),
% 1.40/1.63 inference(rewrite,[status(thm)],[])).
% 1.40/1.63 tff(11774,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s80)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s80))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s80) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s80))))),
% 1.40/1.63 inference(monotonicity,[status(thm)],[11773])).
% 1.40/1.63 tff(11775,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s80)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s80))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s80) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s80)))),
% 1.40/1.63 inference(transitivity,[status(thm)],[11774, 11772])).
% 1.40/1.63 tff(11776,plain,
% 1.40/1.63 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s80)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s80))),
% 1.40/1.63 inference(quant_inst,[status(thm)],[])).
% 1.40/1.63 tff(11777,plain,
% 1.40/1.63 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s80) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s80))),
% 1.40/1.63 inference(modus_ponens,[status(thm)],[11776, 11775])).
% 1.40/1.63 tff(11778,plain,
% 1.40/1.63 ($false),
% 1.40/1.63 inference(unit_resolution,[status(thm)],[11777, 10200, 11771, 11219, 11770, 11220])).
% 1.40/1.63 tff(11779,plain,((~trans(s99, s80)) | until2p29(s80) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.63 tff(11780,plain,
% 1.40/1.63 (~trans(s99, s80)),
% 1.40/1.63 inference(unit_resolution,[status(thm)],[11779, 10419, 10186])).
% 1.40/1.63 tff(11781,assumption,(~until2p29(s16)), introduced(assumption)).
% 1.40/1.63 tff(11782,assumption,(trans(s99, s16)), introduced(assumption)).
% 1.40/1.63 tff(11783,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s16) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s16)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s16) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s16)))),
% 1.40/1.63 inference(rewrite,[status(thm)],[])).
% 1.40/1.63 tff(11784,plain,
% 1.40/1.63 (((~trans(s99, s16)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s16)) <=> (until2p29(s16) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s16)))),
% 1.40/1.63 inference(rewrite,[status(thm)],[])).
% 1.40/1.63 tff(11785,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s16)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s16))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s16) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s16))))),
% 1.40/1.63 inference(monotonicity,[status(thm)],[11784])).
% 1.40/1.63 tff(11786,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s16)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s16))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s16) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s16)))),
% 1.40/1.63 inference(transitivity,[status(thm)],[11785, 11783])).
% 1.40/1.63 tff(11787,plain,
% 1.40/1.63 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s16)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s16))),
% 1.40/1.63 inference(quant_inst,[status(thm)],[])).
% 1.40/1.63 tff(11788,plain,
% 1.40/1.63 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s16) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s16))),
% 1.40/1.63 inference(modus_ponens,[status(thm)],[11787, 11786])).
% 1.40/1.63 tff(11789,plain,
% 1.40/1.63 ($false),
% 1.40/1.63 inference(unit_resolution,[status(thm)],[11788, 10200, 11782, 11219, 11781, 11220])).
% 1.40/1.63 tff(11790,plain,((~trans(s99, s16)) | until2p29(s16) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.63 tff(11791,plain,
% 1.40/1.63 (~trans(s99, s16)),
% 1.40/1.63 inference(unit_resolution,[status(thm)],[11790, 11059, 10186])).
% 1.40/1.63 tff(11792,assumption,(~until2p29(s49)), introduced(assumption)).
% 1.40/1.63 tff(11793,assumption,(trans(s99, s49)), introduced(assumption)).
% 1.40/1.63 tff(11794,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s49) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s49)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s49) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s49)))),
% 1.40/1.63 inference(rewrite,[status(thm)],[])).
% 1.40/1.63 tff(11795,plain,
% 1.40/1.63 (((~trans(s99, s49)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s49)) <=> (until2p29(s49) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s49)))),
% 1.40/1.63 inference(rewrite,[status(thm)],[])).
% 1.40/1.63 tff(11796,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s49)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s49))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s49) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s49))))),
% 1.40/1.63 inference(monotonicity,[status(thm)],[11795])).
% 1.40/1.63 tff(11797,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s49)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s49))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s49) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s49)))),
% 1.40/1.63 inference(transitivity,[status(thm)],[11796, 11794])).
% 1.40/1.63 tff(11798,plain,
% 1.40/1.63 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s49)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s49))),
% 1.40/1.63 inference(quant_inst,[status(thm)],[])).
% 1.40/1.63 tff(11799,plain,
% 1.40/1.63 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s49) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s49))),
% 1.40/1.63 inference(modus_ponens,[status(thm)],[11798, 11797])).
% 1.40/1.63 tff(11800,plain,
% 1.40/1.63 ($false),
% 1.40/1.63 inference(unit_resolution,[status(thm)],[11799, 10200, 11793, 11219, 11792, 11220])).
% 1.40/1.63 tff(11801,plain,((~trans(s99, s49)) | until2p29(s49) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.63 tff(11802,plain,
% 1.40/1.63 (~trans(s99, s49)),
% 1.40/1.63 inference(unit_resolution,[status(thm)],[11801, 10729, 10186])).
% 1.40/1.63 tff(11803,assumption,(~until2p29(s33)), introduced(assumption)).
% 1.40/1.63 tff(11804,assumption,(trans(s99, s33)), introduced(assumption)).
% 1.40/1.63 tff(11805,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s33) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s33)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s33) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s33)))),
% 1.40/1.63 inference(rewrite,[status(thm)],[])).
% 1.40/1.63 tff(11806,plain,
% 1.40/1.63 (((~trans(s99, s33)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s33)) <=> (until2p29(s33) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s33)))),
% 1.40/1.63 inference(rewrite,[status(thm)],[])).
% 1.40/1.63 tff(11807,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s33)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s33))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s33) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s33))))),
% 1.40/1.63 inference(monotonicity,[status(thm)],[11806])).
% 1.40/1.63 tff(11808,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s33)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s33))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s33) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s33)))),
% 1.40/1.63 inference(transitivity,[status(thm)],[11807, 11805])).
% 1.40/1.63 tff(11809,plain,
% 1.40/1.63 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s33)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s33))),
% 1.40/1.63 inference(quant_inst,[status(thm)],[])).
% 1.40/1.63 tff(11810,plain,
% 1.40/1.63 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s33) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s33))),
% 1.40/1.63 inference(modus_ponens,[status(thm)],[11809, 11808])).
% 1.40/1.63 tff(11811,plain,
% 1.40/1.63 ($false),
% 1.40/1.63 inference(unit_resolution,[status(thm)],[11810, 10200, 11804, 11219, 11803, 11220])).
% 1.40/1.63 tff(11812,plain,((~trans(s99, s33)) | until2p29(s33) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.63 tff(11813,plain,
% 1.40/1.63 (~trans(s99, s33)),
% 1.40/1.63 inference(unit_resolution,[status(thm)],[11812, 10889, 10186])).
% 1.40/1.63 tff(11814,assumption,(~until2p29(s13)), introduced(assumption)).
% 1.40/1.63 tff(11815,assumption,(trans(s99, s13)), introduced(assumption)).
% 1.40/1.63 tff(11816,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s13) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s13)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s13) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s13)))),
% 1.40/1.63 inference(rewrite,[status(thm)],[])).
% 1.40/1.63 tff(11817,plain,
% 1.40/1.63 (((~trans(s99, s13)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s13)) <=> (until2p29(s13) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s13)))),
% 1.40/1.63 inference(rewrite,[status(thm)],[])).
% 1.40/1.63 tff(11818,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s13)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s13))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s13) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s13))))),
% 1.40/1.63 inference(monotonicity,[status(thm)],[11817])).
% 1.40/1.63 tff(11819,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s13)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s13))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s13) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s13)))),
% 1.40/1.63 inference(transitivity,[status(thm)],[11818, 11816])).
% 1.40/1.63 tff(11820,plain,
% 1.40/1.63 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s13)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s13))),
% 1.40/1.63 inference(quant_inst,[status(thm)],[])).
% 1.40/1.63 tff(11821,plain,
% 1.40/1.63 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s13) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s13))),
% 1.40/1.63 inference(modus_ponens,[status(thm)],[11820, 11819])).
% 1.40/1.63 tff(11822,plain,
% 1.40/1.63 ($false),
% 1.40/1.63 inference(unit_resolution,[status(thm)],[11821, 10200, 11815, 11219, 11814, 11220])).
% 1.40/1.63 tff(11823,plain,((~trans(s99, s13)) | until2p29(s13) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.63 tff(11824,plain,
% 1.40/1.63 (~trans(s99, s13)),
% 1.40/1.63 inference(unit_resolution,[status(thm)],[11823, 11089, 10186])).
% 1.40/1.63 tff(11825,assumption,(~until2p29(s77)), introduced(assumption)).
% 1.40/1.63 tff(11826,assumption,(trans(s99, s77)), introduced(assumption)).
% 1.40/1.63 tff(11827,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s77) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s77)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s77) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s77)))),
% 1.40/1.63 inference(rewrite,[status(thm)],[])).
% 1.40/1.63 tff(11828,plain,
% 1.40/1.63 (((~trans(s99, s77)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s77)) <=> (until2p29(s77) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s77)))),
% 1.40/1.63 inference(rewrite,[status(thm)],[])).
% 1.40/1.63 tff(11829,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s77)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s77))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s77) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s77))))),
% 1.40/1.63 inference(monotonicity,[status(thm)],[11828])).
% 1.40/1.63 tff(11830,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s77)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s77))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s77) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s77)))),
% 1.40/1.63 inference(transitivity,[status(thm)],[11829, 11827])).
% 1.40/1.63 tff(11831,plain,
% 1.40/1.63 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s77)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s77))),
% 1.40/1.63 inference(quant_inst,[status(thm)],[])).
% 1.40/1.63 tff(11832,plain,
% 1.40/1.63 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s77) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s77))),
% 1.40/1.63 inference(modus_ponens,[status(thm)],[11831, 11830])).
% 1.40/1.63 tff(11833,plain,
% 1.40/1.63 ($false),
% 1.40/1.63 inference(unit_resolution,[status(thm)],[11832, 10200, 11826, 11219, 11825, 11220])).
% 1.40/1.63 tff(11834,plain,((~trans(s99, s77)) | until2p29(s77) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.63 tff(11835,plain,
% 1.40/1.63 (~trans(s99, s77)),
% 1.40/1.63 inference(unit_resolution,[status(thm)],[11834, 10449, 10186])).
% 1.40/1.63 tff(11836,assumption,(~until2p29(s46)), introduced(assumption)).
% 1.40/1.63 tff(11837,assumption,(trans(s99, s46)), introduced(assumption)).
% 1.40/1.63 tff(11838,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s46) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s46)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s46) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s46)))),
% 1.40/1.63 inference(rewrite,[status(thm)],[])).
% 1.40/1.63 tff(11839,plain,
% 1.40/1.63 (((~trans(s99, s46)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s46)) <=> (until2p29(s46) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s46)))),
% 1.40/1.63 inference(rewrite,[status(thm)],[])).
% 1.40/1.63 tff(11840,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s46)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s46))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s46) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s46))))),
% 1.40/1.63 inference(monotonicity,[status(thm)],[11839])).
% 1.40/1.63 tff(11841,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s46)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s46))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s46) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s46)))),
% 1.40/1.63 inference(transitivity,[status(thm)],[11840, 11838])).
% 1.40/1.63 tff(11842,plain,
% 1.40/1.63 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s46)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s46))),
% 1.40/1.63 inference(quant_inst,[status(thm)],[])).
% 1.40/1.63 tff(11843,plain,
% 1.40/1.63 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s46) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s46))),
% 1.40/1.63 inference(modus_ponens,[status(thm)],[11842, 11841])).
% 1.40/1.63 tff(11844,plain,
% 1.40/1.63 ($false),
% 1.40/1.63 inference(unit_resolution,[status(thm)],[11843, 10200, 11837, 11219, 11836, 11220])).
% 1.40/1.63 tff(11845,plain,((~trans(s99, s46)) | until2p29(s46) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.63 tff(11846,plain,
% 1.40/1.63 (~trans(s99, s46)),
% 1.40/1.63 inference(unit_resolution,[status(thm)],[11845, 10759, 10186])).
% 1.40/1.63 tff(11847,assumption,(~until2p29(s47)), introduced(assumption)).
% 1.40/1.63 tff(11848,assumption,(trans(s99, s47)), introduced(assumption)).
% 1.40/1.63 tff(11849,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s47) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s47)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s47) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s47)))),
% 1.40/1.63 inference(rewrite,[status(thm)],[])).
% 1.40/1.63 tff(11850,plain,
% 1.40/1.63 (((~trans(s99, s47)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s47)) <=> (until2p29(s47) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s47)))),
% 1.40/1.63 inference(rewrite,[status(thm)],[])).
% 1.40/1.63 tff(11851,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s47)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s47))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s47) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s47))))),
% 1.40/1.63 inference(monotonicity,[status(thm)],[11850])).
% 1.40/1.63 tff(11852,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s47)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s47))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s47) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s47)))),
% 1.40/1.63 inference(transitivity,[status(thm)],[11851, 11849])).
% 1.40/1.63 tff(11853,plain,
% 1.40/1.63 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s47)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s47))),
% 1.40/1.63 inference(quant_inst,[status(thm)],[])).
% 1.40/1.63 tff(11854,plain,
% 1.40/1.63 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s47) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s47))),
% 1.40/1.63 inference(modus_ponens,[status(thm)],[11853, 11852])).
% 1.40/1.63 tff(11855,plain,
% 1.40/1.63 ($false),
% 1.40/1.63 inference(unit_resolution,[status(thm)],[11854, 10200, 11848, 11219, 11847, 11220])).
% 1.40/1.63 tff(11856,plain,((~trans(s99, s47)) | until2p29(s47) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.63 tff(11857,plain,
% 1.40/1.63 (~trans(s99, s47)),
% 1.40/1.63 inference(unit_resolution,[status(thm)],[11856, 10749, 10186])).
% 1.40/1.63 tff(11858,assumption,(~until2p29(s89)), introduced(assumption)).
% 1.40/1.63 tff(11859,assumption,(trans(s99, s89)), introduced(assumption)).
% 1.40/1.63 tff(11860,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s89) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s89)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s89) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s89)))),
% 1.40/1.63 inference(rewrite,[status(thm)],[])).
% 1.40/1.63 tff(11861,plain,
% 1.40/1.63 (((~trans(s99, s89)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s89)) <=> (until2p29(s89) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s89)))),
% 1.40/1.63 inference(rewrite,[status(thm)],[])).
% 1.40/1.63 tff(11862,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s89)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s89))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s89) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s89))))),
% 1.40/1.63 inference(monotonicity,[status(thm)],[11861])).
% 1.40/1.63 tff(11863,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s89)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s89))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s89) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s89)))),
% 1.40/1.63 inference(transitivity,[status(thm)],[11862, 11860])).
% 1.40/1.63 tff(11864,plain,
% 1.40/1.63 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s89)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s89))),
% 1.40/1.63 inference(quant_inst,[status(thm)],[])).
% 1.40/1.63 tff(11865,plain,
% 1.40/1.63 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s89) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s89))),
% 1.40/1.63 inference(modus_ponens,[status(thm)],[11864, 11863])).
% 1.40/1.63 tff(11866,plain,
% 1.40/1.63 ($false),
% 1.40/1.63 inference(unit_resolution,[status(thm)],[11865, 10200, 11859, 11219, 11858, 11220])).
% 1.40/1.63 tff(11867,plain,((~trans(s99, s89)) | until2p29(s89) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.63 tff(11868,plain,
% 1.40/1.63 (~trans(s99, s89)),
% 1.40/1.63 inference(unit_resolution,[status(thm)],[11867, 10329, 10186])).
% 1.40/1.63 tff(11869,assumption,(~until2p29(s88)), introduced(assumption)).
% 1.40/1.63 tff(11870,assumption,(trans(s99, s88)), introduced(assumption)).
% 1.40/1.63 tff(11871,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s88) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s88)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s88) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s88)))),
% 1.40/1.63 inference(rewrite,[status(thm)],[])).
% 1.40/1.63 tff(11872,plain,
% 1.40/1.63 (((~trans(s99, s88)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s88)) <=> (until2p29(s88) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s88)))),
% 1.40/1.63 inference(rewrite,[status(thm)],[])).
% 1.40/1.63 tff(11873,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s88)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s88))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s88) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s88))))),
% 1.40/1.63 inference(monotonicity,[status(thm)],[11872])).
% 1.40/1.63 tff(11874,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s88)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s88))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s88) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s88)))),
% 1.40/1.63 inference(transitivity,[status(thm)],[11873, 11871])).
% 1.40/1.63 tff(11875,plain,
% 1.40/1.63 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s88)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s88))),
% 1.40/1.63 inference(quant_inst,[status(thm)],[])).
% 1.40/1.63 tff(11876,plain,
% 1.40/1.63 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s88) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s88))),
% 1.40/1.63 inference(modus_ponens,[status(thm)],[11875, 11874])).
% 1.40/1.63 tff(11877,plain,
% 1.40/1.63 ($false),
% 1.40/1.63 inference(unit_resolution,[status(thm)],[11876, 10200, 11870, 11219, 11869, 11220])).
% 1.40/1.63 tff(11878,plain,((~trans(s99, s88)) | until2p29(s88) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.63 tff(11879,plain,
% 1.40/1.63 (~trans(s99, s88)),
% 1.40/1.63 inference(unit_resolution,[status(thm)],[11878, 10339, 10186])).
% 1.40/1.63 tff(11880,assumption,(~until2p29(s60)), introduced(assumption)).
% 1.40/1.63 tff(11881,assumption,(trans(s99, s60)), introduced(assumption)).
% 1.40/1.63 tff(11882,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s60) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s60)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s60) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s60)))),
% 1.40/1.63 inference(rewrite,[status(thm)],[])).
% 1.40/1.63 tff(11883,plain,
% 1.40/1.63 (((~trans(s99, s60)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s60)) <=> (until2p29(s60) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s60)))),
% 1.40/1.63 inference(rewrite,[status(thm)],[])).
% 1.40/1.63 tff(11884,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s60)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s60))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s60) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s60))))),
% 1.40/1.63 inference(monotonicity,[status(thm)],[11883])).
% 1.40/1.63 tff(11885,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s60)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s60))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s60) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s60)))),
% 1.40/1.63 inference(transitivity,[status(thm)],[11884, 11882])).
% 1.40/1.63 tff(11886,plain,
% 1.40/1.63 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s60)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s60))),
% 1.40/1.63 inference(quant_inst,[status(thm)],[])).
% 1.40/1.63 tff(11887,plain,
% 1.40/1.63 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s60) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s60))),
% 1.40/1.63 inference(modus_ponens,[status(thm)],[11886, 11885])).
% 1.40/1.63 tff(11888,plain,
% 1.40/1.63 ($false),
% 1.40/1.63 inference(unit_resolution,[status(thm)],[11887, 10200, 11881, 11219, 11880, 11220])).
% 1.40/1.63 tff(11889,plain,((~trans(s99, s60)) | until2p29(s60) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.63 tff(11890,plain,
% 1.40/1.63 (~trans(s99, s60)),
% 1.40/1.63 inference(unit_resolution,[status(thm)],[11889, 10619, 10186])).
% 1.40/1.63 tff(11891,assumption,(~until2p29(s52)), introduced(assumption)).
% 1.40/1.63 tff(11892,assumption,(trans(s99, s52)), introduced(assumption)).
% 1.40/1.63 tff(11893,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s52) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s52)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s52) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s52)))),
% 1.40/1.63 inference(rewrite,[status(thm)],[])).
% 1.40/1.63 tff(11894,plain,
% 1.40/1.63 (((~trans(s99, s52)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s52)) <=> (until2p29(s52) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s52)))),
% 1.40/1.63 inference(rewrite,[status(thm)],[])).
% 1.40/1.63 tff(11895,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s52)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s52))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s52) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s52))))),
% 1.40/1.63 inference(monotonicity,[status(thm)],[11894])).
% 1.40/1.63 tff(11896,plain,
% 1.40/1.63 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s52)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s52))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s52) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s52)))),
% 1.40/1.64 inference(transitivity,[status(thm)],[11895, 11893])).
% 1.40/1.64 tff(11897,plain,
% 1.40/1.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s52)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s52))),
% 1.40/1.64 inference(quant_inst,[status(thm)],[])).
% 1.40/1.64 tff(11898,plain,
% 1.40/1.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s52) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s52))),
% 1.40/1.64 inference(modus_ponens,[status(thm)],[11897, 11896])).
% 1.40/1.64 tff(11899,plain,
% 1.40/1.64 ($false),
% 1.40/1.64 inference(unit_resolution,[status(thm)],[11898, 10200, 11892, 11219, 11891, 11220])).
% 1.40/1.64 tff(11900,plain,((~trans(s99, s52)) | until2p29(s52) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.64 tff(11901,plain,
% 1.40/1.64 (~trans(s99, s52)),
% 1.40/1.64 inference(unit_resolution,[status(thm)],[11900, 10699, 10186])).
% 1.40/1.64 tff(11902,assumption,(~until2p29(s64)), introduced(assumption)).
% 1.40/1.64 tff(11903,assumption,(trans(s99, s64)), introduced(assumption)).
% 1.40/1.64 tff(11904,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s64) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s64)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s64) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s64)))),
% 1.40/1.64 inference(rewrite,[status(thm)],[])).
% 1.40/1.64 tff(11905,plain,
% 1.40/1.64 (((~trans(s99, s64)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s64)) <=> (until2p29(s64) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s64)))),
% 1.40/1.64 inference(rewrite,[status(thm)],[])).
% 1.40/1.64 tff(11906,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s64)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s64))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s64) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s64))))),
% 1.40/1.64 inference(monotonicity,[status(thm)],[11905])).
% 1.40/1.64 tff(11907,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s64)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s64))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s64) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s64)))),
% 1.40/1.64 inference(transitivity,[status(thm)],[11906, 11904])).
% 1.40/1.64 tff(11908,plain,
% 1.40/1.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s64)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s64))),
% 1.40/1.64 inference(quant_inst,[status(thm)],[])).
% 1.40/1.64 tff(11909,plain,
% 1.40/1.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s64) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s64))),
% 1.40/1.64 inference(modus_ponens,[status(thm)],[11908, 11907])).
% 1.40/1.64 tff(11910,plain,
% 1.40/1.64 ($false),
% 1.40/1.64 inference(unit_resolution,[status(thm)],[11909, 10200, 11903, 11219, 11902, 11220])).
% 1.40/1.64 tff(11911,plain,((~trans(s99, s64)) | until2p29(s64) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.64 tff(11912,plain,
% 1.40/1.64 (~trans(s99, s64)),
% 1.40/1.64 inference(unit_resolution,[status(thm)],[11911, 10579, 10186])).
% 1.40/1.64 tff(11913,assumption,(~until2p29(s67)), introduced(assumption)).
% 1.40/1.64 tff(11914,assumption,(trans(s99, s67)), introduced(assumption)).
% 1.40/1.64 tff(11915,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s67) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s67)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s67) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s67)))),
% 1.40/1.64 inference(rewrite,[status(thm)],[])).
% 1.40/1.64 tff(11916,plain,
% 1.40/1.64 (((~trans(s99, s67)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s67)) <=> (until2p29(s67) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s67)))),
% 1.40/1.64 inference(rewrite,[status(thm)],[])).
% 1.40/1.64 tff(11917,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s67)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s67))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s67) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s67))))),
% 1.40/1.64 inference(monotonicity,[status(thm)],[11916])).
% 1.40/1.64 tff(11918,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s67)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s67))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s67) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s67)))),
% 1.40/1.64 inference(transitivity,[status(thm)],[11917, 11915])).
% 1.40/1.64 tff(11919,plain,
% 1.40/1.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s67)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s67))),
% 1.40/1.64 inference(quant_inst,[status(thm)],[])).
% 1.40/1.64 tff(11920,plain,
% 1.40/1.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s67) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s67))),
% 1.40/1.64 inference(modus_ponens,[status(thm)],[11919, 11918])).
% 1.40/1.64 tff(11921,plain,
% 1.40/1.64 ($false),
% 1.40/1.64 inference(unit_resolution,[status(thm)],[11920, 10200, 11914, 11219, 11913, 11220])).
% 1.40/1.64 tff(11922,plain,((~trans(s99, s67)) | until2p29(s67) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.64 tff(11923,plain,
% 1.40/1.64 (~trans(s99, s67)),
% 1.40/1.64 inference(unit_resolution,[status(thm)],[11922, 10549, 10186])).
% 1.40/1.64 tff(11924,assumption,(~until2p29(s22)), introduced(assumption)).
% 1.40/1.64 tff(11925,assumption,(trans(s99, s22)), introduced(assumption)).
% 1.40/1.64 tff(11926,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s22) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s22)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s22) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s22)))),
% 1.40/1.64 inference(rewrite,[status(thm)],[])).
% 1.40/1.64 tff(11927,plain,
% 1.40/1.64 (((~trans(s99, s22)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s22)) <=> (until2p29(s22) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s22)))),
% 1.40/1.64 inference(rewrite,[status(thm)],[])).
% 1.40/1.64 tff(11928,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s22)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s22))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s22) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s22))))),
% 1.40/1.64 inference(monotonicity,[status(thm)],[11927])).
% 1.40/1.64 tff(11929,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s22)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s22))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s22) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s22)))),
% 1.40/1.64 inference(transitivity,[status(thm)],[11928, 11926])).
% 1.40/1.64 tff(11930,plain,
% 1.40/1.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s22)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s22))),
% 1.40/1.64 inference(quant_inst,[status(thm)],[])).
% 1.40/1.64 tff(11931,plain,
% 1.40/1.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s22) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s22))),
% 1.40/1.64 inference(modus_ponens,[status(thm)],[11930, 11929])).
% 1.40/1.64 tff(11932,plain,
% 1.40/1.64 ($false),
% 1.40/1.64 inference(unit_resolution,[status(thm)],[11931, 10200, 11925, 11219, 11924, 11220])).
% 1.40/1.64 tff(11933,plain,((~trans(s99, s22)) | until2p29(s22) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.64 tff(11934,plain,
% 1.40/1.64 (~trans(s99, s22)),
% 1.40/1.64 inference(unit_resolution,[status(thm)],[11933, 10999, 10186])).
% 1.40/1.64 tff(11935,assumption,(~until2p29(s43)), introduced(assumption)).
% 1.40/1.64 tff(11936,assumption,(trans(s99, s43)), introduced(assumption)).
% 1.40/1.64 tff(11937,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s43) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s43)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s43) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s43)))),
% 1.40/1.64 inference(rewrite,[status(thm)],[])).
% 1.40/1.64 tff(11938,plain,
% 1.40/1.64 (((~trans(s99, s43)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s43)) <=> (until2p29(s43) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s43)))),
% 1.40/1.64 inference(rewrite,[status(thm)],[])).
% 1.40/1.64 tff(11939,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s43)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s43))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s43) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s43))))),
% 1.40/1.64 inference(monotonicity,[status(thm)],[11938])).
% 1.40/1.64 tff(11940,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s43)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s43))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s43) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s43)))),
% 1.40/1.64 inference(transitivity,[status(thm)],[11939, 11937])).
% 1.40/1.64 tff(11941,plain,
% 1.40/1.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s43)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s43))),
% 1.40/1.64 inference(quant_inst,[status(thm)],[])).
% 1.40/1.64 tff(11942,plain,
% 1.40/1.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s43) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s43))),
% 1.40/1.64 inference(modus_ponens,[status(thm)],[11941, 11940])).
% 1.40/1.64 tff(11943,plain,
% 1.40/1.64 ($false),
% 1.40/1.64 inference(unit_resolution,[status(thm)],[11942, 10200, 11936, 11219, 11935, 11220])).
% 1.40/1.64 tff(11944,plain,((~trans(s99, s43)) | until2p29(s43) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.64 tff(11945,plain,
% 1.40/1.64 (~trans(s99, s43)),
% 1.40/1.64 inference(unit_resolution,[status(thm)],[11944, 10789, 10186])).
% 1.40/1.64 tff(11946,assumption,(~until2p29(s34)), introduced(assumption)).
% 1.40/1.64 tff(11947,assumption,(trans(s99, s34)), introduced(assumption)).
% 1.40/1.64 tff(11948,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s34) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s34)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s34) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s34)))),
% 1.40/1.64 inference(rewrite,[status(thm)],[])).
% 1.40/1.64 tff(11949,plain,
% 1.40/1.64 (((~trans(s99, s34)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s34)) <=> (until2p29(s34) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s34)))),
% 1.40/1.64 inference(rewrite,[status(thm)],[])).
% 1.40/1.64 tff(11950,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s34)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s34))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s34) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s34))))),
% 1.40/1.64 inference(monotonicity,[status(thm)],[11949])).
% 1.40/1.64 tff(11951,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s34)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s34))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s34) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s34)))),
% 1.40/1.64 inference(transitivity,[status(thm)],[11950, 11948])).
% 1.40/1.64 tff(11952,plain,
% 1.40/1.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s34)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s34))),
% 1.40/1.64 inference(quant_inst,[status(thm)],[])).
% 1.40/1.64 tff(11953,plain,
% 1.40/1.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s34) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s34))),
% 1.40/1.64 inference(modus_ponens,[status(thm)],[11952, 11951])).
% 1.40/1.64 tff(11954,plain,
% 1.40/1.64 ($false),
% 1.40/1.64 inference(unit_resolution,[status(thm)],[11953, 10200, 11947, 11219, 11946, 11220])).
% 1.40/1.64 tff(11955,plain,((~trans(s99, s34)) | until2p29(s34) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.64 tff(11956,plain,
% 1.40/1.64 (~trans(s99, s34)),
% 1.40/1.64 inference(unit_resolution,[status(thm)],[11955, 10879, 10186])).
% 1.40/1.64 tff(11957,assumption,(~until2p29(s21)), introduced(assumption)).
% 1.40/1.64 tff(11958,assumption,(trans(s99, s21)), introduced(assumption)).
% 1.40/1.64 tff(11959,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s21) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s21)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s21) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s21)))),
% 1.40/1.64 inference(rewrite,[status(thm)],[])).
% 1.40/1.64 tff(11960,plain,
% 1.40/1.64 (((~trans(s99, s21)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s21)) <=> (until2p29(s21) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s21)))),
% 1.40/1.64 inference(rewrite,[status(thm)],[])).
% 1.40/1.64 tff(11961,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s21)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s21))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s21) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s21))))),
% 1.40/1.64 inference(monotonicity,[status(thm)],[11960])).
% 1.40/1.64 tff(11962,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s21)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s21))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s21) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s21)))),
% 1.40/1.64 inference(transitivity,[status(thm)],[11961, 11959])).
% 1.40/1.64 tff(11963,plain,
% 1.40/1.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s21)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s21))),
% 1.40/1.64 inference(quant_inst,[status(thm)],[])).
% 1.40/1.64 tff(11964,plain,
% 1.40/1.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s21) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s21))),
% 1.40/1.64 inference(modus_ponens,[status(thm)],[11963, 11962])).
% 1.40/1.64 tff(11965,plain,
% 1.40/1.64 ($false),
% 1.40/1.64 inference(unit_resolution,[status(thm)],[11964, 10200, 11958, 11219, 11957, 11220])).
% 1.40/1.64 tff(11966,plain,((~trans(s99, s21)) | until2p29(s21) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.64 tff(11967,plain,
% 1.40/1.64 (~trans(s99, s21)),
% 1.40/1.64 inference(unit_resolution,[status(thm)],[11966, 11009, 10186])).
% 1.40/1.64 tff(11968,assumption,(~until2p29(s29)), introduced(assumption)).
% 1.40/1.64 tff(11969,assumption,(trans(s99, s29)), introduced(assumption)).
% 1.40/1.64 tff(11970,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s29) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s29)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s29) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s29)))),
% 1.40/1.64 inference(rewrite,[status(thm)],[])).
% 1.40/1.64 tff(11971,plain,
% 1.40/1.64 (((~trans(s99, s29)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s29)) <=> (until2p29(s29) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s29)))),
% 1.40/1.64 inference(rewrite,[status(thm)],[])).
% 1.40/1.64 tff(11972,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s29)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s29))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s29) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s29))))),
% 1.40/1.64 inference(monotonicity,[status(thm)],[11971])).
% 1.40/1.64 tff(11973,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s29)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s29))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s29) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s29)))),
% 1.40/1.64 inference(transitivity,[status(thm)],[11972, 11970])).
% 1.40/1.64 tff(11974,plain,
% 1.40/1.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s29)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s29))),
% 1.40/1.64 inference(quant_inst,[status(thm)],[])).
% 1.40/1.64 tff(11975,plain,
% 1.40/1.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s29) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s29))),
% 1.40/1.64 inference(modus_ponens,[status(thm)],[11974, 11973])).
% 1.40/1.64 tff(11976,plain,
% 1.40/1.64 ($false),
% 1.40/1.64 inference(unit_resolution,[status(thm)],[11975, 10200, 11969, 11219, 11968, 11220])).
% 1.40/1.64 tff(11977,plain,((~trans(s99, s29)) | until2p29(s29) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.64 tff(11978,plain,
% 1.40/1.64 (~trans(s99, s29)),
% 1.40/1.64 inference(unit_resolution,[status(thm)],[11977, 10929, 10186])).
% 1.40/1.64 tff(11979,assumption,(~until2p29(s17)), introduced(assumption)).
% 1.40/1.64 tff(11980,assumption,(trans(s99, s17)), introduced(assumption)).
% 1.40/1.64 tff(11981,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s17) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s17)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s17) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s17)))),
% 1.40/1.64 inference(rewrite,[status(thm)],[])).
% 1.40/1.64 tff(11982,plain,
% 1.40/1.64 (((~trans(s99, s17)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s17)) <=> (until2p29(s17) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s17)))),
% 1.40/1.64 inference(rewrite,[status(thm)],[])).
% 1.40/1.64 tff(11983,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s17)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s17))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s17) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s17))))),
% 1.40/1.64 inference(monotonicity,[status(thm)],[11982])).
% 1.40/1.64 tff(11984,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s17)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s17))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s17) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s17)))),
% 1.40/1.64 inference(transitivity,[status(thm)],[11983, 11981])).
% 1.40/1.64 tff(11985,plain,
% 1.40/1.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s17)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s17))),
% 1.40/1.64 inference(quant_inst,[status(thm)],[])).
% 1.40/1.64 tff(11986,plain,
% 1.40/1.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s17) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s17))),
% 1.40/1.64 inference(modus_ponens,[status(thm)],[11985, 11984])).
% 1.40/1.64 tff(11987,plain,
% 1.40/1.64 ($false),
% 1.40/1.64 inference(unit_resolution,[status(thm)],[11986, 10200, 11980, 11219, 11979, 11220])).
% 1.40/1.64 tff(11988,plain,((~trans(s99, s17)) | until2p29(s17) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.64 tff(11989,plain,
% 1.40/1.64 (~trans(s99, s17)),
% 1.40/1.64 inference(unit_resolution,[status(thm)],[11988, 11049, 10186])).
% 1.40/1.64 tff(11990,assumption,(~until2p29(s14)), introduced(assumption)).
% 1.40/1.64 tff(11991,assumption,(trans(s99, s14)), introduced(assumption)).
% 1.40/1.64 tff(11992,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s14) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s14)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s14) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s14)))),
% 1.40/1.64 inference(rewrite,[status(thm)],[])).
% 1.40/1.64 tff(11993,plain,
% 1.40/1.64 (((~trans(s99, s14)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s14)) <=> (until2p29(s14) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s14)))),
% 1.40/1.64 inference(rewrite,[status(thm)],[])).
% 1.40/1.64 tff(11994,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s14)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s14))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s14) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s14))))),
% 1.40/1.64 inference(monotonicity,[status(thm)],[11993])).
% 1.40/1.64 tff(11995,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s14)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s14))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s14) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s14)))),
% 1.40/1.64 inference(transitivity,[status(thm)],[11994, 11992])).
% 1.40/1.64 tff(11996,plain,
% 1.40/1.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s14)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s14))),
% 1.40/1.64 inference(quant_inst,[status(thm)],[])).
% 1.40/1.64 tff(11997,plain,
% 1.40/1.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s14) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s14))),
% 1.40/1.64 inference(modus_ponens,[status(thm)],[11996, 11995])).
% 1.40/1.64 tff(11998,plain,
% 1.40/1.64 ($false),
% 1.40/1.64 inference(unit_resolution,[status(thm)],[11997, 10200, 11991, 11219, 11990, 11220])).
% 1.40/1.64 tff(11999,plain,((~trans(s99, s14)) | until2p29(s14) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.64 tff(12000,plain,
% 1.40/1.64 (~trans(s99, s14)),
% 1.40/1.64 inference(unit_resolution,[status(thm)],[11999, 11079, 10186])).
% 1.40/1.64 tff(12001,assumption,(~until2p29(s25)), introduced(assumption)).
% 1.40/1.64 tff(12002,assumption,(trans(s99, s25)), introduced(assumption)).
% 1.40/1.64 tff(12003,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s25) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s25)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s25) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s25)))),
% 1.40/1.64 inference(rewrite,[status(thm)],[])).
% 1.40/1.64 tff(12004,plain,
% 1.40/1.64 (((~trans(s99, s25)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s25)) <=> (until2p29(s25) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s25)))),
% 1.40/1.64 inference(rewrite,[status(thm)],[])).
% 1.40/1.64 tff(12005,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s25)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s25))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s25) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s25))))),
% 1.40/1.64 inference(monotonicity,[status(thm)],[12004])).
% 1.40/1.64 tff(12006,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s25)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s25))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s25) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s25)))),
% 1.40/1.64 inference(transitivity,[status(thm)],[12005, 12003])).
% 1.40/1.64 tff(12007,plain,
% 1.40/1.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s25)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s25))),
% 1.40/1.64 inference(quant_inst,[status(thm)],[])).
% 1.40/1.64 tff(12008,plain,
% 1.40/1.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s25) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s25))),
% 1.40/1.64 inference(modus_ponens,[status(thm)],[12007, 12006])).
% 1.40/1.64 tff(12009,plain,
% 1.40/1.64 ($false),
% 1.40/1.64 inference(unit_resolution,[status(thm)],[12008, 10200, 12002, 11219, 12001, 11220])).
% 1.40/1.64 tff(12010,plain,((~trans(s99, s25)) | until2p29(s25) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.64 tff(12011,plain,
% 1.40/1.64 (~trans(s99, s25)),
% 1.40/1.64 inference(unit_resolution,[status(thm)],[12010, 10969, 10186])).
% 1.40/1.64 tff(12012,assumption,(~until2p29(s31)), introduced(assumption)).
% 1.40/1.64 tff(12013,assumption,(trans(s99, s31)), introduced(assumption)).
% 1.40/1.64 tff(12014,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s31) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s31)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s31) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s31)))),
% 1.40/1.64 inference(rewrite,[status(thm)],[])).
% 1.40/1.64 tff(12015,plain,
% 1.40/1.64 (((~trans(s99, s31)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s31)) <=> (until2p29(s31) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s31)))),
% 1.40/1.64 inference(rewrite,[status(thm)],[])).
% 1.40/1.64 tff(12016,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s31)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s31))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s31) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s31))))),
% 1.40/1.64 inference(monotonicity,[status(thm)],[12015])).
% 1.40/1.64 tff(12017,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s31)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s31))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s31) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s31)))),
% 1.40/1.64 inference(transitivity,[status(thm)],[12016, 12014])).
% 1.40/1.64 tff(12018,plain,
% 1.40/1.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s31)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s31))),
% 1.40/1.64 inference(quant_inst,[status(thm)],[])).
% 1.40/1.64 tff(12019,plain,
% 1.40/1.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s31) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s31))),
% 1.40/1.64 inference(modus_ponens,[status(thm)],[12018, 12017])).
% 1.40/1.64 tff(12020,plain,
% 1.40/1.64 ($false),
% 1.40/1.64 inference(unit_resolution,[status(thm)],[12019, 10200, 12013, 11219, 12012, 11220])).
% 1.40/1.64 tff(12021,plain,((~trans(s99, s31)) | until2p29(s31) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.64 tff(12022,plain,
% 1.40/1.64 (~trans(s99, s31)),
% 1.40/1.64 inference(unit_resolution,[status(thm)],[12021, 10909, 10186])).
% 1.40/1.64 tff(12023,assumption,(~until2p29(s38)), introduced(assumption)).
% 1.40/1.64 tff(12024,assumption,(trans(s99, s38)), introduced(assumption)).
% 1.40/1.64 tff(12025,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s38) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s38)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s38) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s38)))),
% 1.40/1.64 inference(rewrite,[status(thm)],[])).
% 1.40/1.64 tff(12026,plain,
% 1.40/1.64 (((~trans(s99, s38)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s38)) <=> (until2p29(s38) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s38)))),
% 1.40/1.64 inference(rewrite,[status(thm)],[])).
% 1.40/1.64 tff(12027,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s38)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s38))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s38) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s38))))),
% 1.40/1.64 inference(monotonicity,[status(thm)],[12026])).
% 1.40/1.64 tff(12028,plain,
% 1.40/1.64 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s38)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s38))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s38) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s38)))),
% 1.40/1.64 inference(transitivity,[status(thm)],[12027, 12025])).
% 1.40/1.64 tff(12029,plain,
% 1.40/1.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s38)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s38))),
% 1.40/1.64 inference(quant_inst,[status(thm)],[])).
% 1.40/1.64 tff(12030,plain,
% 1.40/1.64 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s38) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s38))),
% 1.40/1.65 inference(modus_ponens,[status(thm)],[12029, 12028])).
% 1.40/1.65 tff(12031,plain,
% 1.40/1.65 ($false),
% 1.40/1.65 inference(unit_resolution,[status(thm)],[12030, 10200, 12024, 11219, 12023, 11220])).
% 1.40/1.65 tff(12032,plain,((~trans(s99, s38)) | until2p29(s38) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.65 tff(12033,plain,
% 1.40/1.65 (~trans(s99, s38)),
% 1.40/1.65 inference(unit_resolution,[status(thm)],[12032, 10839, 10186])).
% 1.40/1.65 tff(12034,assumption,(~until2p29(s3)), introduced(assumption)).
% 1.40/1.65 tff(12035,assumption,(trans(s99, s3)), introduced(assumption)).
% 1.40/1.65 tff(12036,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s3) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s3)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s3) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s3)))),
% 1.40/1.65 inference(rewrite,[status(thm)],[])).
% 1.40/1.65 tff(12037,plain,
% 1.40/1.65 (((~trans(s99, s3)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s3)) <=> (until2p29(s3) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s3)))),
% 1.40/1.65 inference(rewrite,[status(thm)],[])).
% 1.40/1.65 tff(12038,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s3)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s3))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s3) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s3))))),
% 1.40/1.65 inference(monotonicity,[status(thm)],[12037])).
% 1.40/1.65 tff(12039,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s3)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s3))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s3) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s3)))),
% 1.40/1.65 inference(transitivity,[status(thm)],[12038, 12036])).
% 1.40/1.65 tff(12040,plain,
% 1.40/1.65 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s3)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s3))),
% 1.40/1.65 inference(quant_inst,[status(thm)],[])).
% 1.40/1.65 tff(12041,plain,
% 1.40/1.65 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s3) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s3))),
% 1.40/1.65 inference(modus_ponens,[status(thm)],[12040, 12039])).
% 1.40/1.65 tff(12042,plain,
% 1.40/1.65 ($false),
% 1.40/1.65 inference(unit_resolution,[status(thm)],[12041, 10200, 12035, 11219, 12034, 11220])).
% 1.40/1.65 tff(12043,plain,((~trans(s99, s3)) | until2p29(s3) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.65 tff(12044,plain,
% 1.40/1.65 (~trans(s99, s3)),
% 1.40/1.65 inference(unit_resolution,[status(thm)],[12043, 11189, 10186])).
% 1.40/1.65 tff(12045,assumption,(~until2p29(s15)), introduced(assumption)).
% 1.40/1.65 tff(12046,assumption,(trans(s99, s15)), introduced(assumption)).
% 1.40/1.65 tff(12047,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s15) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s15)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s15) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s15)))),
% 1.40/1.65 inference(rewrite,[status(thm)],[])).
% 1.40/1.65 tff(12048,plain,
% 1.40/1.65 (((~trans(s99, s15)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s15)) <=> (until2p29(s15) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s15)))),
% 1.40/1.65 inference(rewrite,[status(thm)],[])).
% 1.40/1.65 tff(12049,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s15)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s15))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s15) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s15))))),
% 1.40/1.65 inference(monotonicity,[status(thm)],[12048])).
% 1.40/1.65 tff(12050,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s15)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s15))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s15) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s15)))),
% 1.40/1.65 inference(transitivity,[status(thm)],[12049, 12047])).
% 1.40/1.65 tff(12051,plain,
% 1.40/1.65 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s15)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s15))),
% 1.40/1.65 inference(quant_inst,[status(thm)],[])).
% 1.40/1.65 tff(12052,plain,
% 1.40/1.65 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s15) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s15))),
% 1.40/1.65 inference(modus_ponens,[status(thm)],[12051, 12050])).
% 1.40/1.65 tff(12053,plain,
% 1.40/1.65 ($false),
% 1.40/1.65 inference(unit_resolution,[status(thm)],[12052, 10200, 12046, 11219, 12045, 11220])).
% 1.40/1.65 tff(12054,plain,((~trans(s99, s15)) | until2p29(s15) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.65 tff(12055,plain,
% 1.40/1.65 (~trans(s99, s15)),
% 1.40/1.65 inference(unit_resolution,[status(thm)],[12054, 11069, 10186])).
% 1.40/1.65 tff(12056,assumption,(~until2p29(s27)), introduced(assumption)).
% 1.40/1.65 tff(12057,assumption,(trans(s99, s27)), introduced(assumption)).
% 1.40/1.65 tff(12058,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s27) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s27)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s27) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s27)))),
% 1.40/1.65 inference(rewrite,[status(thm)],[])).
% 1.40/1.65 tff(12059,plain,
% 1.40/1.65 (((~trans(s99, s27)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s27)) <=> (until2p29(s27) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s27)))),
% 1.40/1.65 inference(rewrite,[status(thm)],[])).
% 1.40/1.65 tff(12060,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s27)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s27))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s27) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s27))))),
% 1.40/1.65 inference(monotonicity,[status(thm)],[12059])).
% 1.40/1.65 tff(12061,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s27)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s27))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s27) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s27)))),
% 1.40/1.65 inference(transitivity,[status(thm)],[12060, 12058])).
% 1.40/1.65 tff(12062,plain,
% 1.40/1.65 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s27)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s27))),
% 1.40/1.65 inference(quant_inst,[status(thm)],[])).
% 1.40/1.65 tff(12063,plain,
% 1.40/1.65 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s27) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s27))),
% 1.40/1.65 inference(modus_ponens,[status(thm)],[12062, 12061])).
% 1.40/1.65 tff(12064,plain,
% 1.40/1.65 ($false),
% 1.40/1.65 inference(unit_resolution,[status(thm)],[12063, 10200, 12057, 11219, 12056, 11220])).
% 1.40/1.65 tff(12065,plain,((~trans(s99, s27)) | until2p29(s27) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.65 tff(12066,plain,
% 1.40/1.65 (~trans(s99, s27)),
% 1.40/1.65 inference(unit_resolution,[status(thm)],[12065, 10949, 10186])).
% 1.40/1.65 tff(12067,assumption,(~until2p29(s7)), introduced(assumption)).
% 1.40/1.65 tff(12068,assumption,(trans(s99, s7)), introduced(assumption)).
% 1.40/1.65 tff(12069,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s7) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s7)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s7) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s7)))),
% 1.40/1.65 inference(rewrite,[status(thm)],[])).
% 1.40/1.65 tff(12070,plain,
% 1.40/1.65 (((~trans(s99, s7)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s7)) <=> (until2p29(s7) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s7)))),
% 1.40/1.65 inference(rewrite,[status(thm)],[])).
% 1.40/1.65 tff(12071,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s7)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s7))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s7) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s7))))),
% 1.40/1.65 inference(monotonicity,[status(thm)],[12070])).
% 1.40/1.65 tff(12072,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s7)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s7))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s7) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s7)))),
% 1.40/1.65 inference(transitivity,[status(thm)],[12071, 12069])).
% 1.40/1.65 tff(12073,plain,
% 1.40/1.65 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s7)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s7))),
% 1.40/1.65 inference(quant_inst,[status(thm)],[])).
% 1.40/1.65 tff(12074,plain,
% 1.40/1.65 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s7) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s7))),
% 1.40/1.65 inference(modus_ponens,[status(thm)],[12073, 12072])).
% 1.40/1.65 tff(12075,plain,
% 1.40/1.65 ($false),
% 1.40/1.65 inference(unit_resolution,[status(thm)],[12074, 10200, 12068, 11219, 12067, 11220])).
% 1.40/1.65 tff(12076,plain,((~trans(s99, s7)) | until2p29(s7) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.65 tff(12077,plain,
% 1.40/1.65 (~trans(s99, s7)),
% 1.40/1.65 inference(unit_resolution,[status(thm)],[12076, 11149, 10186])).
% 1.40/1.65 tff(12078,assumption,(~until2p29(s23)), introduced(assumption)).
% 1.40/1.65 tff(12079,assumption,(trans(s99, s23)), introduced(assumption)).
% 1.40/1.65 tff(12080,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s23) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s23)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s23) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s23)))),
% 1.40/1.65 inference(rewrite,[status(thm)],[])).
% 1.40/1.65 tff(12081,plain,
% 1.40/1.65 (((~trans(s99, s23)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s23)) <=> (until2p29(s23) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s23)))),
% 1.40/1.65 inference(rewrite,[status(thm)],[])).
% 1.40/1.65 tff(12082,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s23)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s23))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s23) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s23))))),
% 1.40/1.65 inference(monotonicity,[status(thm)],[12081])).
% 1.40/1.65 tff(12083,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s23)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s23))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s23) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s23)))),
% 1.40/1.65 inference(transitivity,[status(thm)],[12082, 12080])).
% 1.40/1.65 tff(12084,plain,
% 1.40/1.65 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s23)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s23))),
% 1.40/1.65 inference(quant_inst,[status(thm)],[])).
% 1.40/1.65 tff(12085,plain,
% 1.40/1.65 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s23) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s23))),
% 1.40/1.65 inference(modus_ponens,[status(thm)],[12084, 12083])).
% 1.40/1.65 tff(12086,plain,
% 1.40/1.65 ($false),
% 1.40/1.65 inference(unit_resolution,[status(thm)],[12085, 10200, 12079, 11219, 12078, 11220])).
% 1.40/1.65 tff(12087,plain,((~trans(s99, s23)) | until2p29(s23) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.65 tff(12088,plain,
% 1.40/1.65 (~trans(s99, s23)),
% 1.40/1.65 inference(unit_resolution,[status(thm)],[12087, 10989, 10186])).
% 1.40/1.65 tff(12089,assumption,(~until2p29(s6)), introduced(assumption)).
% 1.40/1.65 tff(12090,assumption,(trans(s99, s6)), introduced(assumption)).
% 1.40/1.65 tff(12091,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s6) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s6)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s6) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s6)))),
% 1.40/1.65 inference(rewrite,[status(thm)],[])).
% 1.40/1.65 tff(12092,plain,
% 1.40/1.65 (((~trans(s99, s6)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s6)) <=> (until2p29(s6) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s6)))),
% 1.40/1.65 inference(rewrite,[status(thm)],[])).
% 1.40/1.65 tff(12093,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s6)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s6))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s6) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s6))))),
% 1.40/1.65 inference(monotonicity,[status(thm)],[12092])).
% 1.40/1.65 tff(12094,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s6)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s6))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s6) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s6)))),
% 1.40/1.65 inference(transitivity,[status(thm)],[12093, 12091])).
% 1.40/1.65 tff(12095,plain,
% 1.40/1.65 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s6)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s6))),
% 1.40/1.65 inference(quant_inst,[status(thm)],[])).
% 1.40/1.65 tff(12096,plain,
% 1.40/1.65 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s6) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s6))),
% 1.40/1.65 inference(modus_ponens,[status(thm)],[12095, 12094])).
% 1.40/1.65 tff(12097,plain,
% 1.40/1.65 ($false),
% 1.40/1.65 inference(unit_resolution,[status(thm)],[12096, 10200, 12090, 11219, 12089, 11220])).
% 1.40/1.65 tff(12098,plain,((~trans(s99, s6)) | until2p29(s6) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.65 tff(12099,plain,
% 1.40/1.65 (~trans(s99, s6)),
% 1.40/1.65 inference(unit_resolution,[status(thm)],[12098, 11159, 10186])).
% 1.40/1.65 tff(12100,assumption,(~until2p29(s9)), introduced(assumption)).
% 1.40/1.65 tff(12101,assumption,(trans(s99, s9)), introduced(assumption)).
% 1.40/1.65 tff(12102,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s9) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s9)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s9) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s9)))),
% 1.40/1.65 inference(rewrite,[status(thm)],[])).
% 1.40/1.65 tff(12103,plain,
% 1.40/1.65 (((~trans(s99, s9)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s9)) <=> (until2p29(s9) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s9)))),
% 1.40/1.65 inference(rewrite,[status(thm)],[])).
% 1.40/1.65 tff(12104,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s9)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s9))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s9) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s9))))),
% 1.40/1.65 inference(monotonicity,[status(thm)],[12103])).
% 1.40/1.65 tff(12105,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s9)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s9))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s9) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s9)))),
% 1.40/1.65 inference(transitivity,[status(thm)],[12104, 12102])).
% 1.40/1.65 tff(12106,plain,
% 1.40/1.65 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s9)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s9))),
% 1.40/1.65 inference(quant_inst,[status(thm)],[])).
% 1.40/1.65 tff(12107,plain,
% 1.40/1.65 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s9) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s9))),
% 1.40/1.65 inference(modus_ponens,[status(thm)],[12106, 12105])).
% 1.40/1.65 tff(12108,plain,
% 1.40/1.65 ($false),
% 1.40/1.65 inference(unit_resolution,[status(thm)],[12107, 10200, 12101, 11219, 12100, 11220])).
% 1.40/1.65 tff(12109,plain,((~trans(s99, s9)) | until2p29(s9) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.65 tff(12110,plain,
% 1.40/1.65 (~trans(s99, s9)),
% 1.40/1.65 inference(unit_resolution,[status(thm)],[12109, 11129, 10186])).
% 1.40/1.65 tff(12111,assumption,(~until2p29(s5)), introduced(assumption)).
% 1.40/1.65 tff(12112,assumption,(trans(s99, s5)), introduced(assumption)).
% 1.40/1.65 tff(12113,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s5) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s5)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s5) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s5)))),
% 1.40/1.65 inference(rewrite,[status(thm)],[])).
% 1.40/1.65 tff(12114,plain,
% 1.40/1.65 (((~trans(s99, s5)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s5)) <=> (until2p29(s5) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s5)))),
% 1.40/1.65 inference(rewrite,[status(thm)],[])).
% 1.40/1.65 tff(12115,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s5)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s5))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s5) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s5))))),
% 1.40/1.65 inference(monotonicity,[status(thm)],[12114])).
% 1.40/1.65 tff(12116,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s5)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s5))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s5) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s5)))),
% 1.40/1.65 inference(transitivity,[status(thm)],[12115, 12113])).
% 1.40/1.65 tff(12117,plain,
% 1.40/1.65 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s5)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s5))),
% 1.40/1.65 inference(quant_inst,[status(thm)],[])).
% 1.40/1.65 tff(12118,plain,
% 1.40/1.65 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s5) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s5))),
% 1.40/1.65 inference(modus_ponens,[status(thm)],[12117, 12116])).
% 1.40/1.65 tff(12119,plain,
% 1.40/1.65 ($false),
% 1.40/1.65 inference(unit_resolution,[status(thm)],[12118, 10200, 12112, 11219, 12111, 11220])).
% 1.40/1.65 tff(12120,plain,((~trans(s99, s5)) | until2p29(s5) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.65 tff(12121,plain,
% 1.40/1.65 (~trans(s99, s5)),
% 1.40/1.65 inference(unit_resolution,[status(thm)],[12120, 11169, 10186])).
% 1.40/1.65 tff(12122,assumption,(~until2p29(s39)), introduced(assumption)).
% 1.40/1.65 tff(12123,assumption,(trans(s99, s39)), introduced(assumption)).
% 1.40/1.65 tff(12124,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s39) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s39)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s39) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s39)))),
% 1.40/1.65 inference(rewrite,[status(thm)],[])).
% 1.40/1.65 tff(12125,plain,
% 1.40/1.65 (((~trans(s99, s39)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s39)) <=> (until2p29(s39) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s39)))),
% 1.40/1.65 inference(rewrite,[status(thm)],[])).
% 1.40/1.65 tff(12126,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s39)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s39))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s39) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s39))))),
% 1.40/1.65 inference(monotonicity,[status(thm)],[12125])).
% 1.40/1.65 tff(12127,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s39)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s39))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s39) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s39)))),
% 1.40/1.65 inference(transitivity,[status(thm)],[12126, 12124])).
% 1.40/1.65 tff(12128,plain,
% 1.40/1.65 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s39)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s39))),
% 1.40/1.65 inference(quant_inst,[status(thm)],[])).
% 1.40/1.65 tff(12129,plain,
% 1.40/1.65 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s39) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s39))),
% 1.40/1.65 inference(modus_ponens,[status(thm)],[12128, 12127])).
% 1.40/1.65 tff(12130,plain,
% 1.40/1.65 ($false),
% 1.40/1.65 inference(unit_resolution,[status(thm)],[12129, 10200, 12123, 11219, 12122, 11220])).
% 1.40/1.65 tff(12131,plain,((~trans(s99, s39)) | until2p29(s39) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.65 tff(12132,plain,
% 1.40/1.65 (~trans(s99, s39)),
% 1.40/1.65 inference(unit_resolution,[status(thm)],[12131, 10829, 10186])).
% 1.40/1.65 tff(12133,assumption,(~until2p29(s8)), introduced(assumption)).
% 1.40/1.65 tff(12134,assumption,(trans(s99, s8)), introduced(assumption)).
% 1.40/1.65 tff(12135,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s8) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s8)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s8) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s8)))),
% 1.40/1.65 inference(rewrite,[status(thm)],[])).
% 1.40/1.65 tff(12136,plain,
% 1.40/1.65 (((~trans(s99, s8)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s8)) <=> (until2p29(s8) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s8)))),
% 1.40/1.65 inference(rewrite,[status(thm)],[])).
% 1.40/1.65 tff(12137,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s8)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s8))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s8) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s8))))),
% 1.40/1.65 inference(monotonicity,[status(thm)],[12136])).
% 1.40/1.65 tff(12138,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s8)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s8))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s8) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s8)))),
% 1.40/1.65 inference(transitivity,[status(thm)],[12137, 12135])).
% 1.40/1.65 tff(12139,plain,
% 1.40/1.65 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s8)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s8))),
% 1.40/1.65 inference(quant_inst,[status(thm)],[])).
% 1.40/1.65 tff(12140,plain,
% 1.40/1.65 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s8) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s8))),
% 1.40/1.65 inference(modus_ponens,[status(thm)],[12139, 12138])).
% 1.40/1.65 tff(12141,plain,
% 1.40/1.65 ($false),
% 1.40/1.65 inference(unit_resolution,[status(thm)],[12140, 10200, 12134, 11219, 12133, 11220])).
% 1.40/1.65 tff(12142,plain,((~trans(s99, s8)) | until2p29(s8) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.40/1.65 tff(12143,plain,
% 1.40/1.65 (~trans(s99, s8)),
% 1.40/1.65 inference(unit_resolution,[status(thm)],[12142, 11139, 10186])).
% 1.40/1.65 tff(12144,assumption,(~until2p29(s32)), introduced(assumption)).
% 1.40/1.65 tff(12145,assumption,(trans(s99, s32)), introduced(assumption)).
% 1.40/1.65 tff(12146,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s32) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s32)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s32) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s32)))),
% 1.40/1.65 inference(rewrite,[status(thm)],[])).
% 1.40/1.65 tff(12147,plain,
% 1.40/1.65 (((~trans(s99, s32)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s32)) <=> (until2p29(s32) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s32)))),
% 1.40/1.65 inference(rewrite,[status(thm)],[])).
% 1.40/1.65 tff(12148,plain,
% 1.40/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s32)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s32))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s32) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s32))))),
% 1.49/1.65 inference(monotonicity,[status(thm)],[12147])).
% 1.49/1.65 tff(12149,plain,
% 1.49/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s32)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s32))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s32) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s32)))),
% 1.49/1.65 inference(transitivity,[status(thm)],[12148, 12146])).
% 1.49/1.65 tff(12150,plain,
% 1.49/1.65 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s32)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s32))),
% 1.49/1.65 inference(quant_inst,[status(thm)],[])).
% 1.49/1.65 tff(12151,plain,
% 1.49/1.65 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s32) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s32))),
% 1.49/1.65 inference(modus_ponens,[status(thm)],[12150, 12149])).
% 1.49/1.65 tff(12152,plain,
% 1.49/1.65 ($false),
% 1.49/1.65 inference(unit_resolution,[status(thm)],[12151, 10200, 12145, 11219, 12144, 11220])).
% 1.49/1.65 tff(12153,plain,((~trans(s99, s32)) | until2p29(s32) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.49/1.65 tff(12154,plain,
% 1.49/1.65 (~trans(s99, s32)),
% 1.49/1.65 inference(unit_resolution,[status(thm)],[12153, 10899, 10186])).
% 1.49/1.65 tff(12155,assumption,(~until2p29(s24)), introduced(assumption)).
% 1.49/1.65 tff(12156,assumption,(trans(s99, s24)), introduced(assumption)).
% 1.49/1.65 tff(12157,plain,
% 1.49/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s24) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s24)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s24) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s24)))),
% 1.49/1.65 inference(rewrite,[status(thm)],[])).
% 1.49/1.65 tff(12158,plain,
% 1.49/1.65 (((~trans(s99, s24)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s24)) <=> (until2p29(s24) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s24)))),
% 1.49/1.65 inference(rewrite,[status(thm)],[])).
% 1.49/1.65 tff(12159,plain,
% 1.49/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s24)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s24))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s24) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s24))))),
% 1.49/1.65 inference(monotonicity,[status(thm)],[12158])).
% 1.49/1.65 tff(12160,plain,
% 1.49/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s24)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s24))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s24) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s24)))),
% 1.49/1.65 inference(transitivity,[status(thm)],[12159, 12157])).
% 1.49/1.65 tff(12161,plain,
% 1.49/1.65 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s24)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s24))),
% 1.49/1.65 inference(quant_inst,[status(thm)],[])).
% 1.49/1.65 tff(12162,plain,
% 1.49/1.65 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s24) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s24))),
% 1.49/1.65 inference(modus_ponens,[status(thm)],[12161, 12160])).
% 1.49/1.65 tff(12163,plain,
% 1.49/1.65 ($false),
% 1.49/1.65 inference(unit_resolution,[status(thm)],[12162, 10200, 12156, 11219, 12155, 11220])).
% 1.49/1.65 tff(12164,plain,((~trans(s99, s24)) | until2p29(s24) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.49/1.65 tff(12165,plain,
% 1.49/1.65 (~trans(s99, s24)),
% 1.49/1.65 inference(unit_resolution,[status(thm)],[12164, 10979, 10186])).
% 1.49/1.65 tff(12166,assumption,(~until2p29(s20)), introduced(assumption)).
% 1.49/1.65 tff(12167,assumption,(trans(s99, s20)), introduced(assumption)).
% 1.49/1.65 tff(12168,plain,
% 1.49/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s20) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s20)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s20) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s20)))),
% 1.49/1.65 inference(rewrite,[status(thm)],[])).
% 1.49/1.65 tff(12169,plain,
% 1.49/1.65 (((~trans(s99, s20)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s20)) <=> (until2p29(s20) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s20)))),
% 1.49/1.65 inference(rewrite,[status(thm)],[])).
% 1.49/1.65 tff(12170,plain,
% 1.49/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s20)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s20))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s20) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s20))))),
% 1.49/1.65 inference(monotonicity,[status(thm)],[12169])).
% 1.49/1.65 tff(12171,plain,
% 1.49/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s20)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s20))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s20) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s20)))),
% 1.49/1.65 inference(transitivity,[status(thm)],[12170, 12168])).
% 1.49/1.65 tff(12172,plain,
% 1.49/1.65 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s20)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s20))),
% 1.49/1.65 inference(quant_inst,[status(thm)],[])).
% 1.49/1.65 tff(12173,plain,
% 1.49/1.65 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s20) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s20))),
% 1.49/1.65 inference(modus_ponens,[status(thm)],[12172, 12171])).
% 1.49/1.65 tff(12174,plain,
% 1.49/1.65 ($false),
% 1.49/1.65 inference(unit_resolution,[status(thm)],[12173, 10200, 12167, 11219, 12166, 11220])).
% 1.49/1.65 tff(12175,plain,((~trans(s99, s20)) | until2p29(s20) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.49/1.65 tff(12176,plain,
% 1.49/1.65 (~trans(s99, s20)),
% 1.49/1.65 inference(unit_resolution,[status(thm)],[12175, 11019, 10186])).
% 1.49/1.65 tff(12177,assumption,(~until2p29(s83)), introduced(assumption)).
% 1.49/1.65 tff(12178,assumption,(trans(s99, s83)), introduced(assumption)).
% 1.49/1.65 tff(12179,plain,
% 1.49/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s83) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s83)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s83) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s83)))),
% 1.49/1.65 inference(rewrite,[status(thm)],[])).
% 1.49/1.65 tff(12180,plain,
% 1.49/1.65 (((~trans(s99, s83)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s83)) <=> (until2p29(s83) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s83)))),
% 1.49/1.65 inference(rewrite,[status(thm)],[])).
% 1.49/1.65 tff(12181,plain,
% 1.49/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s83)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s83))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s83) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s83))))),
% 1.49/1.65 inference(monotonicity,[status(thm)],[12180])).
% 1.49/1.65 tff(12182,plain,
% 1.49/1.65 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s83)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s83))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s83) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s83)))),
% 1.49/1.65 inference(transitivity,[status(thm)],[12181, 12179])).
% 1.49/1.65 tff(12183,plain,
% 1.49/1.65 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s83)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s83))),
% 1.49/1.65 inference(quant_inst,[status(thm)],[])).
% 1.49/1.65 tff(12184,plain,
% 1.49/1.65 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s83) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s83))),
% 1.49/1.65 inference(modus_ponens,[status(thm)],[12183, 12182])).
% 1.49/1.66 tff(12185,plain,
% 1.49/1.66 ($false),
% 1.49/1.66 inference(unit_resolution,[status(thm)],[12184, 10200, 12178, 11219, 12177, 11220])).
% 1.49/1.66 tff(12186,plain,((~trans(s99, s83)) | until2p29(s83) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.49/1.66 tff(12187,plain,
% 1.49/1.66 (~trans(s99, s83)),
% 1.49/1.66 inference(unit_resolution,[status(thm)],[12186, 10389, 10186])).
% 1.49/1.66 tff(12188,assumption,(~until2p29(s71)), introduced(assumption)).
% 1.49/1.66 tff(12189,assumption,(trans(s99, s71)), introduced(assumption)).
% 1.49/1.66 tff(12190,plain,
% 1.49/1.66 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s71) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s71)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s71) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s71)))),
% 1.49/1.66 inference(rewrite,[status(thm)],[])).
% 1.49/1.66 tff(12191,plain,
% 1.49/1.66 (((~trans(s99, s71)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s71)) <=> (until2p29(s71) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s71)))),
% 1.49/1.66 inference(rewrite,[status(thm)],[])).
% 1.49/1.66 tff(12192,plain,
% 1.49/1.66 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s71)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s71))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s71) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s71))))),
% 1.49/1.66 inference(monotonicity,[status(thm)],[12191])).
% 1.49/1.66 tff(12193,plain,
% 1.49/1.66 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s71)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s71))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s71) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s71)))),
% 1.49/1.66 inference(transitivity,[status(thm)],[12192, 12190])).
% 1.49/1.66 tff(12194,plain,
% 1.49/1.66 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s71)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s71))),
% 1.49/1.66 inference(quant_inst,[status(thm)],[])).
% 1.49/1.66 tff(12195,plain,
% 1.49/1.66 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s71) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s71))),
% 1.49/1.66 inference(modus_ponens,[status(thm)],[12194, 12193])).
% 1.49/1.66 tff(12196,plain,
% 1.49/1.66 ($false),
% 1.49/1.66 inference(unit_resolution,[status(thm)],[12195, 10200, 12189, 11219, 12188, 11220])).
% 1.49/1.66 tff(12197,plain,((~trans(s99, s71)) | until2p29(s71) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.49/1.66 tff(12198,plain,
% 1.49/1.66 (~trans(s99, s71)),
% 1.49/1.66 inference(unit_resolution,[status(thm)],[12197, 10509, 10186])).
% 1.49/1.66 tff(12199,assumption,(~until2p29(s28)), introduced(assumption)).
% 1.49/1.66 tff(12200,assumption,(trans(s99, s28)), introduced(assumption)).
% 1.49/1.66 tff(12201,plain,
% 1.49/1.66 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s28) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s28)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s28) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s28)))),
% 1.49/1.66 inference(rewrite,[status(thm)],[])).
% 1.49/1.66 tff(12202,plain,
% 1.49/1.66 (((~trans(s99, s28)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s28)) <=> (until2p29(s28) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s28)))),
% 1.49/1.66 inference(rewrite,[status(thm)],[])).
% 1.49/1.66 tff(12203,plain,
% 1.49/1.66 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s28)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s28))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s28) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s28))))),
% 1.49/1.66 inference(monotonicity,[status(thm)],[12202])).
% 1.49/1.66 tff(12204,plain,
% 1.49/1.66 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s28)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s28))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s28) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s28)))),
% 1.49/1.66 inference(transitivity,[status(thm)],[12203, 12201])).
% 1.49/1.66 tff(12205,plain,
% 1.49/1.66 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s28)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s28))),
% 1.49/1.66 inference(quant_inst,[status(thm)],[])).
% 1.49/1.66 tff(12206,plain,
% 1.49/1.66 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s28) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s28))),
% 1.49/1.66 inference(modus_ponens,[status(thm)],[12205, 12204])).
% 1.49/1.66 tff(12207,plain,
% 1.49/1.66 ($false),
% 1.49/1.66 inference(unit_resolution,[status(thm)],[12206, 10200, 12200, 11219, 12199, 11220])).
% 1.49/1.66 tff(12208,plain,((~trans(s99, s28)) | until2p29(s28) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.49/1.66 tff(12209,plain,
% 1.49/1.66 (~trans(s99, s28)),
% 1.49/1.66 inference(unit_resolution,[status(thm)],[12208, 10939, 10186])).
% 1.49/1.66 tff(12210,assumption,(~until2p29(s48)), introduced(assumption)).
% 1.49/1.66 tff(12211,assumption,(trans(s99, s48)), introduced(assumption)).
% 1.49/1.66 tff(12212,plain,
% 1.49/1.66 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s48) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s48)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s48) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s48)))),
% 1.49/1.66 inference(rewrite,[status(thm)],[])).
% 1.49/1.66 tff(12213,plain,
% 1.49/1.66 (((~trans(s99, s48)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s48)) <=> (until2p29(s48) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s48)))),
% 1.49/1.66 inference(rewrite,[status(thm)],[])).
% 1.49/1.66 tff(12214,plain,
% 1.49/1.66 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s48)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s48))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s48) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s48))))),
% 1.49/1.66 inference(monotonicity,[status(thm)],[12213])).
% 1.49/1.66 tff(12215,plain,
% 1.49/1.66 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s48)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s48))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s48) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s48)))),
% 1.49/1.66 inference(transitivity,[status(thm)],[12214, 12212])).
% 1.49/1.66 tff(12216,plain,
% 1.49/1.66 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s48)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s48))),
% 1.49/1.66 inference(quant_inst,[status(thm)],[])).
% 1.49/1.66 tff(12217,plain,
% 1.49/1.66 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s48) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s48))),
% 1.49/1.66 inference(modus_ponens,[status(thm)],[12216, 12215])).
% 1.49/1.66 tff(12218,plain,
% 1.49/1.66 ($false),
% 1.49/1.66 inference(unit_resolution,[status(thm)],[12217, 10200, 12211, 11219, 12210, 11220])).
% 1.49/1.66 tff(12219,plain,((~trans(s99, s48)) | until2p29(s48) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.49/1.66 tff(12220,plain,
% 1.49/1.66 (~trans(s99, s48)),
% 1.49/1.66 inference(unit_resolution,[status(thm)],[12219, 10739, 10186])).
% 1.49/1.66 tff(12221,assumption,(~until2p29(s79)), introduced(assumption)).
% 1.49/1.66 tff(12222,assumption,(trans(s99, s79)), introduced(assumption)).
% 1.49/1.66 tff(12223,plain,
% 1.49/1.66 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s79) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s79)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s79) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s79)))),
% 1.49/1.66 inference(rewrite,[status(thm)],[])).
% 1.49/1.66 tff(12224,plain,
% 1.49/1.66 (((~trans(s99, s79)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s79)) <=> (until2p29(s79) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s79)))),
% 1.49/1.66 inference(rewrite,[status(thm)],[])).
% 1.49/1.66 tff(12225,plain,
% 1.49/1.66 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s79)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s79))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s79) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s79))))),
% 1.49/1.66 inference(monotonicity,[status(thm)],[12224])).
% 1.49/1.66 tff(12226,plain,
% 1.49/1.66 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s79)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s79))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s79) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s79)))),
% 1.49/1.66 inference(transitivity,[status(thm)],[12225, 12223])).
% 1.49/1.66 tff(12227,plain,
% 1.49/1.66 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s79)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s79))),
% 1.49/1.66 inference(quant_inst,[status(thm)],[])).
% 1.49/1.66 tff(12228,plain,
% 1.49/1.66 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s79) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s79))),
% 1.49/1.66 inference(modus_ponens,[status(thm)],[12227, 12226])).
% 1.49/1.66 tff(12229,plain,
% 1.49/1.66 ($false),
% 1.49/1.66 inference(unit_resolution,[status(thm)],[12228, 10200, 12222, 11219, 12221, 11220])).
% 1.49/1.66 tff(12230,plain,((~trans(s99, s79)) | until2p29(s79) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.49/1.66 tff(12231,plain,
% 1.49/1.66 (~trans(s99, s79)),
% 1.49/1.66 inference(unit_resolution,[status(thm)],[12230, 10429, 10186])).
% 1.49/1.66 tff(12232,assumption,(~until2p29(s42)), introduced(assumption)).
% 1.49/1.66 tff(12233,assumption,(trans(s99, s42)), introduced(assumption)).
% 1.49/1.66 tff(12234,plain,
% 1.49/1.66 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s42) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s42)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s42) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s42)))),
% 1.49/1.66 inference(rewrite,[status(thm)],[])).
% 1.49/1.66 tff(12235,plain,
% 1.49/1.66 (((~trans(s99, s42)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s42)) <=> (until2p29(s42) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s42)))),
% 1.49/1.66 inference(rewrite,[status(thm)],[])).
% 1.49/1.66 tff(12236,plain,
% 1.49/1.66 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s42)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s42))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s42) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s42))))),
% 1.49/1.66 inference(monotonicity,[status(thm)],[12235])).
% 1.49/1.66 tff(12237,plain,
% 1.49/1.66 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s42)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s42))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s42) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s42)))),
% 1.49/1.66 inference(transitivity,[status(thm)],[12236, 12234])).
% 1.49/1.66 tff(12238,plain,
% 1.49/1.66 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s42)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s42))),
% 1.49/1.66 inference(quant_inst,[status(thm)],[])).
% 1.49/1.66 tff(12239,plain,
% 1.49/1.66 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s42) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s42))),
% 1.49/1.66 inference(modus_ponens,[status(thm)],[12238, 12237])).
% 1.49/1.66 tff(12240,plain,
% 1.49/1.66 ($false),
% 1.49/1.66 inference(unit_resolution,[status(thm)],[12239, 10200, 12233, 11219, 12232, 11220])).
% 1.49/1.66 tff(12241,plain,((~trans(s99, s42)) | until2p29(s42) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.49/1.66 tff(12242,plain,
% 1.49/1.66 (~trans(s99, s42)),
% 1.49/1.66 inference(unit_resolution,[status(thm)],[12241, 10799, 10186])).
% 1.49/1.66 tff(12243,assumption,(~until2p29(s96)), introduced(assumption)).
% 1.49/1.66 tff(12244,assumption,(trans(s99, s96)), introduced(assumption)).
% 1.49/1.66 tff(12245,plain,
% 1.49/1.66 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s96) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s96)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s96) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s96)))),
% 1.49/1.66 inference(rewrite,[status(thm)],[])).
% 1.49/1.66 tff(12246,plain,
% 1.49/1.66 (((~trans(s99, s96)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s96)) <=> (until2p29(s96) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s96)))),
% 1.49/1.66 inference(rewrite,[status(thm)],[])).
% 1.49/1.66 tff(12247,plain,
% 1.49/1.66 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s96)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s96))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s96) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s96))))),
% 1.49/1.66 inference(monotonicity,[status(thm)],[12246])).
% 1.49/1.66 tff(12248,plain,
% 1.49/1.66 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s96)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s96))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s96) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s96)))),
% 1.49/1.66 inference(transitivity,[status(thm)],[12247, 12245])).
% 1.49/1.66 tff(12249,plain,
% 1.49/1.66 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s96)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s96))),
% 1.49/1.66 inference(quant_inst,[status(thm)],[])).
% 1.49/1.66 tff(12250,plain,
% 1.49/1.66 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s96) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s96))),
% 1.49/1.66 inference(modus_ponens,[status(thm)],[12249, 12248])).
% 1.49/1.66 tff(12251,plain,
% 1.49/1.66 ($false),
% 1.49/1.66 inference(unit_resolution,[status(thm)],[12250, 10200, 12244, 11219, 12243, 11220])).
% 1.49/1.66 tff(12252,plain,((~trans(s99, s96)) | until2p29(s96) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.49/1.66 tff(12253,plain,
% 1.49/1.66 (~trans(s99, s96)),
% 1.49/1.66 inference(unit_resolution,[status(thm)],[12252, 10259, 10186])).
% 1.49/1.66 tff(12254,assumption,(~until2p29(s85)), introduced(assumption)).
% 1.49/1.66 tff(12255,assumption,(trans(s99, s85)), introduced(assumption)).
% 1.49/1.66 tff(12256,plain,
% 1.49/1.66 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s85) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s85)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s85) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s85)))),
% 1.49/1.66 inference(rewrite,[status(thm)],[])).
% 1.49/1.66 tff(12257,plain,
% 1.49/1.66 (((~trans(s99, s85)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s85)) <=> (until2p29(s85) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s85)))),
% 1.49/1.66 inference(rewrite,[status(thm)],[])).
% 1.49/1.66 tff(12258,plain,
% 1.49/1.66 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s85)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s85))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s85) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s85))))),
% 1.49/1.66 inference(monotonicity,[status(thm)],[12257])).
% 1.49/1.66 tff(12259,plain,
% 1.49/1.66 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s85)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s85))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s85) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s85)))),
% 1.49/1.66 inference(transitivity,[status(thm)],[12258, 12256])).
% 1.49/1.66 tff(12260,plain,
% 1.49/1.66 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s85)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s85))),
% 1.49/1.66 inference(quant_inst,[status(thm)],[])).
% 1.49/1.66 tff(12261,plain,
% 1.49/1.66 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s85) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s85))),
% 1.49/1.66 inference(modus_ponens,[status(thm)],[12260, 12259])).
% 1.49/1.66 tff(12262,plain,
% 1.49/1.66 ($false),
% 1.49/1.66 inference(unit_resolution,[status(thm)],[12261, 10200, 12255, 11219, 12254, 11220])).
% 1.49/1.66 tff(12263,plain,((~trans(s99, s85)) | until2p29(s85) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.49/1.66 tff(12264,plain,
% 1.49/1.66 (~trans(s99, s85)),
% 1.49/1.66 inference(unit_resolution,[status(thm)],[12263, 10369, 10186])).
% 1.49/1.66 tff(12265,assumption,(~until2p29(s95)), introduced(assumption)).
% 1.49/1.66 tff(12266,plain,
% 1.49/1.66 (~xuntil2p30(s94)),
% 1.49/1.66 inference(unit_resolution,[status(thm)],[10273, 12265])).
% 1.49/1.66 tff(12267,plain,
% 1.49/1.66 (~until2p29(s94)),
% 1.49/1.66 inference(unit_resolution,[status(thm)],[10278, 12266])).
% 1.49/1.66 tff(12268,plain,
% 1.49/1.66 (~xuntil2p30(s93)),
% 1.49/1.66 inference(unit_resolution,[status(thm)],[10283, 12267])).
% 1.49/1.66 tff(12269,plain,
% 1.49/1.66 (~until2p29(s93)),
% 1.49/1.66 inference(unit_resolution,[status(thm)],[10288, 12268])).
% 1.49/1.66 tff(12270,assumption,(~trans(s99, s72)), introduced(assumption)).
% 1.49/1.66 tff(12271,assumption,(~trans(s99, s65)), introduced(assumption)).
% 1.49/1.66 tff(12272,assumption,(~trans(s99, s96)), introduced(assumption)).
% 1.49/1.66 tff(12273,assumption,(~trans(s99, s91)), introduced(assumption)).
% 1.49/1.66 tff(12274,assumption,(~trans(s99, s75)), introduced(assumption)).
% 1.49/1.66 tff(12275,assumption,(~trans(s99, s76)), introduced(assumption)).
% 1.49/1.66 tff(12276,assumption,(~trans(s99, s78)), introduced(assumption)).
% 1.49/1.66 tff(12277,assumption,(~trans(s99, s74)), introduced(assumption)).
% 1.49/1.66 tff(12278,assumption,(~trans(s99, s45)), introduced(assumption)).
% 1.49/1.66 tff(12279,assumption,(~trans(s99, s90)), introduced(assumption)).
% 1.49/1.66 tff(12280,assumption,(~trans(s99, s81)), introduced(assumption)).
% 1.49/1.66 tff(12281,assumption,(~trans(s99, s68)), introduced(assumption)).
% 1.49/1.66 tff(12282,assumption,(~trans(s99, s10)), introduced(assumption)).
% 1.49/1.66 tff(12283,assumption,(~trans(s99, s82)), introduced(assumption)).
% 1.49/1.66 tff(12284,assumption,(~trans(s99, s35)), introduced(assumption)).
% 1.49/1.66 tff(12285,assumption,(~trans(s99, s37)), introduced(assumption)).
% 1.49/1.66 tff(12286,assumption,(~trans(s99, s2)), introduced(assumption)).
% 1.49/1.66 tff(12287,assumption,(~trans(s99, s0)), introduced(assumption)).
% 1.49/1.66 tff(12288,assumption,(~trans(s99, s84)), introduced(assumption)).
% 1.49/1.66 tff(12289,assumption,(~trans(s99, s73)), introduced(assumption)).
% 1.49/1.66 tff(12290,assumption,(~trans(s99, s41)), introduced(assumption)).
% 1.49/1.66 tff(12291,assumption,(~trans(s99, s12)), introduced(assumption)).
% 1.49/1.66 tff(12292,assumption,(~trans(s99, s55)), introduced(assumption)).
% 1.49/1.66 tff(12293,assumption,(~trans(s99, s56)), introduced(assumption)).
% 1.49/1.66 tff(12294,assumption,(~trans(s99, s86)), introduced(assumption)).
% 1.49/1.66 tff(12295,assumption,(~trans(s99, s62)), introduced(assumption)).
% 1.49/1.66 tff(12296,assumption,(~trans(s99, s11)), introduced(assumption)).
% 1.49/1.66 tff(12297,assumption,(~trans(s99, s40)), introduced(assumption)).
% 1.49/1.66 tff(12298,assumption,(~trans(s99, s57)), introduced(assumption)).
% 1.49/1.66 tff(12299,assumption,(~trans(s99, s54)), introduced(assumption)).
% 1.49/1.66 tff(12300,assumption,(~trans(s99, s51)), introduced(assumption)).
% 1.49/1.66 tff(12301,assumption,(~trans(s99, s44)), introduced(assumption)).
% 1.49/1.66 tff(12302,assumption,(~trans(s99, s4)), introduced(assumption)).
% 1.49/1.66 tff(12303,assumption,(~trans(s99, s94)), introduced(assumption)).
% 1.49/1.66 tff(12304,assumption,(~trans(s99, s59)), introduced(assumption)).
% 1.49/1.66 tff(12305,assumption,(~trans(s99, s53)), introduced(assumption)).
% 1.49/1.66 tff(12306,assumption,(~trans(s99, s18)), introduced(assumption)).
% 1.49/1.66 tff(12307,assumption,(~trans(s99, s69)), introduced(assumption)).
% 1.49/1.66 tff(12308,assumption,(~trans(s99, s93)), introduced(assumption)).
% 1.49/1.66 tff(12309,assumption,(~trans(s99, s61)), introduced(assumption)).
% 1.49/1.66 tff(12310,assumption,(~trans(s99, s30)), introduced(assumption)).
% 1.49/1.66 tff(12311,assumption,(~trans(s99, s36)), introduced(assumption)).
% 1.49/1.66 tff(12312,assumption,(~trans(s99, s26)), introduced(assumption)).
% 1.49/1.66 tff(12313,assumption,(~trans(s99, s70)), introduced(assumption)).
% 1.49/1.66 tff(12314,assumption,(~trans(s99, s19)), introduced(assumption)).
% 1.49/1.66 tff(12315,assumption,(~trans(s99, s63)), introduced(assumption)).
% 1.49/1.66 tff(12316,assumption,(~trans(s99, s50)), introduced(assumption)).
% 1.49/1.66 tff(12317,assumption,(~trans(s99, s66)), introduced(assumption)).
% 1.49/1.66 tff(12318,assumption,(~trans(s99, s58)), introduced(assumption)).
% 1.49/1.66 tff(12319,assumption,(~trans(s99, s87)), introduced(assumption)).
% 1.49/1.66 tff(12320,assumption,(~trans(s99, s80)), introduced(assumption)).
% 1.49/1.66 tff(12321,assumption,(~trans(s99, s16)), introduced(assumption)).
% 1.49/1.66 tff(12322,assumption,(~trans(s99, s49)), introduced(assumption)).
% 1.49/1.66 tff(12323,assumption,(~trans(s99, s33)), introduced(assumption)).
% 1.49/1.66 tff(12324,assumption,(~trans(s99, s13)), introduced(assumption)).
% 1.49/1.66 tff(12325,assumption,(~trans(s99, s77)), introduced(assumption)).
% 1.49/1.66 tff(12326,assumption,(~trans(s99, s46)), introduced(assumption)).
% 1.49/1.66 tff(12327,assumption,(~trans(s99, s47)), introduced(assumption)).
% 1.49/1.66 tff(12328,assumption,(~trans(s99, s89)), introduced(assumption)).
% 1.49/1.66 tff(12329,assumption,(~trans(s99, s88)), introduced(assumption)).
% 1.49/1.66 tff(12330,assumption,(~trans(s99, s60)), introduced(assumption)).
% 1.49/1.66 tff(12331,assumption,(~trans(s99, s52)), introduced(assumption)).
% 1.49/1.66 tff(12332,assumption,(~trans(s99, s64)), introduced(assumption)).
% 1.49/1.66 tff(12333,assumption,(~trans(s99, s67)), introduced(assumption)).
% 1.49/1.66 tff(12334,assumption,(~trans(s99, s22)), introduced(assumption)).
% 1.49/1.66 tff(12335,assumption,(~trans(s99, s43)), introduced(assumption)).
% 1.49/1.66 tff(12336,assumption,(~trans(s99, s34)), introduced(assumption)).
% 1.49/1.66 tff(12337,assumption,(~trans(s99, s21)), introduced(assumption)).
% 1.49/1.66 tff(12338,assumption,(~trans(s99, s29)), introduced(assumption)).
% 1.49/1.66 tff(12339,assumption,(~trans(s99, s17)), introduced(assumption)).
% 1.49/1.66 tff(12340,assumption,(~trans(s99, s14)), introduced(assumption)).
% 1.49/1.66 tff(12341,assumption,(~trans(s99, s25)), introduced(assumption)).
% 1.49/1.66 tff(12342,assumption,(~trans(s99, s31)), introduced(assumption)).
% 1.49/1.66 tff(12343,assumption,(~trans(s99, s38)), introduced(assumption)).
% 1.49/1.66 tff(12344,assumption,(~trans(s99, s3)), introduced(assumption)).
% 1.49/1.66 tff(12345,assumption,(~trans(s99, s15)), introduced(assumption)).
% 1.49/1.66 tff(12346,assumption,(~trans(s99, s27)), introduced(assumption)).
% 1.49/1.66 tff(12347,assumption,(~trans(s99, s7)), introduced(assumption)).
% 1.49/1.66 tff(12348,assumption,(~trans(s99, s23)), introduced(assumption)).
% 1.49/1.66 tff(12349,assumption,(~trans(s99, s6)), introduced(assumption)).
% 1.49/1.66 tff(12350,assumption,(~trans(s99, s9)), introduced(assumption)).
% 1.49/1.66 tff(12351,assumption,(~trans(s99, s5)), introduced(assumption)).
% 1.49/1.66 tff(12352,assumption,(~trans(s99, s39)), introduced(assumption)).
% 1.49/1.66 tff(12353,assumption,(~trans(s99, s8)), introduced(assumption)).
% 1.49/1.66 tff(12354,assumption,(~trans(s99, s32)), introduced(assumption)).
% 1.49/1.66 tff(12355,assumption,(~trans(s99, s24)), introduced(assumption)).
% 1.49/1.66 tff(12356,assumption,(~trans(s99, s20)), introduced(assumption)).
% 1.49/1.66 tff(12357,assumption,(~trans(s99, s83)), introduced(assumption)).
% 1.49/1.66 tff(12358,assumption,(~trans(s99, s71)), introduced(assumption)).
% 1.49/1.66 tff(12359,assumption,(~trans(s99, s28)), introduced(assumption)).
% 1.49/1.66 tff(12360,assumption,(~trans(s99, s48)), introduced(assumption)).
% 1.49/1.66 tff(12361,assumption,(~trans(s99, s79)), introduced(assumption)).
% 1.49/1.66 tff(12362,assumption,(~trans(s99, s42)), introduced(assumption)).
% 1.49/1.66 tff(12363,assumption,(~trans(s99, s1)), introduced(assumption)).
% 1.49/1.66 tff(12364,assumption,(~trans(s99, s85)), introduced(assumption)).
% 1.49/1.66 tff(12365,assumption,(trans(s99, s95)), introduced(assumption)).
% 1.49/1.66 tff(12366,plain,
% 1.49/1.66 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s95) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s95)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s95) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s95)))),
% 1.49/1.66 inference(rewrite,[status(thm)],[])).
% 1.49/1.66 tff(12367,plain,
% 1.49/1.66 (((~trans(s99, s95)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s95)) <=> (until2p29(s95) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s95)))),
% 1.49/1.66 inference(rewrite,[status(thm)],[])).
% 1.49/1.66 tff(12368,plain,
% 1.49/1.66 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s95)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s95))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s95) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s95))))),
% 1.49/1.66 inference(monotonicity,[status(thm)],[12367])).
% 1.49/1.66 tff(12369,plain,
% 1.49/1.66 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s95)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s95))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s95) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s95)))),
% 1.49/1.66 inference(transitivity,[status(thm)],[12368, 12366])).
% 1.49/1.66 tff(12370,plain,
% 1.49/1.66 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s95)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s95))),
% 1.49/1.66 inference(quant_inst,[status(thm)],[])).
% 1.49/1.66 tff(12371,plain,
% 1.49/1.66 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s95) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s95))),
% 1.49/1.66 inference(modus_ponens,[status(thm)],[12370, 12369])).
% 1.49/1.66 tff(12372,plain,
% 1.49/1.66 ($false),
% 1.49/1.66 inference(unit_resolution,[status(thm)],[12371, 10200, 12365, 11219, 12265, 11220])).
% 1.49/1.66 tff(12373,plain,((~trans(s99, s95)) | until2p29(s95) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.49/1.66 tff(12374,plain,
% 1.49/1.66 (~trans(s99, s95)),
% 1.49/1.66 inference(unit_resolution,[status(thm)],[12373, 12265, 11220])).
% 1.49/1.66 tff(12375,assumption,(node18(s99, s99)), introduced(assumption)).
% 1.49/1.66 tff(12376,plain,
% 1.49/1.66 (((~![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)))),
% 1.49/1.66 inference(rewrite,[status(thm)],[])).
% 1.49/1.66 tff(12377,plain,
% 1.49/1.66 ((~![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)))),
% 1.49/1.66 inference(quant_inst,[status(thm)],[])).
% 1.49/1.66 tff(12378,plain,
% 1.49/1.66 ((~![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))),
% 1.49/1.66 inference(modus_ponens,[status(thm)],[12377, 12376])).
% 1.49/1.66 tff(12379,plain,
% 1.49/1.66 (~m_main_v_state2(s97, c_c2)),
% 1.49/1.66 inference(unit_resolution,[status(thm)],[12378, 697, 8099])).
% 1.49/1.66 tff(12380,plain,
% 1.49/1.66 (((~![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)))),
% 1.49/1.66 inference(rewrite,[status(thm)],[])).
% 1.49/1.66 tff(12381,plain,
% 1.49/1.66 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s97, c_c2) | (~node3(s97)))),
% 1.49/1.66 inference(quant_inst,[status(thm)],[])).
% 1.49/1.66 tff(12382,plain,
% 1.49/1.66 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s97, c_c2) | (~node3(s97))),
% 1.49/1.66 inference(modus_ponens,[status(thm)],[12381, 12380])).
% 1.49/1.66 tff(12383,plain,
% 1.49/1.66 (~node3(s97)),
% 1.49/1.66 inference(unit_resolution,[status(thm)],[12382, 399, 12379])).
% 1.49/1.66 tff(12384,plain,
% 1.49/1.66 (((~![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)))),
% 1.49/1.66 inference(rewrite,[status(thm)],[])).
% 1.49/1.66 tff(12385,plain,
% 1.49/1.66 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s96, c_n1) | (~node1(s96)))),
% 1.49/1.66 inference(quant_inst,[status(thm)],[])).
% 1.49/1.66 tff(12386,plain,
% 1.49/1.66 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s96, c_n1) | (~node1(s96))),
% 1.49/1.66 inference(modus_ponens,[status(thm)],[12385, 12384])).
% 1.49/1.66 tff(12387,plain,
% 1.49/1.66 (~node1(s96)),
% 1.49/1.66 inference(unit_resolution,[status(thm)],[12386, 421, 8056])).
% 1.49/1.66 tff(12388,plain,
% 1.49/1.66 (((~![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))),
% 1.49/1.66 inference(rewrite,[status(thm)],[])).
% 1.49/1.66 tff(12389,plain,
% 1.49/1.66 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s95, s96)) | node18(s95, s96))),
% 1.49/1.66 inference(quant_inst,[status(thm)],[])).
% 1.49/1.66 tff(12390,plain,
% 1.49/1.66 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s95, s96)) | node18(s95, s96)),
% 1.49/1.66 inference(modus_ponens,[status(thm)],[12389, 12388])).
% 1.49/1.66 tff(12391,plain,
% 1.49/1.66 (node18(s95, s96)),
% 1.49/1.66 inference(unit_resolution,[status(thm)],[12390, 125, 8026])).
% 1.49/1.66 tff(12392,plain,
% 1.49/1.66 (((~![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))),
% 1.49/1.66 inference(rewrite,[status(thm)],[])).
% 1.49/1.66 tff(12393,plain,
% 1.49/1.66 ((~![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))),
% 1.49/1.66 inference(quant_inst,[status(thm)],[])).
% 1.49/1.66 tff(12394,plain,
% 1.49/1.66 ((~![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)),
% 1.49/1.66 inference(modus_ponens,[status(thm)],[12393, 12392])).
% 1.49/1.66 tff(12395,plain,
% 1.49/1.66 ((~m_main_v_state1(s95, c_n1)) | (~m_main_v_state2(s95, c_t2)) | m_main_v_turn(s96, c_2)),
% 1.49/1.66 inference(unit_resolution,[status(thm)],[12394, 760, 12391])).
% 1.49/1.66 tff(12396,plain,
% 1.49/1.66 (m_main_v_turn(s96, c_2)),
% 1.49/1.66 inference(unit_resolution,[status(thm)],[12395, 7979, 8015])).
% 1.49/1.66 tff(12397,plain,
% 1.49/1.66 (((~![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)))),
% 1.49/1.66 inference(rewrite,[status(thm)],[])).
% 1.49/1.66 tff(12398,plain,
% 1.49/1.66 ((~![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)))),
% 1.49/1.66 inference(quant_inst,[status(thm)],[])).
% 1.49/1.66 tff(12399,plain,
% 1.49/1.66 ((~![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))),
% 1.49/1.66 inference(modus_ponens,[status(thm)],[12398, 12397])).
% 1.49/1.66 tff(12400,plain,
% 1.49/1.66 (~m_main_v_turn(s96, c_1)),
% 1.49/1.66 inference(unit_resolution,[status(thm)],[12399, 156, 12396])).
% 1.49/1.66 tff(12401,plain,
% 1.49/1.66 (((~![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)))),
% 1.49/1.66 inference(rewrite,[status(thm)],[])).
% 1.49/1.66 tff(12402,plain,
% 1.49/1.66 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s96, c_1) | (~node5(s96)))),
% 1.49/1.66 inference(quant_inst,[status(thm)],[])).
% 1.49/1.66 tff(12403,plain,
% 1.49/1.66 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s96, c_1) | (~node5(s96))),
% 1.49/1.66 inference(modus_ponens,[status(thm)],[12402, 12401])).
% 1.49/1.66 tff(12404,plain,
% 1.49/1.66 (~node5(s96)),
% 1.49/1.66 inference(unit_resolution,[status(thm)],[12403, 776, 12400])).
% 1.49/1.66 tff(12405,plain,
% 1.49/1.66 (((~![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)))),
% 1.49/1.66 inference(rewrite,[status(thm)],[])).
% 1.49/1.66 tff(12406,plain,
% 1.49/1.66 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s96, c_n1) | (~node2(s96)))),
% 1.49/1.66 inference(quant_inst,[status(thm)],[])).
% 1.49/1.66 tff(12407,plain,
% 1.49/1.66 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s96, c_n1) | (~node2(s96))),
% 1.49/1.66 inference(modus_ponens,[status(thm)],[12406, 12405])).
% 1.49/1.66 tff(12408,plain,
% 1.49/1.66 (~node2(s96)),
% 1.49/1.66 inference(unit_resolution,[status(thm)],[12407, 787, 8056])).
% 1.49/1.66 tff(12409,plain,
% 1.49/1.66 (((~![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)))),
% 1.49/1.67 inference(rewrite,[status(thm)],[])).
% 1.49/1.67 tff(12410,plain,
% 1.49/1.67 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s96, c_n1) | (~node3(s96)))),
% 1.49/1.67 inference(quant_inst,[status(thm)],[])).
% 1.49/1.67 tff(12411,plain,
% 1.49/1.67 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s96, c_n1) | (~node3(s96))),
% 1.49/1.67 inference(modus_ponens,[status(thm)],[12410, 12409])).
% 1.49/1.67 tff(12412,plain,
% 1.49/1.67 (~node3(s96)),
% 1.49/1.67 inference(unit_resolution,[status(thm)],[12411, 798, 8056])).
% 1.49/1.67 tff(12413,plain,
% 1.49/1.67 (((~![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)))),
% 1.49/1.67 inference(rewrite,[status(thm)],[])).
% 1.49/1.67 tff(12414,plain,
% 1.49/1.67 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s96, c_n2) | (~node4(s96)))),
% 1.49/1.67 inference(quant_inst,[status(thm)],[])).
% 1.49/1.67 tff(12415,plain,
% 1.49/1.67 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s96, c_n2) | (~node4(s96))),
% 1.49/1.67 inference(modus_ponens,[status(thm)],[12414, 12413])).
% 1.49/1.67 tff(12416,plain,
% 1.49/1.67 (~node4(s96)),
% 1.49/1.67 inference(unit_resolution,[status(thm)],[12415, 388, 8076])).
% 1.49/1.67 tff(12417,plain,
% 1.49/1.67 (((~![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))),
% 1.49/1.67 inference(rewrite,[status(thm)],[])).
% 1.49/1.67 tff(12418,plain,
% 1.49/1.67 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s96, s97)) | node7(s96, s97))),
% 1.49/1.67 inference(quant_inst,[status(thm)],[])).
% 1.49/1.67 tff(12419,plain,
% 1.49/1.67 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s96, s97)) | node7(s96, s97)),
% 1.49/1.67 inference(modus_ponens,[status(thm)],[12418, 12417])).
% 1.49/1.67 tff(12420,plain,
% 1.49/1.67 (node7(s96, s97)),
% 1.49/1.67 inference(unit_resolution,[status(thm)],[12419, 206, 8087])).
% 1.49/1.67 tff(12421,plain,
% 1.49/1.67 (((~![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)))),
% 1.49/1.67 inference(rewrite,[status(thm)],[])).
% 1.49/1.67 tff(12422,plain,
% 1.49/1.67 ((~![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)))),
% 1.49/1.67 inference(quant_inst,[status(thm)],[])).
% 1.49/1.67 tff(12423,plain,
% 1.49/1.67 ((~![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))),
% 1.49/1.67 inference(modus_ponens,[status(thm)],[12422, 12421])).
% 1.49/1.67 tff(12424,plain,
% 1.49/1.67 (m_main_v_state1(s96, c_c1) | node1(s96) | node2(s96) | node3(s96) | node4(s96) | node5(s96) | node6(s96, s97)),
% 1.49/1.67 inference(unit_resolution,[status(thm)],[12423, 820, 12420])).
% 1.49/1.67 tff(12425,plain,
% 1.49/1.67 (node6(s96, s97)),
% 1.49/1.67 inference(unit_resolution,[status(thm)],[12424, 12416, 8064, 12412, 12408, 12404, 12387])).
% 1.49/1.67 tff(12426,plain,
% 1.49/1.67 (((~![V: $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)))),
% 1.49/1.67 inference(rewrite,[status(thm)],[])).
% 1.49/1.67 tff(12427,plain,
% 1.49/1.67 (((~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)))),
% 1.49/1.67 inference(rewrite,[status(thm)],[])).
% 1.49/1.67 tff(12428,plain,
% 1.49/1.67 (((~![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))))),
% 1.49/1.67 inference(monotonicity,[status(thm)],[12427])).
% 1.49/1.67 tff(12429,plain,
% 1.49/1.67 (((~![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)))),
% 1.49/1.67 inference(transitivity,[status(thm)],[12428, 12426])).
% 1.49/1.67 tff(12430,plain,
% 1.49/1.67 ((~![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)))),
% 1.49/1.67 inference(quant_inst,[status(thm)],[])).
% 1.49/1.67 tff(12431,plain,
% 1.49/1.67 ((~![V: $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))),
% 1.49/1.67 inference(modus_ponens,[status(thm)],[12430, 12429])).
% 1.49/1.67 tff(12432,plain,
% 1.49/1.67 (~m_main_v_state1(s97, c_n1)),
% 1.49/1.67 inference(unit_resolution,[status(thm)],[12431, 835, 8056, 12425])).
% 1.49/1.67 tff(12433,plain,
% 1.49/1.67 (((~![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)))),
% 1.49/1.67 inference(rewrite,[status(thm)],[])).
% 1.49/1.67 tff(12434,plain,
% 1.49/1.67 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s97, c_n1) | (~node2(s97)))),
% 1.49/1.67 inference(quant_inst,[status(thm)],[])).
% 1.49/1.67 tff(12435,plain,
% 1.49/1.67 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s97, c_n1) | (~node2(s97))),
% 1.49/1.67 inference(modus_ponens,[status(thm)],[12434, 12433])).
% 1.49/1.67 tff(12436,plain,
% 1.49/1.67 (~node2(s97)),
% 1.49/1.67 inference(unit_resolution,[status(thm)],[12435, 787, 12432])).
% 1.49/1.67 tff(12437,plain,
% 1.49/1.67 (((~![V: $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)))),
% 1.49/1.67 inference(rewrite,[status(thm)],[])).
% 1.49/1.67 tff(12438,plain,
% 1.49/1.67 (((~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)))),
% 1.49/1.67 inference(rewrite,[status(thm)],[])).
% 1.49/1.67 tff(12439,plain,
% 1.49/1.67 (((~![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))))),
% 1.49/1.67 inference(monotonicity,[status(thm)],[12438])).
% 1.49/1.67 tff(12440,plain,
% 1.49/1.67 (((~![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)))),
% 1.49/1.67 inference(transitivity,[status(thm)],[12439, 12437])).
% 1.49/1.67 tff(12441,plain,
% 1.49/1.67 ((~![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))),
% 1.49/1.67 inference(quant_inst,[status(thm)],[])).
% 1.49/1.67 tff(12442,plain,
% 1.49/1.67 ((~![V: $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))),
% 1.49/1.67 inference(modus_ponens,[status(thm)],[12441, 12440])).
% 1.49/1.67 tff(12443,plain,
% 1.49/1.67 (m_main_v_state1(s97, c_t1)),
% 1.49/1.67 inference(unit_resolution,[status(thm)],[12442, 856, 8052, 12425])).
% 1.49/1.67 tff(12444,plain,
% 1.49/1.67 (((~![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)))),
% 1.49/1.67 inference(rewrite,[status(thm)],[])).
% 1.49/1.67 tff(12445,plain,
% 1.49/1.67 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s97, c_t2) | (~node1(s97)))),
% 1.49/1.67 inference(quant_inst,[status(thm)],[])).
% 1.49/1.67 tff(12446,plain,
% 1.49/1.67 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s97, c_t2) | (~node1(s97))),
% 1.49/1.67 inference(modus_ponens,[status(thm)],[12445, 12444])).
% 1.49/1.67 tff(12447,plain,
% 1.49/1.67 (~node1(s97)),
% 1.49/1.67 inference(unit_resolution,[status(thm)],[12446, 195, 8103])).
% 1.49/1.67 tff(12448,plain,
% 1.49/1.67 (((~![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))),
% 1.49/1.67 inference(rewrite,[status(thm)],[])).
% 1.49/1.67 tff(12449,plain,
% 1.49/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s97, s98)) | trans(s97, s98))),
% 1.49/1.67 inference(quant_inst,[status(thm)],[])).
% 1.49/1.67 tff(12450,plain,
% 1.49/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s97, s98)) | trans(s97, s98)),
% 1.49/1.67 inference(modus_ponens,[status(thm)],[12449, 12448])).
% 1.49/1.67 tff(12451,plain,
% 1.49/1.67 (trans(s97, s98)),
% 1.49/1.67 inference(unit_resolution,[status(thm)],[12450, 10155, 32])).
% 1.49/1.67 tff(12452,plain,
% 1.49/1.67 (((~![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))),
% 1.49/1.67 inference(rewrite,[status(thm)],[])).
% 1.49/1.67 tff(12453,plain,
% 1.49/1.67 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s97, s98)) | node7(s97, s98))),
% 1.49/1.67 inference(quant_inst,[status(thm)],[])).
% 1.49/1.67 tff(12454,plain,
% 1.49/1.67 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s97, s98)) | node7(s97, s98)),
% 1.49/1.67 inference(modus_ponens,[status(thm)],[12453, 12452])).
% 1.49/1.67 tff(12455,plain,
% 1.49/1.67 (node7(s97, s98)),
% 1.49/1.67 inference(unit_resolution,[status(thm)],[12454, 206, 12451])).
% 1.49/1.67 tff(12456,plain,
% 1.49/1.67 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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)))),
% 1.49/1.67 inference(rewrite,[status(thm)],[])).
% 1.49/1.67 tff(12457,plain,
% 1.49/1.67 (((~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)))),
% 1.49/1.67 inference(rewrite,[status(thm)],[])).
% 1.49/1.67 tff(12458,plain,
% 1.49/1.67 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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))))),
% 1.49/1.67 inference(monotonicity,[status(thm)],[12457])).
% 1.49/1.67 tff(12459,plain,
% 1.49/1.67 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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)))),
% 1.49/1.67 inference(transitivity,[status(thm)],[12458, 12456])).
% 1.49/1.67 tff(12460,plain,
% 1.49/1.67 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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))),
% 1.49/1.67 inference(quant_inst,[status(thm)],[])).
% 1.49/1.67 tff(12461,plain,
% 1.49/1.67 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_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))),
% 1.49/1.67 inference(modus_ponens,[status(thm)],[12460, 12459])).
% 1.49/1.67 tff(12462,plain,
% 1.49/1.67 ((~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)),
% 1.49/1.67 inference(unit_resolution,[status(thm)],[12461, 892, 12455])).
% 1.49/1.67 tff(12463,plain,
% 1.49/1.67 (m_main_v_state1(s98, c_c1)),
% 1.49/1.67 inference(unit_resolution,[status(thm)],[12462, 12447, 8099, 12443, 12436, 12383])).
% 1.49/1.67 tff(12464,plain,
% 1.49/1.67 (((~![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)))),
% 1.49/1.67 inference(rewrite,[status(thm)],[])).
% 1.49/1.67 tff(12465,plain,
% 1.49/1.67 ((~![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)))),
% 1.49/1.67 inference(quant_inst,[status(thm)],[])).
% 1.49/1.67 tff(12466,plain,
% 1.49/1.67 ((~![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))),
% 1.49/1.67 inference(modus_ponens,[status(thm)],[12465, 12464])).
% 1.49/1.67 tff(12467,plain,
% 1.49/1.67 (~m_main_v_state1(s98, c_t1)),
% 1.49/1.67 inference(unit_resolution,[status(thm)],[12466, 539, 12463])).
% 1.49/1.67 tff(12468,plain,
% 1.49/1.67 (((~![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)))),
% 1.49/1.67 inference(rewrite,[status(thm)],[])).
% 1.49/1.67 tff(12469,plain,
% 1.49/1.67 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s98, c_t1) | (~node5(s98)))),
% 1.49/1.67 inference(quant_inst,[status(thm)],[])).
% 1.49/1.67 tff(12470,plain,
% 1.49/1.67 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s98, c_t1) | (~node5(s98))),
% 1.49/1.67 inference(modus_ponens,[status(thm)],[12469, 12468])).
% 1.49/1.67 tff(12471,plain,
% 1.49/1.67 (~node5(s98)),
% 1.49/1.67 inference(unit_resolution,[status(thm)],[12470, 550, 12467])).
% 1.49/1.67 tff(12472,plain,
% 1.49/1.67 (((~![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))),
% 1.49/1.67 inference(rewrite,[status(thm)],[])).
% 1.49/1.67 tff(12473,plain,
% 1.49/1.67 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s97, s98)) | node14(s97, s98))),
% 1.49/1.67 inference(quant_inst,[status(thm)],[])).
% 1.49/1.67 tff(12474,plain,
% 1.49/1.67 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s97, s98)) | node14(s97, s98)),
% 1.49/1.67 inference(modus_ponens,[status(thm)],[12473, 12472])).
% 1.49/1.67 tff(12475,plain,
% 1.49/1.67 (node14(s97, s98)),
% 1.49/1.67 inference(unit_resolution,[status(thm)],[12474, 46, 12451])).
% 1.49/1.67 tff(12476,plain,
% 1.49/1.67 (((~![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))),
% 1.49/1.67 inference(rewrite,[status(thm)],[])).
% 1.49/1.67 tff(12477,plain,
% 1.49/1.67 ((~![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))),
% 1.49/1.67 inference(quant_inst,[status(thm)],[])).
% 1.49/1.67 tff(12478,plain,
% 1.49/1.67 ((~![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)),
% 1.49/1.67 inference(modus_ponens,[status(thm)],[12477, 12476])).
% 1.49/1.67 tff(12479,plain,
% 1.49/1.67 ((~m_main_v_state1(s97, c_t1)) | (~m_main_v_state2(s97, c_n2)) | m_main_v_state2(s98, c_t2)),
% 1.49/1.67 inference(unit_resolution,[status(thm)],[12478, 922, 12475])).
% 1.49/1.67 tff(12480,plain,
% 1.49/1.67 (m_main_v_state2(s98, c_t2)),
% 1.49/1.67 inference(unit_resolution,[status(thm)],[12479, 12443, 8099])).
% 1.49/1.67 tff(12481,plain,
% 1.49/1.67 (((~![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)))),
% 1.49/1.67 inference(rewrite,[status(thm)],[])).
% 1.49/1.67 tff(12482,plain,
% 1.49/1.67 ((~![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)))),
% 1.49/1.67 inference(quant_inst,[status(thm)],[])).
% 1.49/1.67 tff(12483,plain,
% 1.49/1.67 ((~![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))),
% 1.49/1.67 inference(modus_ponens,[status(thm)],[12482, 12481])).
% 1.49/1.67 tff(12484,plain,
% 1.49/1.67 (~m_main_v_state2(s98, c_n2)),
% 1.49/1.67 inference(unit_resolution,[status(thm)],[12483, 77, 12480])).
% 1.49/1.67 tff(12485,plain,
% 1.49/1.67 (((~![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)))),
% 1.49/1.67 inference(rewrite,[status(thm)],[])).
% 1.49/1.67 tff(12486,plain,
% 1.49/1.67 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s98, c_n2) | (~node2(s98)))),
% 1.49/1.67 inference(quant_inst,[status(thm)],[])).
% 1.49/1.67 tff(12487,plain,
% 1.49/1.67 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s98, c_n2) | (~node2(s98))),
% 1.49/1.67 inference(modus_ponens,[status(thm)],[12486, 12485])).
% 1.49/1.67 tff(12488,plain,
% 1.49/1.67 (~node2(s98)),
% 1.49/1.67 inference(unit_resolution,[status(thm)],[12487, 410, 12484])).
% 1.49/1.67 tff(12489,plain,
% 1.49/1.67 (((~![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)))),
% 1.49/1.67 inference(rewrite,[status(thm)],[])).
% 1.49/1.67 tff(12490,plain,
% 1.49/1.67 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s98, c_n2) | (~node4(s98)))),
% 1.49/1.67 inference(quant_inst,[status(thm)],[])).
% 1.49/1.67 tff(12491,plain,
% 1.49/1.67 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s98, c_n2) | (~node4(s98))),
% 1.49/1.67 inference(modus_ponens,[status(thm)],[12490, 12489])).
% 1.49/1.67 tff(12492,plain,
% 1.49/1.67 (~node4(s98)),
% 1.49/1.67 inference(unit_resolution,[status(thm)],[12491, 388, 12484])).
% 1.49/1.67 tff(12493,plain,
% 1.49/1.67 (((~![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)))),
% 1.49/1.67 inference(rewrite,[status(thm)],[])).
% 1.49/1.67 tff(12494,plain,
% 1.49/1.67 ((~![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)))),
% 1.49/1.67 inference(quant_inst,[status(thm)],[])).
% 1.49/1.67 tff(12495,plain,
% 1.49/1.67 ((~![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))),
% 1.49/1.67 inference(modus_ponens,[status(thm)],[12494, 12493])).
% 1.49/1.67 tff(12496,plain,
% 1.49/1.67 (~m_main_v_state2(s98, c_c2)),
% 1.49/1.67 inference(unit_resolution,[status(thm)],[12495, 260, 12480])).
% 1.49/1.67 tff(12497,plain,
% 1.49/1.67 (((~![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)))),
% 1.49/1.67 inference(rewrite,[status(thm)],[])).
% 1.49/1.67 tff(12498,plain,
% 1.49/1.67 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s98, c_c2) | (~node3(s98)))),
% 1.49/1.67 inference(quant_inst,[status(thm)],[])).
% 1.49/1.67 tff(12499,plain,
% 1.49/1.67 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s98, c_c2) | (~node3(s98))),
% 1.49/1.67 inference(modus_ponens,[status(thm)],[12498, 12497])).
% 1.49/1.67 tff(12500,plain,
% 1.49/1.67 (~node3(s98)),
% 1.49/1.67 inference(unit_resolution,[status(thm)],[12499, 399, 12496])).
% 1.49/1.67 tff(12501,plain,
% 1.49/1.67 (((~![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)))),
% 1.49/1.67 inference(rewrite,[status(thm)],[])).
% 1.49/1.67 tff(12502,plain,
% 1.49/1.67 ((~![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)))),
% 1.49/1.67 inference(quant_inst,[status(thm)],[])).
% 1.49/1.67 tff(12503,plain,
% 1.49/1.67 ((~![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))),
% 1.49/1.67 inference(modus_ponens,[status(thm)],[12502, 12501])).
% 1.49/1.67 tff(12504,plain,
% 1.49/1.67 (~m_main_v_state1(s98, c_n1)),
% 1.49/1.67 inference(unit_resolution,[status(thm)],[12503, 454, 12463])).
% 1.49/1.67 tff(12505,plain,
% 1.49/1.67 (((~![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)))),
% 1.49/1.67 inference(rewrite,[status(thm)],[])).
% 1.49/1.67 tff(12506,plain,
% 1.49/1.67 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s98, c_n1) | (~node1(s98)))),
% 1.49/1.67 inference(quant_inst,[status(thm)],[])).
% 1.49/1.67 tff(12507,plain,
% 1.49/1.67 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s98, c_n1) | (~node1(s98))),
% 1.49/1.67 inference(modus_ponens,[status(thm)],[12506, 12505])).
% 1.49/1.67 tff(12508,plain,
% 1.49/1.67 (~node1(s98)),
% 1.49/1.67 inference(unit_resolution,[status(thm)],[12507, 421, 12504])).
% 1.49/1.67 tff(12509,plain,
% 1.49/1.67 (((~![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))),
% 1.49/1.67 inference(rewrite,[status(thm)],[])).
% 1.49/1.67 tff(12510,plain,
% 1.49/1.67 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s98, s99)) | node7(s98, s99))),
% 1.49/1.67 inference(quant_inst,[status(thm)],[])).
% 1.49/1.67 tff(12511,plain,
% 1.49/1.67 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s98, s99)) | node7(s98, s99)),
% 1.49/1.67 inference(modus_ponens,[status(thm)],[12510, 12509])).
% 1.49/1.67 tff(12512,plain,
% 1.49/1.67 (node7(s98, s99)),
% 1.49/1.67 inference(unit_resolution,[status(thm)],[12511, 206, 3924])).
% 1.49/1.67 tff(12513,plain,
% 1.49/1.67 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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(s98, c_c1)) | node1(s98) | node2(s98) | node3(s98) | node4(s98) | node5(s98) | (~node7(s98, s99)) | m_main_v_state1(s99, c_n1))),
% 1.49/1.67 inference(rewrite,[status(thm)],[])).
% 1.49/1.67 tff(12514,plain,
% 1.49/1.67 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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))),
% 1.49/1.67 inference(quant_inst,[status(thm)],[])).
% 1.49/1.67 tff(12515,plain,
% 1.49/1.67 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_c1)) | 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)),
% 1.49/1.67 inference(modus_ponens,[status(thm)],[12514, 12513])).
% 1.49/1.67 tff(12516,plain,
% 1.49/1.67 ((~m_main_v_state1(s98, c_c1)) | node1(s98) | node2(s98) | node3(s98) | node4(s98) | node5(s98) | m_main_v_state1(s99, c_n1)),
% 1.49/1.67 inference(unit_resolution,[status(thm)],[12515, 584, 12512])).
% 1.49/1.67 tff(12517,plain,
% 1.49/1.67 (m_main_v_state1(s99, c_n1)),
% 1.49/1.67 inference(unit_resolution,[status(thm)],[12516, 12508, 12463, 12500, 12492, 12488, 12471])).
% 1.49/1.67 tff(12518,plain,
% 1.49/1.67 (((~![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)))),
% 1.49/1.67 inference(rewrite,[status(thm)],[])).
% 1.49/1.67 tff(12519,plain,
% 1.49/1.67 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s97, c_t2) | (~node15(s97)))),
% 1.49/1.67 inference(quant_inst,[status(thm)],[])).
% 1.49/1.67 tff(12520,plain,
% 1.49/1.67 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s97, c_t2) | (~node15(s97))),
% 1.49/1.67 inference(modus_ponens,[status(thm)],[12519, 12518])).
% 1.49/1.67 tff(12521,plain,
% 1.49/1.67 (~node15(s97)),
% 1.49/1.67 inference(unit_resolution,[status(thm)],[12520, 103, 8103])).
% 1.49/1.67 tff(12522,plain,
% 1.49/1.67 (((~![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))),
% 1.49/1.67 inference(rewrite,[status(thm)],[])).
% 1.49/1.67 tff(12523,plain,
% 1.49/1.67 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s97, s98)) | node18(s97, s98))),
% 1.49/1.67 inference(quant_inst,[status(thm)],[])).
% 1.49/1.67 tff(12524,plain,
% 1.49/1.67 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s97, s98)) | node18(s97, s98)),
% 1.49/1.67 inference(modus_ponens,[status(thm)],[12523, 12522])).
% 1.49/1.67 tff(12525,plain,
% 1.49/1.67 (node18(s97, s98)),
% 1.49/1.67 inference(unit_resolution,[status(thm)],[12524, 125, 12451])).
% 1.49/1.67 tff(12526,plain,
% 1.49/1.67 (((~![Y: $i, X: $i] : ((~m_main_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))),
% 1.49/1.67 inference(rewrite,[status(thm)],[])).
% 1.49/1.67 tff(12527,plain,
% 1.49/1.67 (((~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))),
% 1.49/1.68 inference(rewrite,[status(thm)],[])).
% 1.49/1.68 tff(12528,plain,
% 1.49/1.68 (((~![Y: $i, X: $i] : ((~m_main_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)))),
% 1.49/1.68 inference(monotonicity,[status(thm)],[12527])).
% 1.49/1.68 tff(12529,plain,
% 1.49/1.68 (((~![Y: $i, X: $i] : ((~m_main_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))),
% 1.49/1.68 inference(transitivity,[status(thm)],[12528, 12526])).
% 1.49/1.68 tff(12530,plain,
% 1.49/1.68 ((~![Y: $i, X: $i] : ((~m_main_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))),
% 1.49/1.68 inference(quant_inst,[status(thm)],[])).
% 1.49/1.68 tff(12531,plain,
% 1.49/1.68 ((~![Y: $i, X: $i] : ((~m_main_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)),
% 1.49/1.68 inference(modus_ponens,[status(thm)],[12530, 12529])).
% 1.49/1.68 tff(12532,plain,
% 1.49/1.68 (node15(s97) | (~m_main_v_state1(s97, c_t1)) | (~m_main_v_state2(s97, c_n2)) | m_main_v_turn(s98, c_1)),
% 1.49/1.68 inference(unit_resolution,[status(thm)],[12531, 992, 12525])).
% 1.49/1.68 tff(12533,plain,
% 1.49/1.68 (m_main_v_turn(s98, c_1)),
% 1.49/1.68 inference(unit_resolution,[status(thm)],[12532, 12521, 8099, 12443])).
% 1.49/1.68 tff(12534,plain,
% 1.49/1.68 (((~![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)))),
% 1.49/1.68 inference(rewrite,[status(thm)],[])).
% 1.49/1.68 tff(12535,plain,
% 1.49/1.68 ((~![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)))),
% 1.49/1.68 inference(quant_inst,[status(thm)],[])).
% 1.49/1.68 tff(12536,plain,
% 1.49/1.68 ((~![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))),
% 1.49/1.68 inference(modus_ponens,[status(thm)],[12535, 12534])).
% 1.49/1.68 tff(12537,plain,
% 1.49/1.68 (~m_main_v_turn(s98, c_2)),
% 1.49/1.68 inference(unit_resolution,[status(thm)],[12536, 156, 12533])).
% 1.49/1.68 tff(12538,plain,
% 1.49/1.68 (((~![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)))),
% 1.49/1.68 inference(rewrite,[status(thm)],[])).
% 1.49/1.68 tff(12539,plain,
% 1.49/1.68 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s98, c_2) | (~node12(s98)))),
% 1.49/1.68 inference(quant_inst,[status(thm)],[])).
% 1.49/1.68 tff(12540,plain,
% 1.49/1.68 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s98, c_2) | (~node12(s98))),
% 1.49/1.68 inference(modus_ponens,[status(thm)],[12539, 12538])).
% 1.49/1.68 tff(12541,plain,
% 1.49/1.68 (~node12(s98)),
% 1.49/1.68 inference(unit_resolution,[status(thm)],[12540, 184, 12537])).
% 1.49/1.68 tff(12542,plain,
% 1.49/1.68 (((~![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)))),
% 1.49/1.68 inference(rewrite,[status(thm)],[])).
% 1.49/1.68 tff(12543,plain,
% 1.49/1.68 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s98, c_n2) | (~node8(s98)))),
% 1.49/1.68 inference(quant_inst,[status(thm)],[])).
% 1.49/1.68 tff(12544,plain,
% 1.49/1.68 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s98, c_n2) | (~node8(s98))),
% 1.49/1.68 inference(modus_ponens,[status(thm)],[12543, 12542])).
% 1.49/1.68 tff(12545,plain,
% 1.49/1.68 (~node8(s98)),
% 1.49/1.68 inference(unit_resolution,[status(thm)],[12544, 271, 12484])).
% 1.49/1.68 tff(12546,plain,
% 1.49/1.68 (((~![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)))),
% 1.49/1.68 inference(rewrite,[status(thm)],[])).
% 1.49/1.68 tff(12547,plain,
% 1.49/1.68 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s98, c_n2) | (~node9(s98)))),
% 1.49/1.68 inference(quant_inst,[status(thm)],[])).
% 1.49/1.68 tff(12548,plain,
% 1.49/1.68 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s98, c_n2) | (~node9(s98))),
% 1.49/1.68 inference(modus_ponens,[status(thm)],[12547, 12546])).
% 1.49/1.68 tff(12549,plain,
% 1.49/1.68 (~node9(s98)),
% 1.49/1.68 inference(unit_resolution,[status(thm)],[12548, 88, 12484])).
% 1.49/1.68 tff(12550,plain,
% 1.49/1.68 (((~![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)))),
% 1.49/1.68 inference(rewrite,[status(thm)],[])).
% 1.49/1.68 tff(12551,plain,
% 1.49/1.68 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s98, c_n2) | (~node10(s98)))),
% 1.49/1.68 inference(quant_inst,[status(thm)],[])).
% 1.49/1.68 tff(12552,plain,
% 1.49/1.68 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s98, c_n2) | (~node10(s98))),
% 1.49/1.68 inference(modus_ponens,[status(thm)],[12551, 12550])).
% 1.49/1.68 tff(12553,plain,
% 1.49/1.68 (~node10(s98)),
% 1.49/1.68 inference(unit_resolution,[status(thm)],[12552, 249, 12484])).
% 1.49/1.68 tff(12554,plain,
% 1.49/1.68 (((~![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)))),
% 1.49/1.68 inference(rewrite,[status(thm)],[])).
% 1.49/1.68 tff(12555,plain,
% 1.49/1.68 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s98, c_n1) | (~node11(s98)))),
% 1.49/1.68 inference(quant_inst,[status(thm)],[])).
% 1.49/1.68 tff(12556,plain,
% 1.49/1.68 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s98, c_n1) | (~node11(s98))),
% 1.49/1.68 inference(modus_ponens,[status(thm)],[12555, 12554])).
% 1.49/1.68 tff(12557,plain,
% 1.49/1.68 (~node11(s98)),
% 1.49/1.68 inference(unit_resolution,[status(thm)],[12556, 238, 12504])).
% 1.49/1.68 tff(12558,plain,
% 1.49/1.68 (((~![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))),
% 1.49/1.68 inference(rewrite,[status(thm)],[])).
% 1.49/1.68 tff(12559,plain,
% 1.49/1.68 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s98, s99)) | node14(s98, s99))),
% 1.49/1.68 inference(quant_inst,[status(thm)],[])).
% 1.49/1.68 tff(12560,plain,
% 1.49/1.68 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s98, s99)) | node14(s98, s99)),
% 1.49/1.68 inference(modus_ponens,[status(thm)],[12559, 12558])).
% 1.49/1.68 tff(12561,plain,
% 1.49/1.68 (node14(s98, s99)),
% 1.49/1.68 inference(unit_resolution,[status(thm)],[12560, 46, 3924])).
% 1.49/1.68 tff(12562,plain,
% 1.49/1.68 (((~![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)))),
% 1.49/1.68 inference(rewrite,[status(thm)],[])).
% 1.49/1.68 tff(12563,plain,
% 1.49/1.68 ((~![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)))),
% 1.49/1.68 inference(quant_inst,[status(thm)],[])).
% 1.49/1.68 tff(12564,plain,
% 1.49/1.68 ((~![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))),
% 1.49/1.68 inference(modus_ponens,[status(thm)],[12563, 12562])).
% 1.49/1.68 tff(12565,plain,
% 1.49/1.68 (m_main_v_state2(s98, c_c2) | node9(s98) | node8(s98) | node10(s98) | node11(s98) | node12(s98) | node13(s98, s99)),
% 1.49/1.68 inference(unit_resolution,[status(thm)],[12564, 296, 12561])).
% 1.49/1.68 tff(12566,plain,
% 1.49/1.68 (node13(s98, s99)),
% 1.49/1.68 inference(unit_resolution,[status(thm)],[12565, 12557, 12496, 12553, 12549, 12545, 12541])).
% 1.49/1.68 tff(12567,plain,
% 1.49/1.68 (((~![V: $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)))),
% 1.49/1.68 inference(rewrite,[status(thm)],[])).
% 1.49/1.68 tff(12568,plain,
% 1.49/1.68 (((~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)))),
% 1.49/1.68 inference(rewrite,[status(thm)],[])).
% 1.49/1.68 tff(12569,plain,
% 1.49/1.68 (((~![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))))),
% 1.49/1.68 inference(monotonicity,[status(thm)],[12568])).
% 1.49/1.68 tff(12570,plain,
% 1.49/1.68 (((~![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)))),
% 1.49/1.68 inference(transitivity,[status(thm)],[12569, 12567])).
% 1.49/1.68 tff(12571,plain,
% 1.49/1.68 ((~![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))),
% 1.49/1.68 inference(quant_inst,[status(thm)],[])).
% 1.49/1.68 tff(12572,plain,
% 1.49/1.68 ((~![V: $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))),
% 1.49/1.68 inference(modus_ponens,[status(thm)],[12571, 12570])).
% 1.49/1.68 tff(12573,plain,
% 1.49/1.68 (m_main_v_state2(s99, c_t2)),
% 1.49/1.68 inference(unit_resolution,[status(thm)],[12572, 518, 12480, 12566])).
% 1.49/1.68 tff(12574,plain,
% 1.49/1.68 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))) | (m_main_v_state2(s98, c_n2) | (~node16(s98)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))) | m_main_v_state2(s98, c_n2) | (~node16(s98)))),
% 1.49/1.68 inference(rewrite,[status(thm)],[])).
% 1.49/1.68 tff(12575,plain,
% 1.49/1.68 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))) | (m_main_v_state2(s98, c_n2) | (~node16(s98)))),
% 1.49/1.68 inference(quant_inst,[status(thm)],[])).
% 1.49/1.68 tff(12576,plain,
% 1.49/1.68 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))) | m_main_v_state2(s98, c_n2) | (~node16(s98))),
% 1.49/1.68 inference(modus_ponens,[status(thm)],[12575, 12574])).
% 1.49/1.68 tff(12577,plain,
% 1.49/1.68 (~node16(s98)),
% 1.49/1.68 inference(unit_resolution,[status(thm)],[12576, 329, 12484])).
% 1.49/1.68 tff(12578,plain,
% 1.49/1.68 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))) | (m_main_v_state1(s98, c_n1) | (~node15(s98)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))) | m_main_v_state1(s98, c_n1) | (~node15(s98)))),
% 1.49/1.68 inference(rewrite,[status(thm)],[])).
% 1.49/1.68 tff(12579,plain,
% 1.49/1.68 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))) | (m_main_v_state1(s98, c_n1) | (~node15(s98)))),
% 1.49/1.68 inference(quant_inst,[status(thm)],[])).
% 1.49/1.68 tff(12580,plain,
% 1.49/1.68 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))) | m_main_v_state1(s98, c_n1) | (~node15(s98))),
% 1.49/1.68 inference(modus_ponens,[status(thm)],[12579, 12578])).
% 1.49/1.68 tff(12581,plain,
% 1.49/1.68 (~node15(s98)),
% 1.49/1.68 inference(unit_resolution,[status(thm)],[12580, 340, 12504])).
% 1.49/1.68 tff(12582,plain,
% 1.49/1.68 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s98, s99)) | node18(s98, s99))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s98, s99)) | node18(s98, s99))),
% 1.49/1.68 inference(rewrite,[status(thm)],[])).
% 1.49/1.68 tff(12583,plain,
% 1.49/1.68 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s98, s99)) | node18(s98, s99))),
% 1.49/1.68 inference(quant_inst,[status(thm)],[])).
% 1.49/1.68 tff(12584,plain,
% 1.49/1.68 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s98, s99)) | node18(s98, s99)),
% 1.49/1.68 inference(modus_ponens,[status(thm)],[12583, 12582])).
% 1.49/1.68 tff(12585,plain,
% 1.49/1.68 (node18(s98, s99)),
% 1.49/1.68 inference(unit_resolution,[status(thm)],[12584, 125, 3924])).
% 1.49/1.68 tff(12586,plain,
% 1.49/1.68 (((~![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))) | (node15(s98) | node16(s98) | node17(s98, s99) | (~node18(s98, s99)))) <=> ((~![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))) | node15(s98) | node16(s98) | node17(s98, s99) | (~node18(s98, s99)))),
% 1.49/1.68 inference(rewrite,[status(thm)],[])).
% 1.49/1.68 tff(12587,plain,
% 1.49/1.68 ((~![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))) | (node15(s98) | node16(s98) | node17(s98, s99) | (~node18(s98, s99)))),
% 1.49/1.68 inference(quant_inst,[status(thm)],[])).
% 1.49/1.68 tff(12588,plain,
% 1.49/1.68 ((~![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))) | node15(s98) | node16(s98) | node17(s98, s99) | (~node18(s98, s99))),
% 1.49/1.68 inference(modus_ponens,[status(thm)],[12587, 12586])).
% 1.49/1.68 tff(12589,plain,
% 1.49/1.68 (node15(s98) | node16(s98) | node17(s98, s99)),
% 1.49/1.68 inference(unit_resolution,[status(thm)],[12588, 139, 12585])).
% 1.49/1.68 tff(12590,plain,
% 1.49/1.68 (node17(s98, s99)),
% 1.49/1.68 inference(unit_resolution,[status(thm)],[12589, 12581, 12577])).
% 1.49/1.68 tff(12591,plain,
% 1.49/1.68 (((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))) | (m_main_v_turn(s98, c_2) | (~node17(s98, s99)) | (~m_main_v_turn(s99, 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(s98, c_2) | (~node17(s98, s99)) | (~m_main_v_turn(s99, c_2)))),
% 1.49/1.68 inference(rewrite,[status(thm)],[])).
% 1.49/1.68 tff(12592,plain,
% 1.49/1.68 (((~node17(s98, s99)) | m_main_v_turn(s98, c_2) | (~m_main_v_turn(s99, c_2))) <=> (m_main_v_turn(s98, c_2) | (~node17(s98, s99)) | (~m_main_v_turn(s99, c_2)))),
% 1.49/1.68 inference(rewrite,[status(thm)],[])).
% 1.49/1.68 tff(12593,plain,
% 1.49/1.68 (((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))) | ((~node17(s98, s99)) | m_main_v_turn(s98, c_2) | (~m_main_v_turn(s99, 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(s98, c_2) | (~node17(s98, s99)) | (~m_main_v_turn(s99, c_2))))),
% 1.49/1.68 inference(monotonicity,[status(thm)],[12592])).
% 1.49/1.68 tff(12594,plain,
% 1.49/1.68 (((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))) | ((~node17(s98, s99)) | m_main_v_turn(s98, c_2) | (~m_main_v_turn(s99, 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(s98, c_2) | (~node17(s98, s99)) | (~m_main_v_turn(s99, c_2)))),
% 1.49/1.68 inference(transitivity,[status(thm)],[12593, 12591])).
% 1.49/1.68 tff(12595,plain,
% 1.49/1.68 ((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))) | ((~node17(s98, s99)) | m_main_v_turn(s98, c_2) | (~m_main_v_turn(s99, c_2)))),
% 1.49/1.68 inference(quant_inst,[status(thm)],[])).
% 1.49/1.68 tff(12596,plain,
% 1.49/1.68 ((~![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))) | m_main_v_turn(s98, c_2) | (~node17(s98, s99)) | (~m_main_v_turn(s99, c_2))),
% 1.49/1.68 inference(modus_ponens,[status(thm)],[12595, 12594])).
% 1.49/1.68 tff(12597,plain,
% 1.49/1.68 (~m_main_v_turn(s99, c_2)),
% 1.49/1.68 inference(unit_resolution,[status(thm)],[12596, 170, 12537, 12590])).
% 1.49/1.68 tff(12598,plain,
% 1.49/1.68 (((~![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, s99)) | m_main_v_turn(s99, 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, s99)) | m_main_v_turn(s99, c_2))),
% 1.49/1.68 inference(rewrite,[status(thm)],[])).
% 1.49/1.68 tff(12599,plain,
% 1.49/1.68 ((~![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, s99)) | m_main_v_turn(s99, c_2))),
% 1.49/1.68 inference(quant_inst,[status(thm)],[])).
% 1.49/1.68 tff(12600,plain,
% 1.49/1.68 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s99, c_n1)) | (~m_main_v_state2(s99, c_t2)) | (~node18(s99, s99)) | m_main_v_turn(s99, c_2)),
% 1.49/1.68 inference(modus_ponens,[status(thm)],[12599, 12598])).
% 1.49/1.68 tff(12601,plain,
% 1.49/1.68 ($false),
% 1.49/1.68 inference(unit_resolution,[status(thm)],[12600, 760, 12597, 12573, 12517, 12375])).
% 1.49/1.68 tff(12602,plain,(~node18(s99, s99)), inference(lemma,lemma(discharge,[]))).
% 1.49/1.68 tff(12603,plain,
% 1.49/1.68 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s99, s99)) | node18(s99, s99))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s99, s99)) | node18(s99, s99))),
% 1.49/1.68 inference(rewrite,[status(thm)],[])).
% 1.49/1.68 tff(12604,plain,
% 1.49/1.68 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s99, s99)) | node18(s99, s99))),
% 1.49/1.68 inference(quant_inst,[status(thm)],[])).
% 1.49/1.68 tff(12605,plain,
% 1.49/1.68 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s99, s99)) | node18(s99, s99)),
% 1.49/1.68 inference(modus_ponens,[status(thm)],[12604, 12603])).
% 1.49/1.68 tff(12606,plain,
% 1.49/1.68 (~trans(s99, s99)),
% 1.49/1.68 inference(unit_resolution,[status(thm)],[12605, 125, 12602])).
% 1.49/1.68 tff(12607,assumption,(node14(s99, s97)), introduced(assumption)).
% 1.49/1.68 tff(12608,plain,
% 1.49/1.68 (((~![V: $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) | (~node13(s98, s99)) | (~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) | (~node13(s98, s99)) | (~m_main_v_state2(s99, c_n2)))),
% 1.49/1.68 inference(rewrite,[status(thm)],[])).
% 1.49/1.68 tff(12609,plain,
% 1.49/1.68 (((~node13(s98, s99)) | m_main_v_state2(s98, c_n2) | (~m_main_v_state2(s99, c_n2))) <=> (m_main_v_state2(s98, c_n2) | (~node13(s98, s99)) | (~m_main_v_state2(s99, c_n2)))),
% 1.49/1.68 inference(rewrite,[status(thm)],[])).
% 1.49/1.68 tff(12610,plain,
% 1.49/1.68 (((~![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) | (~node13(s98, s99)) | (~m_main_v_state2(s99, c_n2))))),
% 1.49/1.68 inference(monotonicity,[status(thm)],[12609])).
% 1.49/1.68 tff(12611,plain,
% 1.49/1.68 (((~![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) | (~node13(s98, s99)) | (~m_main_v_state2(s99, c_n2)))),
% 1.52/1.68 inference(transitivity,[status(thm)],[12610, 12608])).
% 1.52/1.68 tff(12612,plain,
% 1.52/1.68 ((~![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)))),
% 1.52/1.68 inference(quant_inst,[status(thm)],[])).
% 1.52/1.68 tff(12613,plain,
% 1.52/1.68 ((~![V: $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) | (~node13(s98, s99)) | (~m_main_v_state2(s99, c_n2))),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[12612, 12611])).
% 1.52/1.68 tff(12614,plain,
% 1.52/1.68 (~m_main_v_state2(s99, c_n2)),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[12613, 311, 12484, 12566])).
% 1.52/1.68 tff(12615,plain,
% 1.52/1.68 (((~![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)))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(12616,plain,
% 1.52/1.68 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s99, c_n2) | (~node8(s99)))),
% 1.52/1.68 inference(quant_inst,[status(thm)],[])).
% 1.52/1.68 tff(12617,plain,
% 1.52/1.68 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s99, c_n2) | (~node8(s99))),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[12616, 12615])).
% 1.52/1.68 tff(12618,plain,
% 1.52/1.68 (~node8(s99)),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[12617, 271, 12614])).
% 1.52/1.68 tff(12619,plain,
% 1.52/1.68 (((~![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)))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(12620,plain,
% 1.52/1.68 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s99, c_n2) | (~node9(s99)))),
% 1.52/1.68 inference(quant_inst,[status(thm)],[])).
% 1.52/1.68 tff(12621,plain,
% 1.52/1.68 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s99, c_n2) | (~node9(s99))),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[12620, 12619])).
% 1.52/1.68 tff(12622,plain,
% 1.52/1.68 (~node9(s99)),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[12621, 88, 12614])).
% 1.52/1.68 tff(12623,plain,
% 1.52/1.68 (((~![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)))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(12624,plain,
% 1.52/1.68 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s99, c_n2) | (~node10(s99)))),
% 1.52/1.68 inference(quant_inst,[status(thm)],[])).
% 1.52/1.68 tff(12625,plain,
% 1.52/1.68 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s99, c_n2) | (~node10(s99))),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[12624, 12623])).
% 1.52/1.68 tff(12626,plain,
% 1.52/1.68 (~node10(s99)),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[12625, 249, 12614])).
% 1.52/1.68 tff(12627,plain,
% 1.52/1.68 (((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (m_main_v_state2(s97, c_c2) | (~m_main_v_state1(s99, c_n1)) | node10(s99) | node9(s99) | node8(s99) | (~m_main_v_state2(s99, c_t2)) | (~node14(s99, s97)))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | m_main_v_state2(s97, c_c2) | (~m_main_v_state1(s99, c_n1)) | node10(s99) | node9(s99) | node8(s99) | (~m_main_v_state2(s99, c_t2)) | (~node14(s99, s97)))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(12628,plain,
% 1.52/1.68 (((~m_main_v_state1(s99, c_n1)) | (~m_main_v_state2(s99, c_t2)) | node9(s99) | node8(s99) | node10(s99) | (~node14(s99, s97)) | m_main_v_state2(s97, c_c2)) <=> (m_main_v_state2(s97, c_c2) | (~m_main_v_state1(s99, c_n1)) | node10(s99) | node9(s99) | node8(s99) | (~m_main_v_state2(s99, c_t2)) | (~node14(s99, s97)))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(12629,plain,
% 1.52/1.68 (((~![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, s97)) | m_main_v_state2(s97, c_c2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | (m_main_v_state2(s97, c_c2) | (~m_main_v_state1(s99, c_n1)) | node10(s99) | node9(s99) | node8(s99) | (~m_main_v_state2(s99, c_t2)) | (~node14(s99, s97))))),
% 1.52/1.68 inference(monotonicity,[status(thm)],[12628])).
% 1.52/1.68 tff(12630,plain,
% 1.52/1.68 (((~![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, s97)) | m_main_v_state2(s97, c_c2))) <=> ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | m_main_v_state2(s97, c_c2) | (~m_main_v_state1(s99, c_n1)) | node10(s99) | node9(s99) | node8(s99) | (~m_main_v_state2(s99, c_t2)) | (~node14(s99, s97)))),
% 1.52/1.68 inference(transitivity,[status(thm)],[12629, 12627])).
% 1.52/1.68 tff(12631,plain,
% 1.52/1.68 ((~![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, s97)) | m_main_v_state2(s97, c_c2))),
% 1.52/1.68 inference(quant_inst,[status(thm)],[])).
% 1.52/1.68 tff(12632,plain,
% 1.52/1.68 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | node9(X) | node8(X) | node10(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_c2))) | m_main_v_state2(s97, c_c2) | (~m_main_v_state1(s99, c_n1)) | node10(s99) | node9(s99) | node8(s99) | (~m_main_v_state2(s99, c_t2)) | (~node14(s99, s97))),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[12631, 12630])).
% 1.52/1.68 tff(12633,plain,
% 1.52/1.68 ($false),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[12632, 617, 12379, 12573, 12517, 12626, 12622, 12618, 12607])).
% 1.52/1.68 tff(12634,plain,(~node14(s99, s97)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.68 tff(12635,plain,
% 1.52/1.68 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s99, s97)) | node14(s99, s97))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s99, s97)) | node14(s99, s97))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(12636,plain,
% 1.52/1.68 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s99, s97)) | node14(s99, s97))),
% 1.52/1.68 inference(quant_inst,[status(thm)],[])).
% 1.52/1.68 tff(12637,plain,
% 1.52/1.68 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s99, s97)) | node14(s99, s97)),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[12636, 12635])).
% 1.52/1.68 tff(12638,plain,
% 1.52/1.68 (~trans(s99, s97)),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[12637, 46, 12634])).
% 1.52/1.68 tff(12639,assumption,(node18(s99, s98)), introduced(assumption)).
% 1.52/1.68 tff(12640,plain,
% 1.52/1.68 (((~![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, s98)) | m_main_v_turn(s98, 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, s98)) | m_main_v_turn(s98, c_2))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(12641,plain,
% 1.52/1.68 ((~![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, s98)) | m_main_v_turn(s98, c_2))),
% 1.52/1.68 inference(quant_inst,[status(thm)],[])).
% 1.52/1.68 tff(12642,plain,
% 1.52/1.68 ((~![Y: $i, X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state2(X, c_t2)) | (~node18(X, Y)) | m_main_v_turn(Y, c_2))) | (~m_main_v_state1(s99, c_n1)) | (~m_main_v_state2(s99, c_t2)) | (~node18(s99, s98)) | m_main_v_turn(s98, c_2)),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[12641, 12640])).
% 1.52/1.68 tff(12643,plain,
% 1.52/1.68 ($false),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[12642, 760, 12537, 12573, 12517, 12639])).
% 1.52/1.68 tff(12644,plain,(~node18(s99, s98)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.68 tff(12645,plain,
% 1.52/1.68 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s99, s98)) | node18(s99, s98))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s99, s98)) | node18(s99, s98))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(12646,plain,
% 1.52/1.68 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s99, s98)) | node18(s99, s98))),
% 1.52/1.68 inference(quant_inst,[status(thm)],[])).
% 1.52/1.68 tff(12647,plain,
% 1.52/1.68 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s99, s98)) | node18(s99, s98)),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[12646, 12645])).
% 1.52/1.69 tff(12648,plain,
% 1.52/1.69 (~trans(s99, s98)),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[12647, 125, 12644])).
% 1.52/1.69 tff(12649,assumption,(~loop), introduced(assumption)).
% 1.52/1.69 tff(12650,plain,
% 1.52/1.69 (^[X: $i] : refl((loop | (~always25(X)) | (~last(X))) <=> (loop | (~always25(X)) | (~last(X))))),
% 1.52/1.69 inference(bind,[status(th)],[])).
% 1.52/1.69 tff(12651,plain,
% 1.52/1.69 (![X: $i] : (loop | (~always25(X)) | (~last(X))) <=> ![X: $i] : (loop | (~always25(X)) | (~last(X)))),
% 1.52/1.69 inference(quant_intro,[status(thm)],[12650])).
% 1.52/1.69 tff(12652,plain,
% 1.52/1.69 (![X: $i] : (loop | (~always25(X)) | (~last(X))) <=> ![X: $i] : (loop | (~always25(X)) | (~last(X)))),
% 1.52/1.69 inference(rewrite,[status(thm)],[])).
% 1.52/1.69 tff(12653,plain,
% 1.52/1.69 (^[X: $i] : rewrite(((loop | (~always25(X))) | (~last(X))) <=> (loop | (~always25(X)) | (~last(X))))),
% 1.52/1.69 inference(bind,[status(th)],[])).
% 1.52/1.69 tff(12654,plain,
% 1.52/1.69 (![X: $i] : ((loop | (~always25(X))) | (~last(X))) <=> ![X: $i] : (loop | (~always25(X)) | (~last(X)))),
% 1.52/1.69 inference(quant_intro,[status(thm)],[12653])).
% 1.52/1.69 tff(12655,axiom,(![X: $i] : ((loop | (~always25(X))) | (~last(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty16')).
% 1.52/1.69 tff(12656,plain,
% 1.52/1.69 (![X: $i] : (loop | (~always25(X)) | (~last(X)))),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[12655, 12654])).
% 1.52/1.69 tff(12657,plain,
% 1.52/1.69 (![X: $i] : (loop | (~always25(X)) | (~last(X)))),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[12656, 12652])).
% 1.52/1.69 tff(12658,plain,(
% 1.52/1.69 ![X: $i] : (loop | (~always25(X)) | (~last(X)))),
% 1.52/1.69 inference(skolemize,[status(sab)],[12657])).
% 1.52/1.69 tff(12659,plain,
% 1.52/1.69 (![X: $i] : (loop | (~always25(X)) | (~last(X)))),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[12658, 12651])).
% 1.52/1.69 tff(12660,plain,
% 1.52/1.69 (((~![X: $i] : (loop | (~always25(X)) | (~last(X)))) | (loop | (~always25(s99)) | (~last(s99)))) <=> ((~![X: $i] : (loop | (~always25(X)) | (~last(X)))) | loop | (~always25(s99)) | (~last(s99)))),
% 1.52/1.69 inference(rewrite,[status(thm)],[])).
% 1.52/1.69 tff(12661,plain,
% 1.52/1.69 ((~![X: $i] : (loop | (~always25(X)) | (~last(X)))) | (loop | (~always25(s99)) | (~last(s99)))),
% 1.52/1.69 inference(quant_inst,[status(thm)],[])).
% 1.52/1.69 tff(12662,plain,
% 1.52/1.69 ((~![X: $i] : (loop | (~always25(X)) | (~last(X)))) | loop | (~always25(s99)) | (~last(s99))),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[12661, 12660])).
% 1.52/1.69 tff(12663,plain,
% 1.52/1.69 (loop | (~always25(s99))),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[12662, 10200, 12659])).
% 1.52/1.69 tff(12664,plain,
% 1.52/1.69 (~always25(s99)),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[12663, 12649])).
% 1.52/1.69 tff(12665,plain,
% 1.52/1.69 (~node26(s99)),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[10183, 3949, 12664])).
% 1.52/1.69 tff(12666,plain,
% 1.52/1.69 (^[X: $i] : refl((loop | (~last(X)) | (~xuntil28(X))) <=> (loop | (~last(X)) | (~xuntil28(X))))),
% 1.52/1.69 inference(bind,[status(th)],[])).
% 1.52/1.69 tff(12667,plain,
% 1.52/1.69 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 1.52/1.69 inference(quant_intro,[status(thm)],[12666])).
% 1.52/1.69 tff(12668,plain,
% 1.52/1.69 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 1.52/1.69 inference(rewrite,[status(thm)],[])).
% 1.52/1.69 tff(12669,plain,
% 1.52/1.69 (^[X: $i] : rewrite(((loop | (~last(X))) | (~xuntil28(X))) <=> (loop | (~last(X)) | (~xuntil28(X))))),
% 1.52/1.69 inference(bind,[status(th)],[])).
% 1.52/1.69 tff(12670,plain,
% 1.52/1.69 (![X: $i] : ((loop | (~last(X))) | (~xuntil28(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 1.52/1.69 inference(quant_intro,[status(thm)],[12669])).
% 1.52/1.69 tff(12671,axiom,(![X: $i] : ((loop | (~last(X))) | (~xuntil28(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty21')).
% 1.52/1.69 tff(12672,plain,
% 1.52/1.69 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[12671, 12670])).
% 1.52/1.69 tff(12673,plain,
% 1.52/1.69 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[12672, 12668])).
% 1.52/1.69 tff(12674,plain,(
% 1.52/1.69 ![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 1.52/1.69 inference(skolemize,[status(sab)],[12673])).
% 1.52/1.69 tff(12675,plain,
% 1.52/1.69 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[12674, 12667])).
% 1.52/1.69 tff(12676,plain,
% 1.52/1.69 (((~![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))) | (loop | (~last(s99)) | (~xuntil28(s99)))) <=> ((~![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))) | loop | (~last(s99)) | (~xuntil28(s99)))),
% 1.52/1.69 inference(rewrite,[status(thm)],[])).
% 1.52/1.69 tff(12677,plain,
% 1.52/1.69 ((~![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))) | (loop | (~last(s99)) | (~xuntil28(s99)))),
% 1.52/1.69 inference(quant_inst,[status(thm)],[])).
% 1.52/1.69 tff(12678,plain,
% 1.52/1.69 ((~![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))) | loop | (~last(s99)) | (~xuntil28(s99))),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[12677, 12676])).
% 1.52/1.69 tff(12679,plain,
% 1.52/1.69 (loop | (~xuntil28(s99))),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[12678, 10200, 12675])).
% 1.52/1.69 tff(12680,plain,
% 1.52/1.69 (~xuntil28(s99)),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[12679, 12649])).
% 1.52/1.69 tff(12681,plain,
% 1.52/1.69 (~until27(s99)),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[10179, 8821, 12680, 12665])).
% 1.52/1.69 tff(12682,plain,
% 1.52/1.69 (~always25(s98)),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[3941, 12664])).
% 1.52/1.69 tff(12683,plain,
% 1.52/1.69 (~node26(s98)),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[3952, 3949, 12682])).
% 1.52/1.69 tff(12684,plain,
% 1.52/1.69 (xuntil28(s98)),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[10167, 12683])).
% 1.52/1.69 tff(12685,plain,
% 1.52/1.69 ($false),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[10172, 12684, 12681])).
% 1.52/1.69 tff(12686,plain,(loop), inference(lemma,lemma(discharge,[]))).
% 1.52/1.69 tff(12687,plain,
% 1.52/1.69 (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99))),
% 1.52/1.69 inference(rewrite,[status(thm)],[])).
% 1.52/1.69 tff(12688,plain,
% 1.52/1.69 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98)) | trans(s99, s99)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99))),
% 1.52/1.69 inference(rewrite,[status(thm)],[])).
% 1.52/1.69 tff(12689,plain,
% 1.52/1.69 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97)) | trans(s99, s98)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98))),
% 1.52/1.70 inference(rewrite,[status(thm)],[])).
% 1.52/1.70 tff(12690,plain,
% 1.52/1.70 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96)) | trans(s99, s97)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97))),
% 1.52/1.70 inference(rewrite,[status(thm)],[])).
% 1.52/1.70 tff(12691,plain,
% 1.52/1.70 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95)) | trans(s99, s96)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96))),
% 1.52/1.70 inference(rewrite,[status(thm)],[])).
% 1.52/1.70 tff(12692,plain,
% 1.52/1.70 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94)) | trans(s99, s95)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95))),
% 1.52/1.70 inference(rewrite,[status(thm)],[])).
% 1.52/1.70 tff(12693,plain,
% 1.52/1.70 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93)) | trans(s99, s94)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(12694,plain,
% 1.52/1.71 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92)) | trans(s99, s93)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(12695,plain,
% 1.52/1.71 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91)) | trans(s99, s92)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(12696,plain,
% 1.52/1.71 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90)) | trans(s99, s91)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(12697,plain,
% 1.52/1.72 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89)) | trans(s99, s90)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(12698,plain,
% 1.52/1.72 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88)) | trans(s99, s89)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(12699,plain,
% 1.52/1.72 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87)) | trans(s99, s88)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(12700,plain,
% 1.52/1.72 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86)) | trans(s99, s87)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87))),
% 1.52/1.73 inference(rewrite,[status(thm)],[])).
% 1.52/1.73 tff(12701,plain,
% 1.52/1.73 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85)) | trans(s99, s86)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86))),
% 1.52/1.73 inference(rewrite,[status(thm)],[])).
% 1.52/1.73 tff(12702,plain,
% 1.52/1.73 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84)) | trans(s99, s85)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85))),
% 1.52/1.73 inference(rewrite,[status(thm)],[])).
% 1.52/1.73 tff(12703,plain,
% 1.52/1.73 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83)) | trans(s99, s84)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84))),
% 1.52/1.73 inference(rewrite,[status(thm)],[])).
% 1.52/1.73 tff(12704,plain,
% 1.52/1.73 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82)) | trans(s99, s83)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(12705,plain,
% 1.52/1.74 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81)) | trans(s99, s82)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(12706,plain,
% 1.52/1.74 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80)) | trans(s99, s81)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(12707,plain,
% 1.52/1.74 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79)) | trans(s99, s80)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(12708,plain,
% 1.52/1.74 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78)) | trans(s99, s79)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(12709,plain,
% 1.52/1.74 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77)) | trans(s99, s78)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78))),
% 1.58/1.75 inference(rewrite,[status(thm)],[])).
% 1.58/1.75 tff(12710,plain,
% 1.58/1.75 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76)) | trans(s99, s77)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77))),
% 1.58/1.75 inference(rewrite,[status(thm)],[])).
% 1.58/1.75 tff(12711,plain,
% 1.58/1.75 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75)) | trans(s99, s76)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76))),
% 1.58/1.75 inference(rewrite,[status(thm)],[])).
% 1.58/1.75 tff(12712,plain,
% 1.58/1.75 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74)) | trans(s99, s75)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75))),
% 1.58/1.75 inference(rewrite,[status(thm)],[])).
% 1.58/1.75 tff(12713,plain,
% 1.58/1.75 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73)) | trans(s99, s74)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74))),
% 1.58/1.75 inference(rewrite,[status(thm)],[])).
% 1.58/1.75 tff(12714,plain,
% 1.58/1.75 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72)) | trans(s99, s73)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73))),
% 1.58/1.76 inference(rewrite,[status(thm)],[])).
% 1.58/1.76 tff(12715,plain,
% 1.58/1.76 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71)) | trans(s99, s72)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72))),
% 1.58/1.76 inference(rewrite,[status(thm)],[])).
% 1.58/1.76 tff(12716,plain,
% 1.58/1.76 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70)) | trans(s99, s71)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71))),
% 1.58/1.76 inference(rewrite,[status(thm)],[])).
% 1.58/1.76 tff(12717,plain,
% 1.58/1.76 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69)) | trans(s99, s70)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70))),
% 1.60/1.76 inference(rewrite,[status(thm)],[])).
% 1.60/1.76 tff(12718,plain,
% 1.60/1.76 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68)) | trans(s99, s69)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69))),
% 1.60/1.77 inference(rewrite,[status(thm)],[])).
% 1.60/1.77 tff(12719,plain,
% 1.60/1.77 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67)) | trans(s99, s68)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68))),
% 1.60/1.77 inference(rewrite,[status(thm)],[])).
% 1.60/1.77 tff(12720,plain,
% 1.60/1.77 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66)) | trans(s99, s67)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67))),
% 1.60/1.77 inference(rewrite,[status(thm)],[])).
% 1.60/1.77 tff(12721,plain,
% 1.60/1.77 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65)) | trans(s99, s66)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66))),
% 1.60/1.77 inference(rewrite,[status(thm)],[])).
% 1.60/1.77 tff(12722,plain,
% 1.60/1.77 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64)) | trans(s99, s65)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65))),
% 1.60/1.77 inference(rewrite,[status(thm)],[])).
% 1.60/1.77 tff(12723,plain,
% 1.60/1.77 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63)) | trans(s99, s64)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64))),
% 1.60/1.78 inference(rewrite,[status(thm)],[])).
% 1.60/1.78 tff(12724,plain,
% 1.60/1.78 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62)) | trans(s99, s63)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63))),
% 1.60/1.78 inference(rewrite,[status(thm)],[])).
% 1.60/1.78 tff(12725,plain,
% 1.60/1.78 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61)) | trans(s99, s62)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62))),
% 1.60/1.78 inference(rewrite,[status(thm)],[])).
% 1.60/1.78 tff(12726,plain,
% 1.60/1.78 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60)) | trans(s99, s61)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61))),
% 1.60/1.78 inference(rewrite,[status(thm)],[])).
% 1.60/1.78 tff(12727,plain,
% 1.60/1.78 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59)) | trans(s99, s60)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60))),
% 1.60/1.78 inference(rewrite,[status(thm)],[])).
% 1.60/1.78 tff(12728,plain,
% 1.60/1.78 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58)) | trans(s99, s59)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59))),
% 1.60/1.79 inference(rewrite,[status(thm)],[])).
% 1.60/1.79 tff(12729,plain,
% 1.60/1.79 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57)) | trans(s99, s58)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58))),
% 1.60/1.79 inference(rewrite,[status(thm)],[])).
% 1.60/1.79 tff(12730,plain,
% 1.60/1.79 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56)) | trans(s99, s57)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57))),
% 1.60/1.79 inference(rewrite,[status(thm)],[])).
% 1.60/1.79 tff(12731,plain,
% 1.60/1.79 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55)) | trans(s99, s56)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56))),
% 1.60/1.79 inference(rewrite,[status(thm)],[])).
% 1.60/1.79 tff(12732,plain,
% 1.60/1.79 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54)) | trans(s99, s55)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55))),
% 1.60/1.79 inference(rewrite,[status(thm)],[])).
% 1.60/1.79 tff(12733,plain,
% 1.60/1.79 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53)) | trans(s99, s54)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54))),
% 1.60/1.79 inference(rewrite,[status(thm)],[])).
% 1.60/1.79 tff(12734,plain,
% 1.60/1.79 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52)) | trans(s99, s53)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53))),
% 1.60/1.80 inference(rewrite,[status(thm)],[])).
% 1.60/1.80 tff(12735,plain,
% 1.60/1.80 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51)) | trans(s99, s52)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52))),
% 1.60/1.80 inference(rewrite,[status(thm)],[])).
% 1.60/1.80 tff(12736,plain,
% 1.60/1.80 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50)) | trans(s99, s51)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51))),
% 1.60/1.80 inference(rewrite,[status(thm)],[])).
% 1.60/1.80 tff(12737,plain,
% 1.60/1.80 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49)) | trans(s99, s50)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50))),
% 1.60/1.80 inference(rewrite,[status(thm)],[])).
% 1.60/1.80 tff(12738,plain,
% 1.60/1.80 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48)) | trans(s99, s49)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49))),
% 1.60/1.80 inference(rewrite,[status(thm)],[])).
% 1.60/1.80 tff(12739,plain,
% 1.60/1.80 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47)) | trans(s99, s48)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48))),
% 1.60/1.80 inference(rewrite,[status(thm)],[])).
% 1.60/1.80 tff(12740,plain,
% 1.60/1.80 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46)) | trans(s99, s47)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47))),
% 1.60/1.80 inference(rewrite,[status(thm)],[])).
% 1.60/1.80 tff(12741,plain,
% 1.60/1.80 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45)) | trans(s99, s46)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46))),
% 1.60/1.81 inference(rewrite,[status(thm)],[])).
% 1.60/1.81 tff(12742,plain,
% 1.60/1.81 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44)) | trans(s99, s45)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45))),
% 1.60/1.81 inference(rewrite,[status(thm)],[])).
% 1.60/1.81 tff(12743,plain,
% 1.60/1.81 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43)) | trans(s99, s44)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44))),
% 1.60/1.81 inference(rewrite,[status(thm)],[])).
% 1.60/1.81 tff(12744,plain,
% 1.60/1.81 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42)) | trans(s99, s43)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43))),
% 1.60/1.81 inference(rewrite,[status(thm)],[])).
% 1.60/1.81 tff(12745,plain,
% 1.60/1.81 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41)) | trans(s99, s42)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42))),
% 1.60/1.81 inference(rewrite,[status(thm)],[])).
% 1.60/1.81 tff(12746,plain,
% 1.60/1.81 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40)) | trans(s99, s41)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(12747,plain,
% 1.65/1.81 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39)) | trans(s99, s40)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(12748,plain,
% 1.65/1.81 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38)) | trans(s99, s39)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(12749,plain,
% 1.65/1.81 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37)) | trans(s99, s38)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(12750,plain,
% 1.65/1.81 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36)) | trans(s99, s37)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(12751,plain,
% 1.65/1.82 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35)) | trans(s99, s36)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(12752,plain,
% 1.65/1.82 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34)) | trans(s99, s35)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(12753,plain,
% 1.65/1.82 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33)) | trans(s99, s34)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(12754,plain,
% 1.65/1.82 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32)) | trans(s99, s33)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(12755,plain,
% 1.65/1.82 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31)) | trans(s99, s32)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(12756,plain,
% 1.65/1.82 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30)) | trans(s99, s31)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(12757,plain,
% 1.65/1.82 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29)) | trans(s99, s30)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(12758,plain,
% 1.65/1.82 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28)) | trans(s99, s29)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(12759,plain,
% 1.65/1.82 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27)) | trans(s99, s28)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(12760,plain,
% 1.65/1.82 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26)) | trans(s99, s27)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(12761,plain,
% 1.65/1.82 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25)) | trans(s99, s26)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(12762,plain,
% 1.65/1.83 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24)) | trans(s99, s25)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(12763,plain,
% 1.65/1.83 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23)) | trans(s99, s24)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(12764,plain,
% 1.65/1.83 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22)) | trans(s99, s23)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(12765,plain,
% 1.65/1.83 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21)) | trans(s99, s22)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(12766,plain,
% 1.65/1.83 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20)) | trans(s99, s21)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(12767,plain,
% 1.65/1.83 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19)) | trans(s99, s20)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(12768,plain,
% 1.65/1.83 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18)) | trans(s99, s19)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(12769,plain,
% 1.65/1.83 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17)) | trans(s99, s18)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(12770,plain,
% 1.65/1.83 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16)) | trans(s99, s17)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(12771,plain,
% 1.65/1.83 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15)) | trans(s99, s16)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(12772,plain,
% 1.65/1.83 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14)) | trans(s99, s15)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(12773,plain,
% 1.65/1.83 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13)) | trans(s99, s14)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(12774,plain,
% 1.65/1.83 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12)) | trans(s99, s13)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(12775,plain,
% 1.65/1.83 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11)) | trans(s99, s12)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(12776,plain,
% 1.65/1.83 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10)) | trans(s99, s11)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(12777,plain,
% 1.65/1.83 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9)) | trans(s99, s10)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(12778,plain,
% 1.65/1.83 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8)) | trans(s99, s9)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(12779,plain,
% 1.65/1.84 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7)) | trans(s99, s8)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(12780,plain,
% 1.65/1.84 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6)) | trans(s99, s7)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(12781,plain,
% 1.65/1.84 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5)) | trans(s99, s6)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(12782,plain,
% 1.65/1.84 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4)) | trans(s99, s5)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(12783,plain,
% 1.65/1.84 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3)) | trans(s99, s4)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(12784,plain,
% 1.65/1.84 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2)) | trans(s99, s3)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(12785,plain,
% 1.65/1.84 ((((~loop) | trans(s99, s0) | trans(s99, s1)) | trans(s99, s2)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(12786,plain,
% 1.65/1.84 ((((~loop) | trans(s99, s0)) | trans(s99, s1)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(12787,plain,
% 1.65/1.84 (((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1)) | trans(s99, s2))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[12786])).
% 1.65/1.84 tff(12788,plain,
% 1.65/1.84 (((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2))),
% 1.65/1.84 inference(transitivity,[status(thm)],[12787, 12785])).
% 1.65/1.84 tff(12789,plain,
% 1.65/1.84 ((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2)) | trans(s99, s3))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[12788])).
% 1.65/1.84 tff(12790,plain,
% 1.65/1.84 ((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3))),
% 1.65/1.84 inference(transitivity,[status(thm)],[12789, 12784])).
% 1.65/1.84 tff(12791,plain,
% 1.65/1.84 (((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3)) | trans(s99, s4))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[12790])).
% 1.65/1.84 tff(12792,plain,
% 1.65/1.84 (((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4))),
% 1.65/1.84 inference(transitivity,[status(thm)],[12791, 12783])).
% 1.65/1.84 tff(12793,plain,
% 1.65/1.84 ((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4)) | trans(s99, s5))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[12792])).
% 1.65/1.84 tff(12794,plain,
% 1.65/1.84 ((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5))),
% 1.65/1.84 inference(transitivity,[status(thm)],[12793, 12782])).
% 1.65/1.84 tff(12795,plain,
% 1.65/1.84 (((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5)) | trans(s99, s6))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[12794])).
% 1.65/1.84 tff(12796,plain,
% 1.65/1.84 (((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6))),
% 1.65/1.84 inference(transitivity,[status(thm)],[12795, 12781])).
% 1.65/1.84 tff(12797,plain,
% 1.65/1.84 ((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6)) | trans(s99, s7))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[12796])).
% 1.65/1.84 tff(12798,plain,
% 1.65/1.84 ((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7))),
% 1.65/1.84 inference(transitivity,[status(thm)],[12797, 12780])).
% 1.65/1.84 tff(12799,plain,
% 1.65/1.84 (((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7)) | trans(s99, s8))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[12798])).
% 1.65/1.84 tff(12800,plain,
% 1.65/1.84 (((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8))),
% 1.65/1.84 inference(transitivity,[status(thm)],[12799, 12779])).
% 1.65/1.84 tff(12801,plain,
% 1.65/1.84 ((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8)) | trans(s99, s9))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[12800])).
% 1.65/1.84 tff(12802,plain,
% 1.65/1.84 ((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9))),
% 1.65/1.84 inference(transitivity,[status(thm)],[12801, 12778])).
% 1.65/1.84 tff(12803,plain,
% 1.65/1.84 (((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9)) | trans(s99, s10))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[12802])).
% 1.65/1.84 tff(12804,plain,
% 1.65/1.84 (((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10))),
% 1.65/1.84 inference(transitivity,[status(thm)],[12803, 12777])).
% 1.65/1.84 tff(12805,plain,
% 1.65/1.84 ((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10)) | trans(s99, s11))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[12804])).
% 1.65/1.84 tff(12806,plain,
% 1.65/1.84 ((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11))),
% 1.65/1.84 inference(transitivity,[status(thm)],[12805, 12776])).
% 1.65/1.84 tff(12807,plain,
% 1.65/1.84 (((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11)) | trans(s99, s12))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[12806])).
% 1.65/1.84 tff(12808,plain,
% 1.65/1.84 (((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12))),
% 1.65/1.84 inference(transitivity,[status(thm)],[12807, 12775])).
% 1.65/1.84 tff(12809,plain,
% 1.65/1.84 ((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12)) | trans(s99, s13))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[12808])).
% 1.65/1.84 tff(12810,plain,
% 1.65/1.84 ((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13))),
% 1.68/1.84 inference(transitivity,[status(thm)],[12809, 12774])).
% 1.68/1.84 tff(12811,plain,
% 1.68/1.84 (((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13)) | trans(s99, s14))),
% 1.68/1.84 inference(monotonicity,[status(thm)],[12810])).
% 1.68/1.84 tff(12812,plain,
% 1.68/1.84 (((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14))),
% 1.68/1.84 inference(transitivity,[status(thm)],[12811, 12773])).
% 1.68/1.84 tff(12813,plain,
% 1.68/1.84 ((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14)) | trans(s99, s15))),
% 1.68/1.84 inference(monotonicity,[status(thm)],[12812])).
% 1.68/1.84 tff(12814,plain,
% 1.68/1.84 ((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15))),
% 1.68/1.84 inference(transitivity,[status(thm)],[12813, 12772])).
% 1.68/1.84 tff(12815,plain,
% 1.68/1.84 (((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15)) | trans(s99, s16))),
% 1.68/1.84 inference(monotonicity,[status(thm)],[12814])).
% 1.68/1.84 tff(12816,plain,
% 1.68/1.84 (((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16))),
% 1.68/1.85 inference(transitivity,[status(thm)],[12815, 12771])).
% 1.68/1.85 tff(12817,plain,
% 1.68/1.85 ((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16)) | trans(s99, s17))),
% 1.68/1.85 inference(monotonicity,[status(thm)],[12816])).
% 1.68/1.85 tff(12818,plain,
% 1.68/1.85 ((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17))),
% 1.68/1.85 inference(transitivity,[status(thm)],[12817, 12770])).
% 1.68/1.85 tff(12819,plain,
% 1.68/1.85 (((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17)) | trans(s99, s18))),
% 1.68/1.85 inference(monotonicity,[status(thm)],[12818])).
% 1.68/1.85 tff(12820,plain,
% 1.68/1.85 (((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18))),
% 1.68/1.85 inference(transitivity,[status(thm)],[12819, 12769])).
% 1.68/1.85 tff(12821,plain,
% 1.68/1.85 ((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18)) | trans(s99, s19))),
% 1.68/1.85 inference(monotonicity,[status(thm)],[12820])).
% 1.68/1.85 tff(12822,plain,
% 1.68/1.85 ((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19))),
% 1.68/1.85 inference(transitivity,[status(thm)],[12821, 12768])).
% 1.68/1.85 tff(12823,plain,
% 1.68/1.85 (((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19)) | trans(s99, s20))),
% 1.68/1.85 inference(monotonicity,[status(thm)],[12822])).
% 1.68/1.85 tff(12824,plain,
% 1.68/1.85 (((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20))),
% 1.68/1.85 inference(transitivity,[status(thm)],[12823, 12767])).
% 1.68/1.85 tff(12825,plain,
% 1.68/1.85 ((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20)) | trans(s99, s21))),
% 1.68/1.85 inference(monotonicity,[status(thm)],[12824])).
% 1.68/1.85 tff(12826,plain,
% 1.68/1.85 ((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21))),
% 1.68/1.85 inference(transitivity,[status(thm)],[12825, 12766])).
% 1.68/1.85 tff(12827,plain,
% 1.68/1.85 (((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21)) | trans(s99, s22))),
% 1.68/1.85 inference(monotonicity,[status(thm)],[12826])).
% 1.68/1.85 tff(12828,plain,
% 1.68/1.85 (((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22))),
% 1.68/1.85 inference(transitivity,[status(thm)],[12827, 12765])).
% 1.68/1.85 tff(12829,plain,
% 1.68/1.85 ((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22)) | trans(s99, s23))),
% 1.68/1.85 inference(monotonicity,[status(thm)],[12828])).
% 1.68/1.85 tff(12830,plain,
% 1.68/1.85 ((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23))),
% 1.68/1.86 inference(transitivity,[status(thm)],[12829, 12764])).
% 1.68/1.86 tff(12831,plain,
% 1.68/1.86 (((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23)) | trans(s99, s24))),
% 1.68/1.86 inference(monotonicity,[status(thm)],[12830])).
% 1.68/1.86 tff(12832,plain,
% 1.68/1.86 (((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24))),
% 1.68/1.86 inference(transitivity,[status(thm)],[12831, 12763])).
% 1.68/1.86 tff(12833,plain,
% 1.68/1.86 ((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24)) | trans(s99, s25))),
% 1.68/1.86 inference(monotonicity,[status(thm)],[12832])).
% 1.68/1.86 tff(12834,plain,
% 1.68/1.86 ((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25))),
% 1.68/1.86 inference(transitivity,[status(thm)],[12833, 12762])).
% 1.68/1.86 tff(12835,plain,
% 1.68/1.86 (((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25)) | trans(s99, s26))),
% 1.68/1.86 inference(monotonicity,[status(thm)],[12834])).
% 1.68/1.86 tff(12836,plain,
% 1.68/1.86 (((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26))),
% 1.68/1.86 inference(transitivity,[status(thm)],[12835, 12761])).
% 1.68/1.86 tff(12837,plain,
% 1.68/1.86 ((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26)) | trans(s99, s27))),
% 1.68/1.86 inference(monotonicity,[status(thm)],[12836])).
% 1.68/1.86 tff(12838,plain,
% 1.68/1.86 ((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27))),
% 1.68/1.86 inference(transitivity,[status(thm)],[12837, 12760])).
% 1.68/1.86 tff(12839,plain,
% 1.68/1.86 (((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27)) | trans(s99, s28))),
% 1.68/1.86 inference(monotonicity,[status(thm)],[12838])).
% 1.68/1.86 tff(12840,plain,
% 1.68/1.86 (((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28))),
% 1.68/1.86 inference(transitivity,[status(thm)],[12839, 12759])).
% 1.68/1.86 tff(12841,plain,
% 1.68/1.86 ((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28)) | trans(s99, s29))),
% 1.68/1.87 inference(monotonicity,[status(thm)],[12840])).
% 1.68/1.87 tff(12842,plain,
% 1.68/1.87 ((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29))),
% 1.68/1.87 inference(transitivity,[status(thm)],[12841, 12758])).
% 1.68/1.87 tff(12843,plain,
% 1.68/1.87 (((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29)) | trans(s99, s30))),
% 1.68/1.87 inference(monotonicity,[status(thm)],[12842])).
% 1.68/1.87 tff(12844,plain,
% 1.68/1.87 (((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30))),
% 1.68/1.87 inference(transitivity,[status(thm)],[12843, 12757])).
% 1.68/1.87 tff(12845,plain,
% 1.68/1.87 ((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30)) | trans(s99, s31))),
% 1.68/1.87 inference(monotonicity,[status(thm)],[12844])).
% 1.68/1.87 tff(12846,plain,
% 1.68/1.87 ((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31))),
% 1.68/1.87 inference(transitivity,[status(thm)],[12845, 12756])).
% 1.68/1.87 tff(12847,plain,
% 1.68/1.87 (((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31)) | trans(s99, s32))),
% 1.68/1.87 inference(monotonicity,[status(thm)],[12846])).
% 1.68/1.87 tff(12848,plain,
% 1.68/1.87 (((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32))),
% 1.68/1.87 inference(transitivity,[status(thm)],[12847, 12755])).
% 1.68/1.87 tff(12849,plain,
% 1.68/1.87 ((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32)) | trans(s99, s33))),
% 1.68/1.87 inference(monotonicity,[status(thm)],[12848])).
% 1.68/1.87 tff(12850,plain,
% 1.68/1.87 ((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33))),
% 1.68/1.87 inference(transitivity,[status(thm)],[12849, 12754])).
% 1.68/1.87 tff(12851,plain,
% 1.68/1.87 (((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33)) | trans(s99, s34))),
% 1.68/1.87 inference(monotonicity,[status(thm)],[12850])).
% 1.68/1.87 tff(12852,plain,
% 1.68/1.87 (((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34))),
% 1.68/1.87 inference(transitivity,[status(thm)],[12851, 12753])).
% 1.68/1.87 tff(12853,plain,
% 1.68/1.87 ((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34)) | trans(s99, s35))),
% 1.68/1.87 inference(monotonicity,[status(thm)],[12852])).
% 1.68/1.87 tff(12854,plain,
% 1.68/1.87 ((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35))),
% 1.68/1.88 inference(transitivity,[status(thm)],[12853, 12752])).
% 1.68/1.88 tff(12855,plain,
% 1.68/1.88 (((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35)) | trans(s99, s36))),
% 1.68/1.88 inference(monotonicity,[status(thm)],[12854])).
% 1.68/1.88 tff(12856,plain,
% 1.68/1.88 (((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36))),
% 1.68/1.88 inference(transitivity,[status(thm)],[12855, 12751])).
% 1.68/1.88 tff(12857,plain,
% 1.68/1.88 ((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36)) | trans(s99, s37))),
% 1.68/1.88 inference(monotonicity,[status(thm)],[12856])).
% 1.68/1.88 tff(12858,plain,
% 1.68/1.88 ((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37))),
% 1.68/1.88 inference(transitivity,[status(thm)],[12857, 12750])).
% 1.68/1.88 tff(12859,plain,
% 1.68/1.88 (((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37)) | trans(s99, s38))),
% 1.68/1.88 inference(monotonicity,[status(thm)],[12858])).
% 1.68/1.88 tff(12860,plain,
% 1.68/1.88 (((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38))),
% 1.68/1.88 inference(transitivity,[status(thm)],[12859, 12749])).
% 1.68/1.88 tff(12861,plain,
% 1.68/1.88 ((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38)) | trans(s99, s39))),
% 1.68/1.88 inference(monotonicity,[status(thm)],[12860])).
% 1.68/1.88 tff(12862,plain,
% 1.68/1.88 ((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39))),
% 1.68/1.89 inference(transitivity,[status(thm)],[12861, 12748])).
% 1.68/1.89 tff(12863,plain,
% 1.68/1.89 (((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39)) | trans(s99, s40))),
% 1.68/1.89 inference(monotonicity,[status(thm)],[12862])).
% 1.68/1.89 tff(12864,plain,
% 1.68/1.89 (((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40))),
% 1.68/1.89 inference(transitivity,[status(thm)],[12863, 12747])).
% 1.68/1.89 tff(12865,plain,
% 1.68/1.89 ((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40)) | trans(s99, s41))),
% 1.68/1.89 inference(monotonicity,[status(thm)],[12864])).
% 1.68/1.89 tff(12866,plain,
% 1.68/1.89 ((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41))),
% 1.68/1.89 inference(transitivity,[status(thm)],[12865, 12746])).
% 1.68/1.89 tff(12867,plain,
% 1.68/1.89 (((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41)) | trans(s99, s42))),
% 1.68/1.89 inference(monotonicity,[status(thm)],[12866])).
% 1.68/1.89 tff(12868,plain,
% 1.68/1.89 (((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42))),
% 1.68/1.89 inference(transitivity,[status(thm)],[12867, 12745])).
% 1.68/1.89 tff(12869,plain,
% 1.68/1.89 ((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42)) | trans(s99, s43))),
% 1.68/1.90 inference(monotonicity,[status(thm)],[12868])).
% 1.68/1.90 tff(12870,plain,
% 1.68/1.90 ((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43))),
% 1.68/1.90 inference(transitivity,[status(thm)],[12869, 12744])).
% 1.68/1.90 tff(12871,plain,
% 1.68/1.90 (((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43)) | trans(s99, s44))),
% 1.68/1.90 inference(monotonicity,[status(thm)],[12870])).
% 1.68/1.90 tff(12872,plain,
% 1.68/1.90 (((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44))),
% 1.68/1.90 inference(transitivity,[status(thm)],[12871, 12743])).
% 1.68/1.90 tff(12873,plain,
% 1.68/1.90 ((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44)) | trans(s99, s45))),
% 1.68/1.90 inference(monotonicity,[status(thm)],[12872])).
% 1.68/1.90 tff(12874,plain,
% 1.68/1.90 ((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45))),
% 1.68/1.90 inference(transitivity,[status(thm)],[12873, 12742])).
% 1.68/1.90 tff(12875,plain,
% 1.68/1.90 (((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45)) | trans(s99, s46))),
% 1.68/1.90 inference(monotonicity,[status(thm)],[12874])).
% 1.68/1.90 tff(12876,plain,
% 1.68/1.90 (((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46))),
% 1.68/1.91 inference(transitivity,[status(thm)],[12875, 12741])).
% 1.68/1.91 tff(12877,plain,
% 1.68/1.91 ((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46)) | trans(s99, s47))),
% 1.68/1.91 inference(monotonicity,[status(thm)],[12876])).
% 1.68/1.91 tff(12878,plain,
% 1.68/1.91 ((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47))),
% 1.68/1.91 inference(transitivity,[status(thm)],[12877, 12740])).
% 1.68/1.91 tff(12879,plain,
% 1.68/1.91 (((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47)) | trans(s99, s48))),
% 1.68/1.91 inference(monotonicity,[status(thm)],[12878])).
% 1.68/1.91 tff(12880,plain,
% 1.68/1.91 (((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48))),
% 1.68/1.91 inference(transitivity,[status(thm)],[12879, 12739])).
% 1.68/1.91 tff(12881,plain,
% 1.68/1.91 ((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48)) | trans(s99, s49))),
% 1.68/1.91 inference(monotonicity,[status(thm)],[12880])).
% 1.68/1.91 tff(12882,plain,
% 1.68/1.91 ((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49))),
% 1.68/1.91 inference(transitivity,[status(thm)],[12881, 12738])).
% 1.68/1.91 tff(12883,plain,
% 1.68/1.91 (((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49)) | trans(s99, s50))),
% 1.68/1.91 inference(monotonicity,[status(thm)],[12882])).
% 1.68/1.91 tff(12884,plain,
% 1.68/1.91 (((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50))),
% 1.68/1.92 inference(transitivity,[status(thm)],[12883, 12737])).
% 1.68/1.92 tff(12885,plain,
% 1.68/1.92 ((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50)) | trans(s99, s51))),
% 1.68/1.92 inference(monotonicity,[status(thm)],[12884])).
% 1.68/1.92 tff(12886,plain,
% 1.68/1.92 ((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51))),
% 1.68/1.92 inference(transitivity,[status(thm)],[12885, 12736])).
% 1.68/1.92 tff(12887,plain,
% 1.68/1.92 (((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51)) | trans(s99, s52))),
% 1.68/1.92 inference(monotonicity,[status(thm)],[12886])).
% 1.68/1.92 tff(12888,plain,
% 1.68/1.92 (((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52))),
% 1.68/1.92 inference(transitivity,[status(thm)],[12887, 12735])).
% 1.68/1.92 tff(12889,plain,
% 1.68/1.92 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52)) | trans(s99, s53))),
% 1.68/1.92 inference(monotonicity,[status(thm)],[12888])).
% 1.68/1.92 tff(12890,plain,
% 1.68/1.92 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53))),
% 1.68/1.93 inference(transitivity,[status(thm)],[12889, 12734])).
% 1.68/1.93 tff(12891,plain,
% 1.68/1.93 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53)) | trans(s99, s54))),
% 1.68/1.93 inference(monotonicity,[status(thm)],[12890])).
% 1.68/1.93 tff(12892,plain,
% 1.68/1.93 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54))),
% 1.68/1.93 inference(transitivity,[status(thm)],[12891, 12733])).
% 1.68/1.93 tff(12893,plain,
% 1.68/1.93 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54)) | trans(s99, s55))),
% 1.68/1.93 inference(monotonicity,[status(thm)],[12892])).
% 1.68/1.93 tff(12894,plain,
% 1.68/1.93 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55))),
% 1.77/1.93 inference(transitivity,[status(thm)],[12893, 12732])).
% 1.77/1.93 tff(12895,plain,
% 1.77/1.93 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55)) | trans(s99, s56))),
% 1.77/1.93 inference(monotonicity,[status(thm)],[12894])).
% 1.77/1.93 tff(12896,plain,
% 1.77/1.93 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56))),
% 1.77/1.94 inference(transitivity,[status(thm)],[12895, 12731])).
% 1.77/1.94 tff(12897,plain,
% 1.77/1.94 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56)) | trans(s99, s57))),
% 1.77/1.94 inference(monotonicity,[status(thm)],[12896])).
% 1.77/1.94 tff(12898,plain,
% 1.77/1.94 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57))),
% 1.77/1.94 inference(transitivity,[status(thm)],[12897, 12730])).
% 1.77/1.94 tff(12899,plain,
% 1.77/1.94 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57)) | trans(s99, s58))),
% 1.77/1.94 inference(monotonicity,[status(thm)],[12898])).
% 1.77/1.94 tff(12900,plain,
% 1.77/1.94 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58))),
% 1.77/1.94 inference(transitivity,[status(thm)],[12899, 12729])).
% 1.77/1.94 tff(12901,plain,
% 1.77/1.94 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58)) | trans(s99, s59))),
% 1.77/1.94 inference(monotonicity,[status(thm)],[12900])).
% 1.77/1.94 tff(12902,plain,
% 1.77/1.94 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59))),
% 1.77/1.94 inference(transitivity,[status(thm)],[12901, 12728])).
% 1.77/1.94 tff(12903,plain,
% 1.77/1.94 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59)) | trans(s99, s60))),
% 1.77/1.95 inference(monotonicity,[status(thm)],[12902])).
% 1.77/1.95 tff(12904,plain,
% 1.77/1.95 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60))),
% 1.77/1.95 inference(transitivity,[status(thm)],[12903, 12727])).
% 1.77/1.95 tff(12905,plain,
% 1.77/1.95 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60)) | trans(s99, s61))),
% 1.77/1.95 inference(monotonicity,[status(thm)],[12904])).
% 1.77/1.95 tff(12906,plain,
% 1.77/1.95 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61))),
% 1.77/1.95 inference(transitivity,[status(thm)],[12905, 12726])).
% 1.77/1.95 tff(12907,plain,
% 1.77/1.95 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61)) | trans(s99, s62))),
% 1.77/1.95 inference(monotonicity,[status(thm)],[12906])).
% 1.77/1.95 tff(12908,plain,
% 1.77/1.95 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62))),
% 1.77/1.96 inference(transitivity,[status(thm)],[12907, 12725])).
% 1.77/1.96 tff(12909,plain,
% 1.77/1.96 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62)) | trans(s99, s63))),
% 1.77/1.96 inference(monotonicity,[status(thm)],[12908])).
% 1.77/1.96 tff(12910,plain,
% 1.77/1.96 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63))),
% 1.77/1.96 inference(transitivity,[status(thm)],[12909, 12724])).
% 1.77/1.96 tff(12911,plain,
% 1.77/1.96 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63)) | trans(s99, s64))),
% 1.77/1.96 inference(monotonicity,[status(thm)],[12910])).
% 1.77/1.96 tff(12912,plain,
% 1.77/1.96 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64))),
% 1.77/1.96 inference(transitivity,[status(thm)],[12911, 12723])).
% 1.77/1.96 tff(12913,plain,
% 1.77/1.96 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64)) | trans(s99, s65))),
% 1.77/1.97 inference(monotonicity,[status(thm)],[12912])).
% 1.77/1.97 tff(12914,plain,
% 1.77/1.97 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65))),
% 1.77/1.97 inference(transitivity,[status(thm)],[12913, 12722])).
% 1.77/1.97 tff(12915,plain,
% 1.77/1.97 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65)) | trans(s99, s66))),
% 1.77/1.97 inference(monotonicity,[status(thm)],[12914])).
% 1.77/1.97 tff(12916,plain,
% 1.77/1.97 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66))),
% 1.77/1.97 inference(transitivity,[status(thm)],[12915, 12721])).
% 1.77/1.97 tff(12917,plain,
% 1.77/1.97 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66)) | trans(s99, s67))),
% 1.77/1.98 inference(monotonicity,[status(thm)],[12916])).
% 1.77/1.98 tff(12918,plain,
% 1.77/1.98 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67))),
% 1.77/1.98 inference(transitivity,[status(thm)],[12917, 12720])).
% 1.77/1.98 tff(12919,plain,
% 1.77/1.98 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67)) | trans(s99, s68))),
% 1.77/1.98 inference(monotonicity,[status(thm)],[12918])).
% 1.77/1.98 tff(12920,plain,
% 1.77/1.98 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68))),
% 1.82/1.98 inference(transitivity,[status(thm)],[12919, 12719])).
% 1.82/1.98 tff(12921,plain,
% 1.82/1.98 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68)) | trans(s99, s69))),
% 1.82/1.98 inference(monotonicity,[status(thm)],[12920])).
% 1.82/1.98 tff(12922,plain,
% 1.82/1.98 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69))),
% 1.82/1.98 inference(transitivity,[status(thm)],[12921, 12718])).
% 1.82/1.98 tff(12923,plain,
% 1.82/1.98 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69)) | trans(s99, s70))),
% 1.82/1.99 inference(monotonicity,[status(thm)],[12922])).
% 1.82/1.99 tff(12924,plain,
% 1.82/1.99 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70))),
% 1.82/1.99 inference(transitivity,[status(thm)],[12923, 12717])).
% 1.82/1.99 tff(12925,plain,
% 1.82/1.99 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70)) | trans(s99, s71))),
% 1.82/1.99 inference(monotonicity,[status(thm)],[12924])).
% 1.82/1.99 tff(12926,plain,
% 1.82/1.99 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71))),
% 1.82/1.99 inference(transitivity,[status(thm)],[12925, 12716])).
% 1.82/1.99 tff(12927,plain,
% 1.82/1.99 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71)) | trans(s99, s72))),
% 1.82/1.99 inference(monotonicity,[status(thm)],[12926])).
% 1.82/1.99 tff(12928,plain,
% 1.82/1.99 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72))),
% 1.82/2.00 inference(transitivity,[status(thm)],[12927, 12715])).
% 1.82/2.00 tff(12929,plain,
% 1.82/2.00 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72)) | trans(s99, s73))),
% 1.82/2.00 inference(monotonicity,[status(thm)],[12928])).
% 1.82/2.00 tff(12930,plain,
% 1.82/2.00 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73))),
% 1.82/2.00 inference(transitivity,[status(thm)],[12929, 12714])).
% 1.82/2.00 tff(12931,plain,
% 1.82/2.00 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73)) | trans(s99, s74))),
% 1.82/2.00 inference(monotonicity,[status(thm)],[12930])).
% 1.82/2.00 tff(12932,plain,
% 1.82/2.00 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74))),
% 1.82/2.01 inference(transitivity,[status(thm)],[12931, 12713])).
% 1.82/2.01 tff(12933,plain,
% 1.82/2.01 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74)) | trans(s99, s75))),
% 1.82/2.01 inference(monotonicity,[status(thm)],[12932])).
% 1.82/2.01 tff(12934,plain,
% 1.82/2.01 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75))),
% 1.82/2.01 inference(transitivity,[status(thm)],[12933, 12712])).
% 1.82/2.01 tff(12935,plain,
% 1.82/2.01 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75)) | trans(s99, s76))),
% 1.82/2.01 inference(monotonicity,[status(thm)],[12934])).
% 1.82/2.01 tff(12936,plain,
% 1.82/2.01 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76))),
% 1.82/2.02 inference(transitivity,[status(thm)],[12935, 12711])).
% 1.82/2.02 tff(12937,plain,
% 1.82/2.02 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76)) | trans(s99, s77))),
% 1.82/2.02 inference(monotonicity,[status(thm)],[12936])).
% 1.82/2.02 tff(12938,plain,
% 1.82/2.02 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77))),
% 1.82/2.02 inference(transitivity,[status(thm)],[12937, 12710])).
% 1.82/2.02 tff(12939,plain,
% 1.82/2.02 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77)) | trans(s99, s78))),
% 1.82/2.02 inference(monotonicity,[status(thm)],[12938])).
% 1.82/2.02 tff(12940,plain,
% 1.82/2.02 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78))),
% 1.82/2.02 inference(transitivity,[status(thm)],[12939, 12709])).
% 1.82/2.02 tff(12941,plain,
% 1.82/2.02 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78)) | trans(s99, s79))),
% 1.82/2.03 inference(monotonicity,[status(thm)],[12940])).
% 1.82/2.03 tff(12942,plain,
% 1.82/2.03 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79))),
% 1.82/2.03 inference(transitivity,[status(thm)],[12941, 12708])).
% 1.82/2.03 tff(12943,plain,
% 1.82/2.03 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79)) | trans(s99, s80))),
% 1.82/2.03 inference(monotonicity,[status(thm)],[12942])).
% 1.82/2.03 tff(12944,plain,
% 1.82/2.03 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80))),
% 1.82/2.03 inference(transitivity,[status(thm)],[12943, 12707])).
% 1.82/2.03 tff(12945,plain,
% 1.82/2.03 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80)) | trans(s99, s81))),
% 1.82/2.04 inference(monotonicity,[status(thm)],[12944])).
% 1.82/2.04 tff(12946,plain,
% 1.82/2.04 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81))),
% 1.82/2.04 inference(transitivity,[status(thm)],[12945, 12706])).
% 1.82/2.04 tff(12947,plain,
% 1.82/2.04 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81)) | trans(s99, s82))),
% 1.82/2.04 inference(monotonicity,[status(thm)],[12946])).
% 1.82/2.04 tff(12948,plain,
% 1.82/2.04 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82))),
% 1.82/2.04 inference(transitivity,[status(thm)],[12947, 12705])).
% 1.82/2.04 tff(12949,plain,
% 1.82/2.04 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82)) | trans(s99, s83))),
% 1.82/2.05 inference(monotonicity,[status(thm)],[12948])).
% 1.82/2.05 tff(12950,plain,
% 1.82/2.05 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83))),
% 1.88/2.05 inference(transitivity,[status(thm)],[12949, 12704])).
% 1.88/2.05 tff(12951,plain,
% 1.88/2.05 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83)) | trans(s99, s84))),
% 1.88/2.05 inference(monotonicity,[status(thm)],[12950])).
% 1.88/2.05 tff(12952,plain,
% 1.88/2.05 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84))),
% 1.88/2.05 inference(transitivity,[status(thm)],[12951, 12703])).
% 1.88/2.05 tff(12953,plain,
% 1.88/2.05 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84)) | trans(s99, s85))),
% 1.88/2.06 inference(monotonicity,[status(thm)],[12952])).
% 1.88/2.06 tff(12954,plain,
% 1.88/2.06 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85))),
% 1.88/2.06 inference(transitivity,[status(thm)],[12953, 12702])).
% 1.88/2.06 tff(12955,plain,
% 1.88/2.06 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85)) | trans(s99, s86))),
% 1.90/2.06 inference(monotonicity,[status(thm)],[12954])).
% 1.90/2.06 tff(12956,plain,
% 1.90/2.06 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86))),
% 1.90/2.07 inference(transitivity,[status(thm)],[12955, 12701])).
% 1.90/2.07 tff(12957,plain,
% 1.90/2.07 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86)) | trans(s99, s87))),
% 1.90/2.07 inference(monotonicity,[status(thm)],[12956])).
% 1.90/2.07 tff(12958,plain,
% 1.90/2.07 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87))),
% 1.90/2.07 inference(transitivity,[status(thm)],[12957, 12700])).
% 1.90/2.07 tff(12959,plain,
% 1.90/2.07 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87)) | trans(s99, s88))),
% 1.90/2.07 inference(monotonicity,[status(thm)],[12958])).
% 1.90/2.07 tff(12960,plain,
% 1.90/2.07 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88))),
% 1.90/2.07 inference(transitivity,[status(thm)],[12959, 12699])).
% 1.90/2.07 tff(12961,plain,
% 1.90/2.07 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88)) | trans(s99, s89))),
% 1.90/2.08 inference(monotonicity,[status(thm)],[12960])).
% 1.90/2.08 tff(12962,plain,
% 1.90/2.08 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89))),
% 1.90/2.08 inference(transitivity,[status(thm)],[12961, 12698])).
% 1.90/2.08 tff(12963,plain,
% 1.90/2.08 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89)) | trans(s99, s90))),
% 1.90/2.08 inference(monotonicity,[status(thm)],[12962])).
% 1.90/2.08 tff(12964,plain,
% 1.90/2.08 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90))),
% 1.90/2.08 inference(transitivity,[status(thm)],[12963, 12697])).
% 1.90/2.08 tff(12965,plain,
% 1.90/2.08 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90)) | trans(s99, s91))),
% 1.90/2.09 inference(monotonicity,[status(thm)],[12964])).
% 1.90/2.09 tff(12966,plain,
% 1.90/2.09 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91))),
% 1.90/2.09 inference(transitivity,[status(thm)],[12965, 12696])).
% 1.90/2.09 tff(12967,plain,
% 1.90/2.09 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91)) | trans(s99, s92))),
% 1.90/2.09 inference(monotonicity,[status(thm)],[12966])).
% 1.90/2.09 tff(12968,plain,
% 1.90/2.09 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92))),
% 1.90/2.10 inference(transitivity,[status(thm)],[12967, 12695])).
% 1.90/2.10 tff(12969,plain,
% 1.90/2.10 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92)) | trans(s99, s93))),
% 1.90/2.10 inference(monotonicity,[status(thm)],[12968])).
% 1.90/2.10 tff(12970,plain,
% 1.90/2.10 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93))),
% 1.90/2.10 inference(transitivity,[status(thm)],[12969, 12694])).
% 1.90/2.10 tff(12971,plain,
% 1.90/2.10 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93)) | trans(s99, s94))),
% 1.90/2.11 inference(monotonicity,[status(thm)],[12970])).
% 1.90/2.11 tff(12972,plain,
% 1.90/2.11 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94))),
% 1.90/2.11 inference(transitivity,[status(thm)],[12971, 12693])).
% 1.90/2.11 tff(12973,plain,
% 1.90/2.11 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94)) | trans(s99, s95))),
% 1.90/2.11 inference(monotonicity,[status(thm)],[12972])).
% 1.90/2.11 tff(12974,plain,
% 1.90/2.11 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95))),
% 1.95/2.11 inference(transitivity,[status(thm)],[12973, 12692])).
% 1.95/2.11 tff(12975,plain,
% 1.95/2.11 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) | trans(s99, s96)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95)) | trans(s99, s96))),
% 1.95/2.11 inference(monotonicity,[status(thm)],[12974])).
% 1.95/2.11 tff(12976,plain,
% 1.95/2.11 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) | trans(s99, s96)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96))),
% 1.95/2.12 inference(transitivity,[status(thm)],[12975, 12691])).
% 1.95/2.12 tff(12977,plain,
% 1.95/2.12 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) | trans(s99, s96)) | trans(s99, s97)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96)) | trans(s99, s97))),
% 1.95/2.12 inference(monotonicity,[status(thm)],[12976])).
% 1.95/2.12 tff(12978,plain,
% 1.95/2.12 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) | trans(s99, s96)) | trans(s99, s97)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97))),
% 1.95/2.12 inference(transitivity,[status(thm)],[12977, 12690])).
% 1.95/2.12 tff(12979,plain,
% 1.95/2.12 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) | trans(s99, s96)) | trans(s99, s97)) | trans(s99, s98)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97)) | trans(s99, s98))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[12978])).
% 1.95/2.13 tff(12980,plain,
% 1.95/2.13 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) | trans(s99, s96)) | trans(s99, s97)) | trans(s99, s98)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98))),
% 1.95/2.13 inference(transitivity,[status(thm)],[12979, 12689])).
% 1.95/2.13 tff(12981,plain,
% 1.95/2.13 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) | trans(s99, s96)) | trans(s99, s97)) | trans(s99, s98)) | trans(s99, s99)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98)) | trans(s99, s99))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[12980])).
% 1.95/2.13 tff(12982,plain,
% 1.95/2.13 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) | trans(s99, s96)) | trans(s99, s97)) | trans(s99, s98)) | trans(s99, s99)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99))),
% 1.95/2.14 inference(transitivity,[status(thm)],[12981, 12688])).
% 1.95/2.14 tff(12983,axiom,(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) | trans(s99, s96)) | trans(s99, s97)) | trans(s99, s98)) | trans(s99, s99)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound102')).
% 1.95/2.14 tff(12984,plain,
% 1.95/2.14 ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99)),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[12983, 12982])).
% 1.95/2.14 tff(12985,plain,
% 1.95/2.14 ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99)),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[12984, 12687])).
% 1.95/2.14 tff(12986,plain,
% 1.95/2.14 ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99)),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[12985, 12687])).
% 1.95/2.14 tff(12987,plain,
% 1.95/2.14 ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99)),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[12986, 12687])).
% 1.95/2.14 tff(12988,plain,
% 1.95/2.14 ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99)),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[12987, 12687])).
% 1.95/2.15 tff(12989,plain,
% 1.95/2.15 (trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[12988, 12686])).
% 1.95/2.15 tff(12990,plain,
% 1.95/2.15 (trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s99)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[12989, 12648])).
% 1.95/2.15 tff(12991,plain,
% 1.95/2.15 (trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s99)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[12990, 12638])).
% 1.95/2.15 tff(12992,plain,
% 1.95/2.15 (trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[12991, 12606])).
% 1.95/2.15 tff(12993,plain,
% 1.95/2.15 (trans(s99, s92)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[12992, 12374, 12364, 12363, 12362, 12361, 12360, 12359, 12358, 12357, 12356, 12355, 12354, 12353, 12352, 12351, 12350, 12349, 12348, 12347, 12346, 12345, 12344, 12343, 12342, 12341, 12340, 12339, 12338, 12337, 12336, 12335, 12334, 12333, 12332, 12331, 12330, 12329, 12328, 12327, 12326, 12325, 12324, 12323, 12322, 12321, 12320, 12319, 12318, 12317, 12316, 12315, 12314, 12313, 12312, 12311, 12310, 12309, 12308, 12307, 12306, 12305, 12304, 12303, 12302, 12301, 12300, 12299, 12298, 12297, 12296, 12295, 12294, 12293, 12292, 12291, 12290, 12289, 12288, 12287, 12286, 12285, 12284, 12283, 12282, 12281, 12280, 12279, 12278, 12277, 12276, 12275, 12274, 12273, 12272, 12271, 12270])).
% 1.95/2.15 tff(12994,assumption,(~until2p29(s92)), introduced(assumption)).
% 1.95/2.15 tff(12995,assumption,(trans(s99, s92)), introduced(assumption)).
% 1.95/2.15 tff(12996,plain,
% 1.95/2.15 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s92) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s92)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s92) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s92)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(12997,plain,
% 1.95/2.15 (((~trans(s99, s92)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s92)) <=> (until2p29(s92) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s92)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(12998,plain,
% 1.95/2.15 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s92)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s92))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s92) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s92))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[12997])).
% 1.95/2.15 tff(12999,plain,
% 1.95/2.15 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s92)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s92))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s92) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s92)))),
% 1.95/2.15 inference(transitivity,[status(thm)],[12998, 12996])).
% 1.95/2.15 tff(13000,plain,
% 1.95/2.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s92)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s92))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(13001,plain,
% 1.95/2.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s92) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s92))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[13000, 12999])).
% 1.95/2.15 tff(13002,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[13001, 10200, 12995, 11219, 12994, 11220])).
% 1.95/2.15 tff(13003,plain,((~trans(s99, s92)) | until2p29(s92) | (~xuntil28(s99))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(13004,plain,
% 1.95/2.15 (until2p29(s92)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[13003, 12993, 11220])).
% 1.95/2.15 tff(13005,plain,
% 1.95/2.15 (xuntil2p30(s92)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[10298, 13004])).
% 1.95/2.15 tff(13006,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[10293, 13005, 12269])).
% 1.95/2.15 tff(13007,plain,(until2p29(s95) | (~xuntil28(s99)) | trans(s99, s85) | trans(s99, s1) | trans(s99, s42) | trans(s99, s79) | trans(s99, s48) | trans(s99, s28) | trans(s99, s71) | trans(s99, s83) | trans(s99, s20) | trans(s99, s24) | trans(s99, s32) | trans(s99, s8) | trans(s99, s39) | trans(s99, s5) | trans(s99, s9) | trans(s99, s6) | trans(s99, s23) | trans(s99, s7) | trans(s99, s27) | trans(s99, s15) | trans(s99, s3) | trans(s99, s38) | trans(s99, s31) | trans(s99, s25) | trans(s99, s14) | trans(s99, s17) | trans(s99, s29) | trans(s99, s21) | trans(s99, s34) | trans(s99, s43) | trans(s99, s22) | trans(s99, s67) | trans(s99, s64) | trans(s99, s52) | trans(s99, s60) | trans(s99, s88) | trans(s99, s89) | trans(s99, s47) | trans(s99, s46) | trans(s99, s77) | trans(s99, s13) | trans(s99, s33) | trans(s99, s49) | trans(s99, s16) | trans(s99, s80) | trans(s99, s87) | trans(s99, s58) | trans(s99, s66) | trans(s99, s50) | trans(s99, s63) | trans(s99, s19) | trans(s99, s70) | trans(s99, s26) | trans(s99, s36) | trans(s99, s30) | trans(s99, s61) | trans(s99, s93) | trans(s99, s69) | trans(s99, s18) | trans(s99, s53) | trans(s99, s59) | trans(s99, s94) | trans(s99, s4) | trans(s99, s44) | trans(s99, s51) | trans(s99, s54) | trans(s99, s57) | trans(s99, s40) | trans(s99, s11) | trans(s99, s62) | trans(s99, s86) | trans(s99, s56) | trans(s99, s55) | trans(s99, s12) | trans(s99, s41) | trans(s99, s73) | trans(s99, s84) | trans(s99, s0) | trans(s99, s2) | trans(s99, s37) | trans(s99, s35) | trans(s99, s82) | trans(s99, s10) | trans(s99, s68) | trans(s99, s81) | trans(s99, s90) | trans(s99, s45) | trans(s99, s74) | trans(s99, s78) | trans(s99, s76) | trans(s99, s75) | trans(s99, s91) | trans(s99, s96) | trans(s99, s65) | trans(s99, s72)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(13008,plain,
% 1.95/2.15 (trans(s99, s1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[13007, 12264, 12253, 10269, 12242, 12231, 12220, 12209, 12198, 12187, 12176, 12165, 12154, 12143, 12132, 12121, 12110, 12099, 12088, 12077, 12066, 12055, 12044, 12033, 12022, 12011, 12000, 11989, 11978, 11967, 11956, 11945, 11934, 11923, 11912, 11901, 11890, 11879, 11868, 11857, 11846, 11835, 11824, 11813, 11802, 11791, 11780, 11769, 11758, 11747, 11736, 11725, 11714, 11703, 11692, 11681, 11670, 11659, 11648, 11637, 11626, 11615, 11604, 11593, 11582, 11571, 11560, 11549, 11538, 11527, 11516, 11505, 11494, 11483, 11472, 11461, 11450, 11439, 11428, 11417, 11396, 11385, 11374, 11363, 11352, 11341, 11330, 11319, 11308, 11297, 11286, 11275, 11264, 11253, 10186, 11242, 11231])).
% 1.95/2.15 tff(13009,plain,
% 1.95/2.15 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s1) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s1)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s1) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s1)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(13010,plain,
% 1.95/2.15 (((~trans(s99, s1)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s1)) <=> (until2p29(s1) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s1)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(13011,plain,
% 1.95/2.15 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s1)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s1))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | (until2p29(s1) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s1))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[13010])).
% 1.95/2.15 tff(13012,plain,
% 1.95/2.15 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s1)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s1))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s1) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s1)))),
% 1.95/2.15 inference(transitivity,[status(thm)],[13011, 13009])).
% 1.95/2.15 tff(13013,plain,
% 1.95/2.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | ((~trans(s99, s1)) | (~last(s99)) | (~xuntil28(s99)) | until2p29(s1))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(13014,plain,
% 1.95/2.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil28(X)) | until2p29(Y))) | until2p29(s1) | (~last(s99)) | (~xuntil28(s99)) | (~trans(s99, s1))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[13013, 13012])).
% 1.95/2.15 tff(13015,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[13014, 10200, 13008, 11219, 11209, 10186])).
% 1.95/2.15 tff(13016,plain,(always25(s99)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(13017,plain,
% 1.95/2.15 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s10) | (~trans(s99, s10)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s10) | (~trans(s99, s10)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(13018,plain,
% 1.95/2.15 (((~trans(s99, s10)) | (~always25(s99)) | always25(s10)) <=> ((~always25(s99)) | always25(s10) | (~trans(s99, s10)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(13019,plain,
% 1.95/2.15 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s10)) | (~always25(s99)) | always25(s10))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s10) | (~trans(s99, s10))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[13018])).
% 1.95/2.15 tff(13020,plain,
% 1.95/2.15 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s10)) | (~always25(s99)) | always25(s10))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s10) | (~trans(s99, s10)))),
% 1.95/2.15 inference(transitivity,[status(thm)],[13019, 13017])).
% 1.95/2.15 tff(13021,plain,
% 1.95/2.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s10)) | (~always25(s99)) | always25(s10))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(13022,plain,
% 1.95/2.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s10) | (~trans(s99, s10))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[13021, 13020])).
% 1.95/2.15 tff(13023,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[13022, 11343, 3934, 13016, 8737])).
% 1.95/2.15 tff(13024,plain,(~trans(s99, s10)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(13025,plain,
% 1.95/2.15 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s35) | (~trans(s99, s35)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s35) | (~trans(s99, s35)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(13026,plain,
% 1.95/2.15 (((~trans(s99, s35)) | (~always25(s99)) | always25(s35)) <=> ((~always25(s99)) | always25(s35) | (~trans(s99, s35)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(13027,plain,
% 1.95/2.15 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s35)) | (~always25(s99)) | always25(s35))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s35) | (~trans(s99, s35))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[13026])).
% 1.95/2.15 tff(13028,plain,
% 1.95/2.15 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s35)) | (~always25(s99)) | always25(s35))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s35) | (~trans(s99, s35)))),
% 1.95/2.15 inference(transitivity,[status(thm)],[13027, 13025])).
% 1.95/2.15 tff(13029,plain,
% 1.95/2.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s35)) | (~always25(s99)) | always25(s35))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(13030,plain,
% 1.95/2.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s35) | (~trans(s99, s35))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[13029, 13028])).
% 1.95/2.15 tff(13031,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[13030, 11365, 3934, 13016, 8554])).
% 1.95/2.15 tff(13032,plain,(~trans(s99, s35)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(13033,plain,
% 1.95/2.15 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s68) | (~trans(s99, s68)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s68) | (~trans(s99, s68)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(13034,plain,
% 1.95/2.15 (((~trans(s99, s68)) | (~always25(s99)) | always25(s68)) <=> ((~always25(s99)) | always25(s68) | (~trans(s99, s68)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(13035,plain,
% 1.95/2.15 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s68)) | (~always25(s99)) | always25(s68))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s68) | (~trans(s99, s68))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[13034])).
% 1.95/2.15 tff(13036,plain,
% 1.95/2.15 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s68)) | (~always25(s99)) | always25(s68))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s68) | (~trans(s99, s68)))),
% 1.95/2.15 inference(transitivity,[status(thm)],[13035, 13033])).
% 1.95/2.15 tff(13037,plain,
% 1.95/2.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s68)) | (~always25(s99)) | always25(s68))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(13038,plain,
% 1.95/2.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s68) | (~trans(s99, s68))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[13037, 13036])).
% 1.95/2.16 tff(13039,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[13038, 11332, 3934, 13016, 8324])).
% 1.95/2.16 tff(13040,plain,(~trans(s99, s68)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(13041,plain,
% 1.95/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s37, s38)) | (~always25(s37)) | always25(s38))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s37, s38)) | (~always25(s37)) | always25(s38))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(13042,plain,
% 1.95/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s37, s38)) | (~always25(s37)) | always25(s38))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(13043,plain,
% 1.95/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s37, s38)) | (~always25(s37)) | always25(s38)),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[13042, 13041])).
% 1.95/2.16 tff(13044,plain,
% 1.95/2.16 ((~always25(s37)) | always25(s38)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[13043, 3934, 3420])).
% 1.95/2.16 tff(13045,plain,
% 1.95/2.16 (~always25(s37)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[13044, 8534])).
% 1.95/2.16 tff(13046,plain,
% 1.95/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s37) | (~trans(s99, s37)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s37) | (~trans(s99, s37)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(13047,plain,
% 1.95/2.16 (((~trans(s99, s37)) | (~always25(s99)) | always25(s37)) <=> ((~always25(s99)) | always25(s37) | (~trans(s99, s37)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(13048,plain,
% 1.95/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s37)) | (~always25(s99)) | always25(s37))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s37) | (~trans(s99, s37))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[13047])).
% 1.95/2.16 tff(13049,plain,
% 1.95/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s37)) | (~always25(s99)) | always25(s37))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s37) | (~trans(s99, s37)))),
% 1.95/2.16 inference(transitivity,[status(thm)],[13048, 13046])).
% 1.95/2.16 tff(13050,plain,
% 1.95/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s37)) | (~always25(s99)) | always25(s37))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(13051,plain,
% 1.95/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s37) | (~trans(s99, s37))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[13050, 13049])).
% 1.95/2.16 tff(13052,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[13051, 11376, 3934, 13016, 13045])).
% 1.95/2.16 tff(13053,plain,(~trans(s99, s37)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(13054,plain,
% 1.95/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s2) | (~trans(s99, s2)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s2) | (~trans(s99, s2)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(13055,plain,
% 1.95/2.16 (((~trans(s99, s2)) | (~always25(s99)) | always25(s2)) <=> ((~always25(s99)) | always25(s2) | (~trans(s99, s2)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(13056,plain,
% 1.95/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s2)) | (~always25(s99)) | always25(s2))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s2) | (~trans(s99, s2))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[13055])).
% 1.95/2.16 tff(13057,plain,
% 1.95/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s2)) | (~always25(s99)) | always25(s2))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s2) | (~trans(s99, s2)))),
% 1.95/2.16 inference(transitivity,[status(thm)],[13056, 13054])).
% 1.95/2.16 tff(13058,plain,
% 1.95/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s2)) | (~always25(s99)) | always25(s2))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(13059,plain,
% 1.95/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s2) | (~trans(s99, s2))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[13058, 13057])).
% 1.95/2.16 tff(13060,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[13059, 11387, 3934, 13016, 8791])).
% 1.95/2.16 tff(13061,plain,(~trans(s99, s2)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(13062,plain,
% 1.95/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s0, s1)) | (~always25(s0)) | always25(s1))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s0, s1)) | (~always25(s0)) | always25(s1))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(13063,plain,
% 1.95/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s0, s1)) | (~always25(s0)) | always25(s1))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(13064,plain,
% 1.95/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s0, s1)) | (~always25(s0)) | always25(s1)),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[13063, 13062])).
% 1.95/2.16 tff(13065,plain,
% 1.95/2.16 ((~always25(s0)) | always25(s1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[13064, 3934, 39])).
% 1.95/2.16 tff(13066,plain,
% 1.95/2.16 (~always25(s0)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[13065, 8800])).
% 1.95/2.16 tff(13067,plain,
% 1.95/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s0) | (~trans(s99, s0)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s0) | (~trans(s99, s0)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(13068,plain,
% 1.95/2.16 (((~trans(s99, s0)) | (~always25(s99)) | always25(s0)) <=> ((~always25(s99)) | always25(s0) | (~trans(s99, s0)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(13069,plain,
% 1.95/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s0)) | (~always25(s99)) | always25(s0))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s0) | (~trans(s99, s0))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[13068])).
% 1.95/2.16 tff(13070,plain,
% 1.95/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s0)) | (~always25(s99)) | always25(s0))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s0) | (~trans(s99, s0)))),
% 1.95/2.16 inference(transitivity,[status(thm)],[13069, 13067])).
% 1.95/2.16 tff(13071,plain,
% 1.95/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s0)) | (~always25(s99)) | always25(s0))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(13072,plain,
% 1.95/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s0) | (~trans(s99, s0))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[13071, 13070])).
% 1.95/2.16 tff(13073,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[13072, 11408, 3934, 13016, 13066])).
% 1.95/2.16 tff(13074,plain,(~trans(s99, s0)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(13075,plain,
% 1.95/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s82) | (~trans(s99, s82)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s82) | (~trans(s99, s82)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(13076,plain,
% 1.95/2.16 (((~trans(s99, s82)) | (~always25(s99)) | always25(s82)) <=> ((~always25(s99)) | always25(s82) | (~trans(s99, s82)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(13077,plain,
% 1.95/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s82)) | (~always25(s99)) | always25(s82))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s82) | (~trans(s99, s82))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[13076])).
% 1.95/2.16 tff(13078,plain,
% 1.95/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s82)) | (~always25(s99)) | always25(s82))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s82) | (~trans(s99, s82)))),
% 1.95/2.16 inference(transitivity,[status(thm)],[13077, 13075])).
% 1.95/2.16 tff(13079,plain,
% 1.95/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s82)) | (~always25(s99)) | always25(s82))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(13080,plain,
% 1.95/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s82) | (~trans(s99, s82))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[13079, 13078])).
% 1.95/2.16 tff(13081,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[13080, 11354, 3934, 13016, 8222])).
% 1.95/2.16 tff(13082,plain,(~trans(s99, s82)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(13083,plain,
% 1.95/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s73, s74)) | (~always25(s73)) | always25(s74))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s73, s74)) | (~always25(s73)) | always25(s74))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(13084,plain,
% 1.95/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s73, s74)) | (~always25(s73)) | always25(s74))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(13085,plain,
% 1.95/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s73, s74)) | (~always25(s73)) | always25(s74)),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[13084, 13083])).
% 1.95/2.16 tff(13086,plain,
% 1.95/2.16 ((~always25(s73)) | always25(s74)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[13085, 3934, 6298])).
% 1.95/2.16 tff(13087,plain,
% 1.95/2.16 (~always25(s73)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[13086, 8280])).
% 1.95/2.16 tff(13088,plain,
% 1.95/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s73) | (~trans(s99, s73)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s73) | (~trans(s99, s73)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(13089,plain,
% 1.95/2.16 (((~trans(s99, s73)) | (~always25(s99)) | always25(s73)) <=> ((~always25(s99)) | always25(s73) | (~trans(s99, s73)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(13090,plain,
% 1.95/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s73)) | (~always25(s99)) | always25(s73))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s73) | (~trans(s99, s73))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[13089])).
% 1.95/2.16 tff(13091,plain,
% 1.95/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s73)) | (~always25(s99)) | always25(s73))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s73) | (~trans(s99, s73)))),
% 1.95/2.16 inference(transitivity,[status(thm)],[13090, 13088])).
% 1.95/2.16 tff(13092,plain,
% 1.95/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s73)) | (~always25(s99)) | always25(s73))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(13093,plain,
% 1.95/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s73) | (~trans(s99, s73))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[13092, 13091])).
% 1.95/2.16 tff(13094,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[13093, 11430, 3934, 13016, 13087])).
% 1.95/2.16 tff(13095,plain,(~trans(s99, s73)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(13096,plain,
% 1.95/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s41, s42)) | (~always25(s41)) | always25(s42))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s41, s42)) | (~always25(s41)) | always25(s42))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(13097,plain,
% 1.95/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s41, s42)) | (~always25(s41)) | always25(s42))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(13098,plain,
% 1.95/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s41, s42)) | (~always25(s41)) | always25(s42)),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[13097, 13096])).
% 1.95/2.16 tff(13099,plain,
% 1.95/2.16 ((~always25(s41)) | always25(s42)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[13098, 3934, 3715])).
% 1.95/2.16 tff(13100,plain,
% 1.95/2.16 (~always25(s41)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[13099, 8505])).
% 1.95/2.16 tff(13101,plain,
% 1.95/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s41) | (~trans(s99, s41)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s41) | (~trans(s99, s41)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(13102,plain,
% 1.95/2.16 (((~trans(s99, s41)) | (~always25(s99)) | always25(s41)) <=> ((~always25(s99)) | always25(s41) | (~trans(s99, s41)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(13103,plain,
% 1.95/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s41)) | (~always25(s99)) | always25(s41))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s41) | (~trans(s99, s41))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[13102])).
% 1.95/2.16 tff(13104,plain,
% 1.95/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s41)) | (~always25(s99)) | always25(s41))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s41) | (~trans(s99, s41)))),
% 1.95/2.16 inference(transitivity,[status(thm)],[13103, 13101])).
% 1.95/2.16 tff(13105,plain,
% 1.95/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s41)) | (~always25(s99)) | always25(s41))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(13106,plain,
% 1.95/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s41) | (~trans(s99, s41))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[13105, 13104])).
% 1.95/2.16 tff(13107,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[13106, 11441, 3934, 13016, 13100])).
% 1.95/2.16 tff(13108,plain,(~trans(s99, s41)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(13109,plain,
% 1.95/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s12) | (~trans(s99, s12)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s12) | (~trans(s99, s12)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(13110,plain,
% 1.95/2.16 (((~trans(s99, s12)) | (~always25(s99)) | always25(s12)) <=> ((~always25(s99)) | always25(s12) | (~trans(s99, s12)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(13111,plain,
% 1.95/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s12)) | (~always25(s99)) | always25(s12))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s12) | (~trans(s99, s12))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[13110])).
% 1.95/2.16 tff(13112,plain,
% 1.95/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s12)) | (~always25(s99)) | always25(s12))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s12) | (~trans(s99, s12)))),
% 1.95/2.16 inference(transitivity,[status(thm)],[13111, 13109])).
% 1.95/2.16 tff(13113,plain,
% 1.95/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s12)) | (~always25(s99)) | always25(s12))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(13114,plain,
% 1.95/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s12) | (~trans(s99, s12))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[13113, 13112])).
% 2.00/2.16 tff(13115,plain,
% 2.00/2.16 ($false),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[13114, 11452, 3934, 13016, 8723])).
% 2.00/2.16 tff(13116,plain,(~trans(s99, s12)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.16 tff(13117,plain,
% 2.00/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s55) | (~trans(s99, s55)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s55) | (~trans(s99, s55)))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(13118,plain,
% 2.00/2.16 (((~trans(s99, s55)) | (~always25(s99)) | always25(s55)) <=> ((~always25(s99)) | always25(s55) | (~trans(s99, s55)))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(13119,plain,
% 2.00/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s55)) | (~always25(s99)) | always25(s55))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s55) | (~trans(s99, s55))))),
% 2.00/2.16 inference(monotonicity,[status(thm)],[13118])).
% 2.00/2.16 tff(13120,plain,
% 2.00/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s55)) | (~always25(s99)) | always25(s55))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s55) | (~trans(s99, s55)))),
% 2.00/2.16 inference(transitivity,[status(thm)],[13119, 13117])).
% 2.00/2.16 tff(13121,plain,
% 2.00/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s55)) | (~always25(s99)) | always25(s55))),
% 2.00/2.16 inference(quant_inst,[status(thm)],[])).
% 2.00/2.16 tff(13122,plain,
% 2.00/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s55) | (~trans(s99, s55))),
% 2.00/2.16 inference(modus_ponens,[status(thm)],[13121, 13120])).
% 2.00/2.16 tff(13123,plain,
% 2.00/2.16 ($false),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[13122, 11463, 3934, 13016, 8416])).
% 2.00/2.16 tff(13124,plain,(~trans(s99, s55)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.16 tff(13125,plain,
% 2.00/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s56) | (~trans(s99, s56)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s56) | (~trans(s99, s56)))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(13126,plain,
% 2.00/2.16 (((~trans(s99, s56)) | (~always25(s99)) | always25(s56)) <=> ((~always25(s99)) | always25(s56) | (~trans(s99, s56)))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(13127,plain,
% 2.00/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s56)) | (~always25(s99)) | always25(s56))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s56) | (~trans(s99, s56))))),
% 2.00/2.16 inference(monotonicity,[status(thm)],[13126])).
% 2.00/2.16 tff(13128,plain,
% 2.00/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s56)) | (~always25(s99)) | always25(s56))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s56) | (~trans(s99, s56)))),
% 2.00/2.16 inference(transitivity,[status(thm)],[13127, 13125])).
% 2.00/2.16 tff(13129,plain,
% 2.00/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s56)) | (~always25(s99)) | always25(s56))),
% 2.00/2.16 inference(quant_inst,[status(thm)],[])).
% 2.00/2.16 tff(13130,plain,
% 2.00/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s56) | (~trans(s99, s56))),
% 2.00/2.16 inference(modus_ponens,[status(thm)],[13129, 13128])).
% 2.00/2.16 tff(13131,plain,
% 2.00/2.16 ($false),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[13130, 11474, 3934, 13016, 8411])).
% 2.00/2.16 tff(13132,plain,(~trans(s99, s56)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.16 tff(13133,plain,
% 2.00/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s76) | (~trans(s99, s76)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s76) | (~trans(s99, s76)))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(13134,plain,
% 2.00/2.16 (((~trans(s99, s76)) | (~always25(s99)) | always25(s76)) <=> ((~always25(s99)) | always25(s76) | (~trans(s99, s76)))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(13135,plain,
% 2.00/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s76)) | (~always25(s99)) | always25(s76))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s76) | (~trans(s99, s76))))),
% 2.00/2.16 inference(monotonicity,[status(thm)],[13134])).
% 2.00/2.16 tff(13136,plain,
% 2.00/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s76)) | (~always25(s99)) | always25(s76))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s76) | (~trans(s99, s76)))),
% 2.00/2.16 inference(transitivity,[status(thm)],[13135, 13133])).
% 2.00/2.16 tff(13137,plain,
% 2.00/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s76)) | (~always25(s99)) | always25(s76))),
% 2.00/2.16 inference(quant_inst,[status(thm)],[])).
% 2.00/2.16 tff(13138,plain,
% 2.00/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s76) | (~trans(s99, s76))),
% 2.00/2.16 inference(modus_ponens,[status(thm)],[13137, 13136])).
% 2.00/2.16 tff(13139,plain,
% 2.00/2.16 ($false),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[13138, 11266, 3934, 13016, 8266])).
% 2.00/2.16 tff(13140,plain,(~trans(s99, s76)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.16 tff(13141,plain,
% 2.00/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s62) | (~trans(s99, s62)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s62) | (~trans(s99, s62)))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(13142,plain,
% 2.00/2.16 (((~trans(s99, s62)) | (~always25(s99)) | always25(s62)) <=> ((~always25(s99)) | always25(s62) | (~trans(s99, s62)))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(13143,plain,
% 2.00/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s62)) | (~always25(s99)) | always25(s62))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s62) | (~trans(s99, s62))))),
% 2.00/2.16 inference(monotonicity,[status(thm)],[13142])).
% 2.00/2.16 tff(13144,plain,
% 2.00/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s62)) | (~always25(s99)) | always25(s62))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s62) | (~trans(s99, s62)))),
% 2.00/2.16 inference(transitivity,[status(thm)],[13143, 13141])).
% 2.00/2.16 tff(13145,plain,
% 2.00/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s62)) | (~always25(s99)) | always25(s62))),
% 2.00/2.16 inference(quant_inst,[status(thm)],[])).
% 2.00/2.16 tff(13146,plain,
% 2.00/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s62) | (~trans(s99, s62))),
% 2.00/2.16 inference(modus_ponens,[status(thm)],[13145, 13144])).
% 2.00/2.16 tff(13147,plain,
% 2.00/2.16 ($false),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[13146, 11496, 3934, 13016, 8367])).
% 2.00/2.16 tff(13148,plain,(~trans(s99, s62)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.16 tff(13149,plain,
% 2.00/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s11) | (~trans(s99, s11)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s11) | (~trans(s99, s11)))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(13150,plain,
% 2.00/2.16 (((~trans(s99, s11)) | (~always25(s99)) | always25(s11)) <=> ((~always25(s99)) | always25(s11) | (~trans(s99, s11)))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(13151,plain,
% 2.00/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s11)) | (~always25(s99)) | always25(s11))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s11) | (~trans(s99, s11))))),
% 2.00/2.16 inference(monotonicity,[status(thm)],[13150])).
% 2.00/2.16 tff(13152,plain,
% 2.00/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s11)) | (~always25(s99)) | always25(s11))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s11) | (~trans(s99, s11)))),
% 2.00/2.16 inference(transitivity,[status(thm)],[13151, 13149])).
% 2.00/2.16 tff(13153,plain,
% 2.00/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s11)) | (~always25(s99)) | always25(s11))),
% 2.00/2.16 inference(quant_inst,[status(thm)],[])).
% 2.00/2.16 tff(13154,plain,
% 2.00/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s11) | (~trans(s99, s11))),
% 2.00/2.16 inference(modus_ponens,[status(thm)],[13153, 13152])).
% 2.00/2.16 tff(13155,plain,
% 2.00/2.16 ($false),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[13154, 11507, 3934, 13016, 8728])).
% 2.00/2.16 tff(13156,plain,(~trans(s99, s11)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.16 tff(13157,plain,
% 2.00/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s40) | (~trans(s99, s40)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s40) | (~trans(s99, s40)))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(13158,plain,
% 2.00/2.16 (((~trans(s99, s40)) | (~always25(s99)) | always25(s40)) <=> ((~always25(s99)) | always25(s40) | (~trans(s99, s40)))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(13159,plain,
% 2.00/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s40)) | (~always25(s99)) | always25(s40))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s40) | (~trans(s99, s40))))),
% 2.00/2.16 inference(monotonicity,[status(thm)],[13158])).
% 2.00/2.16 tff(13160,plain,
% 2.00/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s40)) | (~always25(s99)) | always25(s40))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s40) | (~trans(s99, s40)))),
% 2.00/2.16 inference(transitivity,[status(thm)],[13159, 13157])).
% 2.00/2.16 tff(13161,plain,
% 2.00/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s40)) | (~always25(s99)) | always25(s40))),
% 2.00/2.16 inference(quant_inst,[status(thm)],[])).
% 2.00/2.16 tff(13162,plain,
% 2.00/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s40) | (~trans(s99, s40))),
% 2.00/2.16 inference(modus_ponens,[status(thm)],[13161, 13160])).
% 2.00/2.16 tff(13163,plain,
% 2.00/2.16 ($false),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[13162, 11518, 3934, 13016, 8520])).
% 2.00/2.16 tff(13164,plain,(~trans(s99, s40)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.16 tff(13165,plain,
% 2.00/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s57, s58)) | (~always25(s57)) | always25(s58))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s57, s58)) | (~always25(s57)) | always25(s58))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(13166,plain,
% 2.00/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s57, s58)) | (~always25(s57)) | always25(s58))),
% 2.00/2.16 inference(quant_inst,[status(thm)],[])).
% 2.00/2.16 tff(13167,plain,
% 2.00/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s57, s58)) | (~always25(s57)) | always25(s58)),
% 2.00/2.16 inference(modus_ponens,[status(thm)],[13166, 13165])).
% 2.00/2.16 tff(13168,plain,
% 2.00/2.16 ((~always25(s57)) | always25(s58)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[13167, 3934, 5042])).
% 2.00/2.16 tff(13169,plain,
% 2.00/2.16 (~always25(s57)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[13168, 8396])).
% 2.00/2.16 tff(13170,plain,
% 2.00/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s57) | (~trans(s99, s57)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s57) | (~trans(s99, s57)))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(13171,plain,
% 2.00/2.16 (((~trans(s99, s57)) | (~always25(s99)) | always25(s57)) <=> ((~always25(s99)) | always25(s57) | (~trans(s99, s57)))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(13172,plain,
% 2.00/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s57)) | (~always25(s99)) | always25(s57))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s57) | (~trans(s99, s57))))),
% 2.00/2.16 inference(monotonicity,[status(thm)],[13171])).
% 2.00/2.16 tff(13173,plain,
% 2.00/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s57)) | (~always25(s99)) | always25(s57))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s57) | (~trans(s99, s57)))),
% 2.00/2.16 inference(transitivity,[status(thm)],[13172, 13170])).
% 2.00/2.16 tff(13174,plain,
% 2.00/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s57)) | (~always25(s99)) | always25(s57))),
% 2.00/2.16 inference(quant_inst,[status(thm)],[])).
% 2.00/2.16 tff(13175,plain,
% 2.00/2.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s57) | (~trans(s99, s57))),
% 2.00/2.16 inference(modus_ponens,[status(thm)],[13174, 13173])).
% 2.00/2.16 tff(13176,plain,
% 2.00/2.16 ($false),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[13175, 11529, 3934, 13016, 13169])).
% 2.00/2.16 tff(13177,plain,(~trans(s99, s57)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.16 tff(13178,plain,
% 2.00/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s54) | (~trans(s99, s54)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s54) | (~trans(s99, s54)))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(13179,plain,
% 2.00/2.16 (((~trans(s99, s54)) | (~always25(s99)) | always25(s54)) <=> ((~always25(s99)) | always25(s54) | (~trans(s99, s54)))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(13180,plain,
% 2.00/2.16 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s54)) | (~always25(s99)) | always25(s54))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s54) | (~trans(s99, s54))))),
% 2.00/2.17 inference(monotonicity,[status(thm)],[13179])).
% 2.00/2.17 tff(13181,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s54)) | (~always25(s99)) | always25(s54))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s54) | (~trans(s99, s54)))),
% 2.00/2.17 inference(transitivity,[status(thm)],[13180, 13178])).
% 2.00/2.17 tff(13182,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s54)) | (~always25(s99)) | always25(s54))),
% 2.00/2.17 inference(quant_inst,[status(thm)],[])).
% 2.00/2.17 tff(13183,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s54) | (~trans(s99, s54))),
% 2.00/2.17 inference(modus_ponens,[status(thm)],[13182, 13181])).
% 2.00/2.17 tff(13184,plain,
% 2.00/2.17 ($false),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[13183, 11540, 3934, 13016, 8425])).
% 2.00/2.17 tff(13185,plain,(~trans(s99, s54)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.17 tff(13186,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s51) | (~trans(s99, s51)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s51) | (~trans(s99, s51)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13187,plain,
% 2.00/2.17 (((~trans(s99, s51)) | (~always25(s99)) | always25(s51)) <=> ((~always25(s99)) | always25(s51) | (~trans(s99, s51)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13188,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s51)) | (~always25(s99)) | always25(s51))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s51) | (~trans(s99, s51))))),
% 2.00/2.17 inference(monotonicity,[status(thm)],[13187])).
% 2.00/2.17 tff(13189,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s51)) | (~always25(s99)) | always25(s51))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s51) | (~trans(s99, s51)))),
% 2.00/2.17 inference(transitivity,[status(thm)],[13188, 13186])).
% 2.00/2.17 tff(13190,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s51)) | (~always25(s99)) | always25(s51))),
% 2.00/2.17 inference(quant_inst,[status(thm)],[])).
% 2.00/2.17 tff(13191,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s51) | (~trans(s99, s51))),
% 2.00/2.17 inference(modus_ponens,[status(thm)],[13190, 13189])).
% 2.00/2.17 tff(13192,plain,
% 2.00/2.17 ($false),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[13191, 11551, 3934, 13016, 8445])).
% 2.00/2.17 tff(13193,plain,(~trans(s99, s51)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.17 tff(13194,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s65, s66)) | (~always25(s65)) | always25(s66))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s65, s66)) | (~always25(s65)) | always25(s66))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13195,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s65, s66)) | (~always25(s65)) | always25(s66))),
% 2.00/2.17 inference(quant_inst,[status(thm)],[])).
% 2.00/2.17 tff(13196,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s65, s66)) | (~always25(s65)) | always25(s66)),
% 2.00/2.17 inference(modus_ponens,[status(thm)],[13195, 13194])).
% 2.00/2.17 tff(13197,plain,
% 2.00/2.17 ((~always25(s65)) | always25(s66)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[13196, 3934, 5670])).
% 2.00/2.17 tff(13198,plain,
% 2.00/2.17 (~always25(s65)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[13197, 8338])).
% 2.00/2.17 tff(13199,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s65) | (~trans(s99, s65)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s65) | (~trans(s99, s65)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13200,plain,
% 2.00/2.17 (((~trans(s99, s65)) | (~always25(s99)) | always25(s65)) <=> ((~always25(s99)) | always25(s65) | (~trans(s99, s65)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13201,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s65)) | (~always25(s99)) | always25(s65))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s65) | (~trans(s99, s65))))),
% 2.00/2.17 inference(monotonicity,[status(thm)],[13200])).
% 2.00/2.17 tff(13202,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s65)) | (~always25(s99)) | always25(s65))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s65) | (~trans(s99, s65)))),
% 2.00/2.17 inference(transitivity,[status(thm)],[13201, 13199])).
% 2.00/2.17 tff(13203,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s65)) | (~always25(s99)) | always25(s65))),
% 2.00/2.17 inference(quant_inst,[status(thm)],[])).
% 2.00/2.17 tff(13204,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s65) | (~trans(s99, s65))),
% 2.00/2.17 inference(modus_ponens,[status(thm)],[13203, 13202])).
% 2.00/2.17 tff(13205,plain,
% 2.00/2.17 ($false),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[13204, 11233, 3934, 13016, 13198])).
% 2.00/2.17 tff(13206,plain,(~trans(s99, s65)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.17 tff(13207,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s72) | (~trans(s99, s72)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s72) | (~trans(s99, s72)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13208,plain,
% 2.00/2.17 (((~trans(s99, s72)) | (~always25(s99)) | always25(s72)) <=> ((~always25(s99)) | always25(s72) | (~trans(s99, s72)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13209,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s72)) | (~always25(s99)) | always25(s72))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s72) | (~trans(s99, s72))))),
% 2.00/2.17 inference(monotonicity,[status(thm)],[13208])).
% 2.00/2.17 tff(13210,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s72)) | (~always25(s99)) | always25(s72))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s72) | (~trans(s99, s72)))),
% 2.00/2.17 inference(transitivity,[status(thm)],[13209, 13207])).
% 2.00/2.17 tff(13211,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s72)) | (~always25(s99)) | always25(s72))),
% 2.00/2.17 inference(quant_inst,[status(thm)],[])).
% 2.00/2.17 tff(13212,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s72) | (~trans(s99, s72))),
% 2.00/2.17 inference(modus_ponens,[status(thm)],[13211, 13210])).
% 2.00/2.17 tff(13213,plain,
% 2.00/2.17 ($false),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[13212, 11222, 3934, 13016, 8295])).
% 2.00/2.17 tff(13214,plain,(~trans(s99, s72)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.17 tff(13215,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s81, s82)) | (~always25(s81)) | always25(s82))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s81, s82)) | (~always25(s81)) | always25(s82))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13216,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s81, s82)) | (~always25(s81)) | always25(s82))),
% 2.00/2.17 inference(quant_inst,[status(thm)],[])).
% 2.00/2.17 tff(13217,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s81, s82)) | (~always25(s81)) | always25(s82)),
% 2.00/2.17 inference(modus_ponens,[status(thm)],[13216, 13215])).
% 2.00/2.17 tff(13218,plain,
% 2.00/2.17 ((~always25(s81)) | always25(s82)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[13217, 3934, 6926])).
% 2.00/2.17 tff(13219,plain,
% 2.00/2.17 (~always25(s81)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[13218, 8222])).
% 2.00/2.17 tff(13220,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s81) | (~trans(s99, s81)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s81) | (~trans(s99, s81)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13221,plain,
% 2.00/2.17 (((~trans(s99, s81)) | (~always25(s99)) | always25(s81)) <=> ((~always25(s99)) | always25(s81) | (~trans(s99, s81)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13222,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s81)) | (~always25(s99)) | always25(s81))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s81) | (~trans(s99, s81))))),
% 2.00/2.17 inference(monotonicity,[status(thm)],[13221])).
% 2.00/2.17 tff(13223,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s81)) | (~always25(s99)) | always25(s81))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s81) | (~trans(s99, s81)))),
% 2.00/2.17 inference(transitivity,[status(thm)],[13222, 13220])).
% 2.00/2.17 tff(13224,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s81)) | (~always25(s99)) | always25(s81))),
% 2.00/2.17 inference(quant_inst,[status(thm)],[])).
% 2.00/2.17 tff(13225,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s81) | (~trans(s99, s81))),
% 2.00/2.17 inference(modus_ponens,[status(thm)],[13224, 13223])).
% 2.00/2.17 tff(13226,plain,
% 2.00/2.17 ($false),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[13225, 11321, 3934, 13016, 13219])).
% 2.00/2.17 tff(13227,plain,(~trans(s99, s81)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.17 tff(13228,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s92) | (~trans(s99, s92)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s92) | (~trans(s99, s92)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13229,plain,
% 2.00/2.17 (((~trans(s99, s92)) | (~always25(s99)) | always25(s92)) <=> ((~always25(s99)) | always25(s92) | (~trans(s99, s92)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13230,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s92)) | (~always25(s99)) | always25(s92))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s92) | (~trans(s99, s92))))),
% 2.00/2.17 inference(monotonicity,[status(thm)],[13229])).
% 2.00/2.17 tff(13231,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s92)) | (~always25(s99)) | always25(s92))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s92) | (~trans(s99, s92)))),
% 2.00/2.17 inference(transitivity,[status(thm)],[13230, 13228])).
% 2.00/2.17 tff(13232,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s92)) | (~always25(s99)) | always25(s92))),
% 2.00/2.17 inference(quant_inst,[status(thm)],[])).
% 2.00/2.17 tff(13233,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s92) | (~trans(s99, s92))),
% 2.00/2.17 inference(modus_ponens,[status(thm)],[13232, 13231])).
% 2.00/2.17 tff(13234,plain,
% 2.00/2.17 ($false),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[13233, 12995, 3934, 13016, 8150])).
% 2.00/2.17 tff(13235,plain,(~trans(s99, s92)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.17 tff(13236,assumption,(always25(s99)), introduced(assumption)).
% 2.00/2.17 tff(13237,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s96) | (~trans(s99, s96)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s96) | (~trans(s99, s96)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13238,plain,
% 2.00/2.17 (((~trans(s99, s96)) | (~always25(s99)) | always25(s96)) <=> ((~always25(s99)) | always25(s96) | (~trans(s99, s96)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13239,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s96)) | (~always25(s99)) | always25(s96))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s96) | (~trans(s99, s96))))),
% 2.00/2.17 inference(monotonicity,[status(thm)],[13238])).
% 2.00/2.17 tff(13240,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s96)) | (~always25(s99)) | always25(s96))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s96) | (~trans(s99, s96)))),
% 2.00/2.17 inference(transitivity,[status(thm)],[13239, 13237])).
% 2.00/2.17 tff(13241,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s96)) | (~always25(s99)) | always25(s96))),
% 2.00/2.17 inference(quant_inst,[status(thm)],[])).
% 2.00/2.17 tff(13242,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s96) | (~trans(s99, s96))),
% 2.00/2.17 inference(modus_ponens,[status(thm)],[13241, 13240])).
% 2.00/2.17 tff(13243,plain,
% 2.00/2.17 ($false),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[13242, 12244, 3934, 13236, 8121])).
% 2.00/2.17 tff(13244,plain,((~trans(s99, s96)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.17 tff(13245,plain,
% 2.00/2.17 (~trans(s99, s96)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[13244, 13016])).
% 2.00/2.17 tff(13246,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s91) | (~trans(s99, s91)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s91) | (~trans(s99, s91)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13247,plain,
% 2.00/2.17 (((~trans(s99, s91)) | (~always25(s99)) | always25(s91)) <=> ((~always25(s99)) | always25(s91) | (~trans(s99, s91)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13248,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s91)) | (~always25(s99)) | always25(s91))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s91) | (~trans(s99, s91))))),
% 2.00/2.17 inference(monotonicity,[status(thm)],[13247])).
% 2.00/2.17 tff(13249,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s91)) | (~always25(s99)) | always25(s91))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s91) | (~trans(s99, s91)))),
% 2.00/2.17 inference(transitivity,[status(thm)],[13248, 13246])).
% 2.00/2.17 tff(13250,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s91)) | (~always25(s99)) | always25(s91))),
% 2.00/2.17 inference(quant_inst,[status(thm)],[])).
% 2.00/2.17 tff(13251,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s91) | (~trans(s99, s91))),
% 2.00/2.17 inference(modus_ponens,[status(thm)],[13250, 13249])).
% 2.00/2.17 tff(13252,plain,
% 2.00/2.17 ($false),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[13251, 11244, 3934, 13236, 8155])).
% 2.00/2.17 tff(13253,plain,((~trans(s99, s91)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.17 tff(13254,plain,
% 2.00/2.17 (~trans(s99, s91)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[13253, 13016])).
% 2.00/2.17 tff(13255,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s75) | (~trans(s99, s75)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s75) | (~trans(s99, s75)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13256,plain,
% 2.00/2.17 (((~trans(s99, s75)) | (~always25(s99)) | always25(s75)) <=> ((~always25(s99)) | always25(s75) | (~trans(s99, s75)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13257,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s75)) | (~always25(s99)) | always25(s75))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s75) | (~trans(s99, s75))))),
% 2.00/2.17 inference(monotonicity,[status(thm)],[13256])).
% 2.00/2.17 tff(13258,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s75)) | (~always25(s99)) | always25(s75))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s75) | (~trans(s99, s75)))),
% 2.00/2.17 inference(transitivity,[status(thm)],[13257, 13255])).
% 2.00/2.17 tff(13259,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s75)) | (~always25(s99)) | always25(s75))),
% 2.00/2.17 inference(quant_inst,[status(thm)],[])).
% 2.00/2.17 tff(13260,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s75) | (~trans(s99, s75))),
% 2.00/2.17 inference(modus_ponens,[status(thm)],[13259, 13258])).
% 2.00/2.17 tff(13261,plain,
% 2.00/2.17 ($false),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[13260, 11255, 3934, 13236, 8271])).
% 2.00/2.17 tff(13262,plain,((~trans(s99, s75)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.17 tff(13263,plain,
% 2.00/2.17 (~trans(s99, s75)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[13262, 13016])).
% 2.00/2.17 tff(13264,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s78) | (~trans(s99, s78)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s78) | (~trans(s99, s78)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13265,plain,
% 2.00/2.17 (((~trans(s99, s78)) | (~always25(s99)) | always25(s78)) <=> ((~always25(s99)) | always25(s78) | (~trans(s99, s78)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13266,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s78)) | (~always25(s99)) | always25(s78))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s78) | (~trans(s99, s78))))),
% 2.00/2.17 inference(monotonicity,[status(thm)],[13265])).
% 2.00/2.17 tff(13267,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s78)) | (~always25(s99)) | always25(s78))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s78) | (~trans(s99, s78)))),
% 2.00/2.17 inference(transitivity,[status(thm)],[13266, 13264])).
% 2.00/2.17 tff(13268,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s78)) | (~always25(s99)) | always25(s78))),
% 2.00/2.17 inference(quant_inst,[status(thm)],[])).
% 2.00/2.17 tff(13269,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s78) | (~trans(s99, s78))),
% 2.00/2.17 inference(modus_ponens,[status(thm)],[13268, 13267])).
% 2.00/2.17 tff(13270,plain,
% 2.00/2.17 ($false),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[13269, 11277, 3934, 13236, 8251])).
% 2.00/2.17 tff(13271,plain,((~trans(s99, s78)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.17 tff(13272,plain,
% 2.00/2.17 (~trans(s99, s78)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[13271, 13016])).
% 2.00/2.17 tff(13273,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s74) | (~trans(s99, s74)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s74) | (~trans(s99, s74)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13274,plain,
% 2.00/2.17 (((~trans(s99, s74)) | (~always25(s99)) | always25(s74)) <=> ((~always25(s99)) | always25(s74) | (~trans(s99, s74)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13275,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s74)) | (~always25(s99)) | always25(s74))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s74) | (~trans(s99, s74))))),
% 2.00/2.17 inference(monotonicity,[status(thm)],[13274])).
% 2.00/2.17 tff(13276,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s74)) | (~always25(s99)) | always25(s74))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s74) | (~trans(s99, s74)))),
% 2.00/2.17 inference(transitivity,[status(thm)],[13275, 13273])).
% 2.00/2.17 tff(13277,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s74)) | (~always25(s99)) | always25(s74))),
% 2.00/2.17 inference(quant_inst,[status(thm)],[])).
% 2.00/2.17 tff(13278,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s74) | (~trans(s99, s74))),
% 2.00/2.17 inference(modus_ponens,[status(thm)],[13277, 13276])).
% 2.00/2.17 tff(13279,plain,
% 2.00/2.17 ($false),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[13278, 11288, 3934, 13236, 8280])).
% 2.00/2.17 tff(13280,plain,((~trans(s99, s74)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.17 tff(13281,plain,
% 2.00/2.17 (~trans(s99, s74)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[13280, 13016])).
% 2.00/2.17 tff(13282,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s45, s46)) | (~always25(s45)) | always25(s46))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s45, s46)) | (~always25(s45)) | always25(s46))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13283,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s45, s46)) | (~always25(s45)) | always25(s46))),
% 2.00/2.17 inference(quant_inst,[status(thm)],[])).
% 2.00/2.17 tff(13284,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s45, s46)) | (~always25(s45)) | always25(s46)),
% 2.00/2.17 inference(modus_ponens,[status(thm)],[13283, 13282])).
% 2.00/2.17 tff(13285,plain,
% 2.00/2.17 ((~always25(s45)) | always25(s46)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[13284, 3934, 4081])).
% 2.00/2.17 tff(13286,plain,
% 2.00/2.17 (~always25(s45)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[13285, 8483])).
% 2.00/2.17 tff(13287,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s45) | (~trans(s99, s45)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s45) | (~trans(s99, s45)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13288,plain,
% 2.00/2.17 (((~trans(s99, s45)) | (~always25(s99)) | always25(s45)) <=> ((~always25(s99)) | always25(s45) | (~trans(s99, s45)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13289,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s45)) | (~always25(s99)) | always25(s45))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s45) | (~trans(s99, s45))))),
% 2.00/2.17 inference(monotonicity,[status(thm)],[13288])).
% 2.00/2.17 tff(13290,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s45)) | (~always25(s99)) | always25(s45))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s45) | (~trans(s99, s45)))),
% 2.00/2.17 inference(transitivity,[status(thm)],[13289, 13287])).
% 2.00/2.17 tff(13291,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s45)) | (~always25(s99)) | always25(s45))),
% 2.00/2.17 inference(quant_inst,[status(thm)],[])).
% 2.00/2.17 tff(13292,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s45) | (~trans(s99, s45))),
% 2.00/2.17 inference(modus_ponens,[status(thm)],[13291, 13290])).
% 2.00/2.17 tff(13293,plain,
% 2.00/2.17 ($false),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[13292, 11299, 3934, 13236, 13286])).
% 2.00/2.17 tff(13294,plain,((~trans(s99, s45)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.17 tff(13295,plain,
% 2.00/2.17 (~trans(s99, s45)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[13294, 13016])).
% 2.00/2.17 tff(13296,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s90) | (~trans(s99, s90)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s90) | (~trans(s99, s90)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13297,plain,
% 2.00/2.17 (((~trans(s99, s90)) | (~always25(s99)) | always25(s90)) <=> ((~always25(s99)) | always25(s90) | (~trans(s99, s90)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13298,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s90)) | (~always25(s99)) | always25(s90))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s90) | (~trans(s99, s90))))),
% 2.00/2.17 inference(monotonicity,[status(thm)],[13297])).
% 2.00/2.17 tff(13299,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s90)) | (~always25(s99)) | always25(s90))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s90) | (~trans(s99, s90)))),
% 2.00/2.17 inference(transitivity,[status(thm)],[13298, 13296])).
% 2.00/2.17 tff(13300,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s90)) | (~always25(s99)) | always25(s90))),
% 2.00/2.17 inference(quant_inst,[status(thm)],[])).
% 2.00/2.17 tff(13301,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s90) | (~trans(s99, s90))),
% 2.00/2.17 inference(modus_ponens,[status(thm)],[13300, 13299])).
% 2.00/2.17 tff(13302,plain,
% 2.00/2.17 ($false),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[13301, 11310, 3934, 13236, 8164])).
% 2.00/2.17 tff(13303,plain,((~trans(s99, s90)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.17 tff(13304,plain,
% 2.00/2.17 (~trans(s99, s90)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[13303, 13016])).
% 2.00/2.17 tff(13305,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s84) | (~trans(s99, s84)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s84) | (~trans(s99, s84)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13306,plain,
% 2.00/2.17 (((~trans(s99, s84)) | (~always25(s99)) | always25(s84)) <=> ((~always25(s99)) | always25(s84) | (~trans(s99, s84)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13307,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s84)) | (~always25(s99)) | always25(s84))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s84) | (~trans(s99, s84))))),
% 2.00/2.17 inference(monotonicity,[status(thm)],[13306])).
% 2.00/2.17 tff(13308,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s84)) | (~always25(s99)) | always25(s84))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s84) | (~trans(s99, s84)))),
% 2.00/2.17 inference(transitivity,[status(thm)],[13307, 13305])).
% 2.00/2.17 tff(13309,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s84)) | (~always25(s99)) | always25(s84))),
% 2.00/2.17 inference(quant_inst,[status(thm)],[])).
% 2.00/2.17 tff(13310,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s84) | (~trans(s99, s84))),
% 2.00/2.17 inference(modus_ponens,[status(thm)],[13309, 13308])).
% 2.00/2.17 tff(13311,plain,
% 2.00/2.17 ($false),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[13310, 11419, 3934, 13236, 8208])).
% 2.00/2.17 tff(13312,plain,((~trans(s99, s84)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.17 tff(13313,plain,
% 2.00/2.17 (~trans(s99, s84)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[13312, 13016])).
% 2.00/2.17 tff(13314,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s86) | (~trans(s99, s86)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s86) | (~trans(s99, s86)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13315,plain,
% 2.00/2.17 (((~trans(s99, s86)) | (~always25(s99)) | always25(s86)) <=> ((~always25(s99)) | always25(s86) | (~trans(s99, s86)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13316,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s86)) | (~always25(s99)) | always25(s86))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s86) | (~trans(s99, s86))))),
% 2.00/2.17 inference(monotonicity,[status(thm)],[13315])).
% 2.00/2.17 tff(13317,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s86)) | (~always25(s99)) | always25(s86))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s86) | (~trans(s99, s86)))),
% 2.00/2.17 inference(transitivity,[status(thm)],[13316, 13314])).
% 2.00/2.17 tff(13318,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s86)) | (~always25(s99)) | always25(s86))),
% 2.00/2.17 inference(quant_inst,[status(thm)],[])).
% 2.00/2.17 tff(13319,plain,
% 2.00/2.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s86) | (~trans(s99, s86))),
% 2.00/2.17 inference(modus_ponens,[status(thm)],[13318, 13317])).
% 2.00/2.17 tff(13320,plain,
% 2.00/2.17 ($false),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[13319, 11485, 3934, 13236, 8193])).
% 2.00/2.17 tff(13321,plain,((~trans(s99, s86)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.17 tff(13322,plain,
% 2.00/2.17 (~trans(s99, s86)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[13321, 13016])).
% 2.00/2.17 tff(13323,assumption,(trans(s99, s1)), introduced(assumption)).
% 2.00/2.17 tff(13324,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s1) | (~trans(s99, s1)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s1) | (~trans(s99, s1)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13325,plain,
% 2.00/2.17 (((~trans(s99, s1)) | (~always25(s99)) | always25(s1)) <=> ((~always25(s99)) | always25(s1) | (~trans(s99, s1)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(13326,plain,
% 2.00/2.17 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s1)) | (~always25(s99)) | always25(s1))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s1) | (~trans(s99, s1))))),
% 2.00/2.18 inference(monotonicity,[status(thm)],[13325])).
% 2.00/2.18 tff(13327,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s1)) | (~always25(s99)) | always25(s1))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s1) | (~trans(s99, s1)))),
% 2.00/2.18 inference(transitivity,[status(thm)],[13326, 13324])).
% 2.00/2.18 tff(13328,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s1)) | (~always25(s99)) | always25(s1))),
% 2.00/2.18 inference(quant_inst,[status(thm)],[])).
% 2.00/2.18 tff(13329,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s1) | (~trans(s99, s1))),
% 2.00/2.18 inference(modus_ponens,[status(thm)],[13328, 13327])).
% 2.00/2.18 tff(13330,plain,
% 2.00/2.18 ($false),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13329, 13323, 3934, 13236, 8800])).
% 2.00/2.18 tff(13331,plain,((~trans(s99, s1)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.18 tff(13332,plain,
% 2.00/2.18 (~trans(s99, s1)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13331, 13016])).
% 2.00/2.18 tff(13333,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s4) | (~trans(s99, s4)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s4) | (~trans(s99, s4)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13334,plain,
% 2.00/2.18 (((~trans(s99, s4)) | (~always25(s99)) | always25(s4)) <=> ((~always25(s99)) | always25(s4) | (~trans(s99, s4)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13335,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s4)) | (~always25(s99)) | always25(s4))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s4) | (~trans(s99, s4))))),
% 2.00/2.18 inference(monotonicity,[status(thm)],[13334])).
% 2.00/2.18 tff(13336,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s4)) | (~always25(s99)) | always25(s4))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s4) | (~trans(s99, s4)))),
% 2.00/2.18 inference(transitivity,[status(thm)],[13335, 13333])).
% 2.00/2.18 tff(13337,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s4)) | (~always25(s99)) | always25(s4))),
% 2.00/2.18 inference(quant_inst,[status(thm)],[])).
% 2.00/2.18 tff(13338,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s4) | (~trans(s99, s4))),
% 2.00/2.18 inference(modus_ponens,[status(thm)],[13337, 13336])).
% 2.00/2.18 tff(13339,plain,
% 2.00/2.18 ($false),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13338, 11573, 3934, 13236, 8781])).
% 2.00/2.18 tff(13340,plain,((~trans(s99, s4)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.18 tff(13341,plain,
% 2.00/2.18 (~trans(s99, s4)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13340, 13016])).
% 2.00/2.18 tff(13342,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s94) | (~trans(s99, s94)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s94) | (~trans(s99, s94)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13343,plain,
% 2.00/2.18 (((~trans(s99, s94)) | (~always25(s99)) | always25(s94)) <=> ((~always25(s99)) | always25(s94) | (~trans(s99, s94)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13344,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s94)) | (~always25(s99)) | always25(s94))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s94) | (~trans(s99, s94))))),
% 2.00/2.18 inference(monotonicity,[status(thm)],[13343])).
% 2.00/2.18 tff(13345,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s94)) | (~always25(s99)) | always25(s94))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s94) | (~trans(s99, s94)))),
% 2.00/2.18 inference(transitivity,[status(thm)],[13344, 13342])).
% 2.00/2.18 tff(13346,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s94)) | (~always25(s99)) | always25(s94))),
% 2.00/2.18 inference(quant_inst,[status(thm)],[])).
% 2.00/2.18 tff(13347,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s94) | (~trans(s99, s94))),
% 2.00/2.18 inference(modus_ponens,[status(thm)],[13346, 13345])).
% 2.00/2.18 tff(13348,plain,
% 2.00/2.18 ($false),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13347, 11584, 3934, 13236, 8135])).
% 2.00/2.18 tff(13349,plain,((~trans(s99, s94)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.18 tff(13350,plain,
% 2.00/2.18 (~trans(s99, s94)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13349, 13016])).
% 2.00/2.18 tff(13351,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s59) | (~trans(s99, s59)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s59) | (~trans(s99, s59)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13352,plain,
% 2.00/2.18 (((~trans(s99, s59)) | (~always25(s99)) | always25(s59)) <=> ((~always25(s99)) | always25(s59) | (~trans(s99, s59)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13353,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s59)) | (~always25(s99)) | always25(s59))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s59) | (~trans(s99, s59))))),
% 2.00/2.18 inference(monotonicity,[status(thm)],[13352])).
% 2.00/2.18 tff(13354,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s59)) | (~always25(s99)) | always25(s59))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s59) | (~trans(s99, s59)))),
% 2.00/2.18 inference(transitivity,[status(thm)],[13353, 13351])).
% 2.00/2.18 tff(13355,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s59)) | (~always25(s99)) | always25(s59))),
% 2.00/2.18 inference(quant_inst,[status(thm)],[])).
% 2.00/2.18 tff(13356,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s59) | (~trans(s99, s59))),
% 2.00/2.18 inference(modus_ponens,[status(thm)],[13355, 13354])).
% 2.00/2.18 tff(13357,plain,
% 2.00/2.18 ($false),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13356, 11595, 3934, 13236, 8387])).
% 2.00/2.18 tff(13358,plain,((~trans(s99, s59)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.18 tff(13359,plain,
% 2.00/2.18 (~trans(s99, s59)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13358, 13016])).
% 2.00/2.18 tff(13360,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s53, s54)) | (~always25(s53)) | always25(s54))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s53, s54)) | (~always25(s53)) | always25(s54))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13361,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s53, s54)) | (~always25(s53)) | always25(s54))),
% 2.00/2.18 inference(quant_inst,[status(thm)],[])).
% 2.00/2.18 tff(13362,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s53, s54)) | (~always25(s53)) | always25(s54)),
% 2.00/2.18 inference(modus_ponens,[status(thm)],[13361, 13360])).
% 2.00/2.18 tff(13363,plain,
% 2.00/2.18 ((~always25(s53)) | always25(s54)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13362, 3934, 4709])).
% 2.00/2.18 tff(13364,plain,
% 2.00/2.18 (~always25(s53)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13363, 8425])).
% 2.00/2.18 tff(13365,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s53) | (~trans(s99, s53)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s53) | (~trans(s99, s53)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13366,plain,
% 2.00/2.18 (((~trans(s99, s53)) | (~always25(s99)) | always25(s53)) <=> ((~always25(s99)) | always25(s53) | (~trans(s99, s53)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13367,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s53)) | (~always25(s99)) | always25(s53))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s53) | (~trans(s99, s53))))),
% 2.00/2.18 inference(monotonicity,[status(thm)],[13366])).
% 2.00/2.18 tff(13368,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s53)) | (~always25(s99)) | always25(s53))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s53) | (~trans(s99, s53)))),
% 2.00/2.18 inference(transitivity,[status(thm)],[13367, 13365])).
% 2.00/2.18 tff(13369,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s53)) | (~always25(s99)) | always25(s53))),
% 2.00/2.18 inference(quant_inst,[status(thm)],[])).
% 2.00/2.18 tff(13370,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s53) | (~trans(s99, s53))),
% 2.00/2.18 inference(modus_ponens,[status(thm)],[13369, 13368])).
% 2.00/2.18 tff(13371,plain,
% 2.00/2.18 ($false),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13370, 11606, 3934, 13236, 13364])).
% 2.00/2.18 tff(13372,plain,((~trans(s99, s53)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.18 tff(13373,plain,
% 2.00/2.18 (~trans(s99, s53)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13372, 13016])).
% 2.00/2.18 tff(13374,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s18) | (~trans(s99, s18)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s18) | (~trans(s99, s18)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13375,plain,
% 2.00/2.18 (((~trans(s99, s18)) | (~always25(s99)) | always25(s18)) <=> ((~always25(s99)) | always25(s18) | (~trans(s99, s18)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13376,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s18)) | (~always25(s99)) | always25(s18))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s18) | (~trans(s99, s18))))),
% 2.00/2.18 inference(monotonicity,[status(thm)],[13375])).
% 2.00/2.18 tff(13377,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s18)) | (~always25(s99)) | always25(s18))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s18) | (~trans(s99, s18)))),
% 2.00/2.18 inference(transitivity,[status(thm)],[13376, 13374])).
% 2.00/2.18 tff(13378,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s18)) | (~always25(s99)) | always25(s18))),
% 2.00/2.18 inference(quant_inst,[status(thm)],[])).
% 2.00/2.18 tff(13379,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s18) | (~trans(s99, s18))),
% 2.00/2.18 inference(modus_ponens,[status(thm)],[13378, 13377])).
% 2.00/2.18 tff(13380,plain,
% 2.00/2.18 ($false),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13379, 11617, 3934, 13236, 8679])).
% 2.00/2.18 tff(13381,plain,((~trans(s99, s18)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.18 tff(13382,plain,
% 2.00/2.18 (~trans(s99, s18)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13381, 13016])).
% 2.00/2.18 tff(13383,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s69, s70)) | (~always25(s69)) | always25(s70))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s69, s70)) | (~always25(s69)) | always25(s70))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13384,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s69, s70)) | (~always25(s69)) | always25(s70))),
% 2.00/2.18 inference(quant_inst,[status(thm)],[])).
% 2.00/2.18 tff(13385,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s69, s70)) | (~always25(s69)) | always25(s70)),
% 2.00/2.18 inference(modus_ponens,[status(thm)],[13384, 13383])).
% 2.00/2.18 tff(13386,plain,
% 2.00/2.18 ((~always25(s69)) | always25(s70)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13385, 3934, 5965])).
% 2.00/2.18 tff(13387,plain,
% 2.00/2.18 (~always25(s69)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13386, 8309])).
% 2.00/2.18 tff(13388,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s69) | (~trans(s99, s69)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s69) | (~trans(s99, s69)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13389,plain,
% 2.00/2.18 (((~trans(s99, s69)) | (~always25(s99)) | always25(s69)) <=> ((~always25(s99)) | always25(s69) | (~trans(s99, s69)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13390,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s69)) | (~always25(s99)) | always25(s69))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s69) | (~trans(s99, s69))))),
% 2.00/2.18 inference(monotonicity,[status(thm)],[13389])).
% 2.00/2.18 tff(13391,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s69)) | (~always25(s99)) | always25(s69))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s69) | (~trans(s99, s69)))),
% 2.00/2.18 inference(transitivity,[status(thm)],[13390, 13388])).
% 2.00/2.18 tff(13392,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s69)) | (~always25(s99)) | always25(s69))),
% 2.00/2.18 inference(quant_inst,[status(thm)],[])).
% 2.00/2.18 tff(13393,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s69) | (~trans(s99, s69))),
% 2.00/2.18 inference(modus_ponens,[status(thm)],[13392, 13391])).
% 2.00/2.18 tff(13394,plain,
% 2.00/2.18 ($false),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13393, 11628, 3934, 13236, 13387])).
% 2.00/2.18 tff(13395,plain,((~trans(s99, s69)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.18 tff(13396,plain,
% 2.00/2.18 (~trans(s99, s69)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13395, 13016])).
% 2.00/2.18 tff(13397,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s93, s94)) | (~always25(s93)) | always25(s94))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s93, s94)) | (~always25(s93)) | always25(s94))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13398,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s93, s94)) | (~always25(s93)) | always25(s94))),
% 2.00/2.18 inference(quant_inst,[status(thm)],[])).
% 2.00/2.18 tff(13399,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s93, s94)) | (~always25(s93)) | always25(s94)),
% 2.00/2.18 inference(modus_ponens,[status(thm)],[13398, 13397])).
% 2.00/2.18 tff(13400,plain,
% 2.00/2.18 ((~always25(s93)) | always25(s94)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13399, 3934, 7849])).
% 2.00/2.18 tff(13401,plain,
% 2.00/2.18 (~always25(s93)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13400, 8135])).
% 2.00/2.18 tff(13402,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s93) | (~trans(s99, s93)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s93) | (~trans(s99, s93)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13403,plain,
% 2.00/2.18 (((~trans(s99, s93)) | (~always25(s99)) | always25(s93)) <=> ((~always25(s99)) | always25(s93) | (~trans(s99, s93)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13404,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s93)) | (~always25(s99)) | always25(s93))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s93) | (~trans(s99, s93))))),
% 2.00/2.18 inference(monotonicity,[status(thm)],[13403])).
% 2.00/2.18 tff(13405,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s93)) | (~always25(s99)) | always25(s93))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s93) | (~trans(s99, s93)))),
% 2.00/2.18 inference(transitivity,[status(thm)],[13404, 13402])).
% 2.00/2.18 tff(13406,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s93)) | (~always25(s99)) | always25(s93))),
% 2.00/2.18 inference(quant_inst,[status(thm)],[])).
% 2.00/2.18 tff(13407,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s93) | (~trans(s99, s93))),
% 2.00/2.18 inference(modus_ponens,[status(thm)],[13406, 13405])).
% 2.00/2.18 tff(13408,plain,
% 2.00/2.18 ($false),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13407, 11639, 3934, 13236, 13401])).
% 2.00/2.18 tff(13409,plain,((~trans(s99, s93)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.18 tff(13410,plain,
% 2.00/2.18 (~trans(s99, s93)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13409, 13016])).
% 2.00/2.18 tff(13411,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s61, s62)) | (~always25(s61)) | always25(s62))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s61, s62)) | (~always25(s61)) | always25(s62))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13412,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s61, s62)) | (~always25(s61)) | always25(s62))),
% 2.00/2.18 inference(quant_inst,[status(thm)],[])).
% 2.00/2.18 tff(13413,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s61, s62)) | (~always25(s61)) | always25(s62)),
% 2.00/2.18 inference(modus_ponens,[status(thm)],[13412, 13411])).
% 2.00/2.18 tff(13414,plain,
% 2.00/2.18 ((~always25(s61)) | always25(s62)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13413, 3934, 5337])).
% 2.00/2.18 tff(13415,plain,
% 2.00/2.18 (~always25(s61)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13414, 8367])).
% 2.00/2.18 tff(13416,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s61) | (~trans(s99, s61)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s61) | (~trans(s99, s61)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13417,plain,
% 2.00/2.18 (((~trans(s99, s61)) | (~always25(s99)) | always25(s61)) <=> ((~always25(s99)) | always25(s61) | (~trans(s99, s61)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13418,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s61)) | (~always25(s99)) | always25(s61))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s61) | (~trans(s99, s61))))),
% 2.00/2.18 inference(monotonicity,[status(thm)],[13417])).
% 2.00/2.18 tff(13419,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s61)) | (~always25(s99)) | always25(s61))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s61) | (~trans(s99, s61)))),
% 2.00/2.18 inference(transitivity,[status(thm)],[13418, 13416])).
% 2.00/2.18 tff(13420,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s61)) | (~always25(s99)) | always25(s61))),
% 2.00/2.18 inference(quant_inst,[status(thm)],[])).
% 2.00/2.18 tff(13421,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s61) | (~trans(s99, s61))),
% 2.00/2.18 inference(modus_ponens,[status(thm)],[13420, 13419])).
% 2.00/2.18 tff(13422,plain,
% 2.00/2.18 ($false),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13421, 11650, 3934, 13236, 13415])).
% 2.00/2.18 tff(13423,plain,((~trans(s99, s61)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.18 tff(13424,plain,
% 2.00/2.18 (~trans(s99, s61)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13423, 13016])).
% 2.00/2.18 tff(13425,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s30) | (~trans(s99, s30)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s30) | (~trans(s99, s30)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13426,plain,
% 2.00/2.18 (((~trans(s99, s30)) | (~always25(s99)) | always25(s30)) <=> ((~always25(s99)) | always25(s30) | (~trans(s99, s30)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13427,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s30)) | (~always25(s99)) | always25(s30))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s30) | (~trans(s99, s30))))),
% 2.00/2.18 inference(monotonicity,[status(thm)],[13426])).
% 2.00/2.18 tff(13428,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s30)) | (~always25(s99)) | always25(s30))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s30) | (~trans(s99, s30)))),
% 2.00/2.18 inference(transitivity,[status(thm)],[13427, 13425])).
% 2.00/2.18 tff(13429,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s30)) | (~always25(s99)) | always25(s30))),
% 2.00/2.18 inference(quant_inst,[status(thm)],[])).
% 2.00/2.18 tff(13430,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s30) | (~trans(s99, s30))),
% 2.00/2.18 inference(modus_ponens,[status(thm)],[13429, 13428])).
% 2.00/2.18 tff(13431,plain,
% 2.00/2.18 ($false),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13430, 11661, 3934, 13236, 8592])).
% 2.00/2.18 tff(13432,plain,((~trans(s99, s30)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.18 tff(13433,plain,
% 2.00/2.18 (~trans(s99, s30)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13432, 13016])).
% 2.00/2.18 tff(13434,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s36) | (~trans(s99, s36)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s36) | (~trans(s99, s36)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13435,plain,
% 2.00/2.18 (((~trans(s99, s36)) | (~always25(s99)) | always25(s36)) <=> ((~always25(s99)) | always25(s36) | (~trans(s99, s36)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13436,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s36)) | (~always25(s99)) | always25(s36))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s36) | (~trans(s99, s36))))),
% 2.00/2.18 inference(monotonicity,[status(thm)],[13435])).
% 2.00/2.18 tff(13437,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s36)) | (~always25(s99)) | always25(s36))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s36) | (~trans(s99, s36)))),
% 2.00/2.18 inference(transitivity,[status(thm)],[13436, 13434])).
% 2.00/2.18 tff(13438,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s36)) | (~always25(s99)) | always25(s36))),
% 2.00/2.18 inference(quant_inst,[status(thm)],[])).
% 2.00/2.18 tff(13439,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s36) | (~trans(s99, s36))),
% 2.00/2.18 inference(modus_ponens,[status(thm)],[13438, 13437])).
% 2.00/2.18 tff(13440,plain,
% 2.00/2.18 ($false),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13439, 11672, 3934, 13236, 8549])).
% 2.00/2.18 tff(13441,plain,((~trans(s99, s36)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.18 tff(13442,plain,
% 2.00/2.18 (~trans(s99, s36)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13441, 13016])).
% 2.00/2.18 tff(13443,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s26) | (~trans(s99, s26)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s26) | (~trans(s99, s26)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13444,plain,
% 2.00/2.18 (((~trans(s99, s26)) | (~always25(s99)) | always25(s26)) <=> ((~always25(s99)) | always25(s26) | (~trans(s99, s26)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13445,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s26)) | (~always25(s99)) | always25(s26))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s26) | (~trans(s99, s26))))),
% 2.00/2.18 inference(monotonicity,[status(thm)],[13444])).
% 2.00/2.18 tff(13446,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s26)) | (~always25(s99)) | always25(s26))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s26) | (~trans(s99, s26)))),
% 2.00/2.18 inference(transitivity,[status(thm)],[13445, 13443])).
% 2.00/2.18 tff(13447,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s26)) | (~always25(s99)) | always25(s26))),
% 2.00/2.18 inference(quant_inst,[status(thm)],[])).
% 2.00/2.18 tff(13448,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s26) | (~trans(s99, s26))),
% 2.00/2.18 inference(modus_ponens,[status(thm)],[13447, 13446])).
% 2.00/2.18 tff(13449,plain,
% 2.00/2.18 ($false),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13448, 11683, 3934, 13236, 8621])).
% 2.00/2.18 tff(13450,plain,((~trans(s99, s26)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.18 tff(13451,plain,
% 2.00/2.18 (~trans(s99, s26)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13450, 13016])).
% 2.00/2.18 tff(13452,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s70) | (~trans(s99, s70)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s70) | (~trans(s99, s70)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13453,plain,
% 2.00/2.18 (((~trans(s99, s70)) | (~always25(s99)) | always25(s70)) <=> ((~always25(s99)) | always25(s70) | (~trans(s99, s70)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13454,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s70)) | (~always25(s99)) | always25(s70))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s70) | (~trans(s99, s70))))),
% 2.00/2.18 inference(monotonicity,[status(thm)],[13453])).
% 2.00/2.18 tff(13455,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s70)) | (~always25(s99)) | always25(s70))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s70) | (~trans(s99, s70)))),
% 2.00/2.18 inference(transitivity,[status(thm)],[13454, 13452])).
% 2.00/2.18 tff(13456,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s70)) | (~always25(s99)) | always25(s70))),
% 2.00/2.18 inference(quant_inst,[status(thm)],[])).
% 2.00/2.18 tff(13457,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s70) | (~trans(s99, s70))),
% 2.00/2.18 inference(modus_ponens,[status(thm)],[13456, 13455])).
% 2.00/2.18 tff(13458,plain,
% 2.00/2.18 ($false),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13457, 11694, 3934, 13236, 8309])).
% 2.00/2.18 tff(13459,plain,((~trans(s99, s70)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.18 tff(13460,plain,
% 2.00/2.18 (~trans(s99, s70)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13459, 13016])).
% 2.00/2.18 tff(13461,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s19) | (~trans(s99, s19)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s19) | (~trans(s99, s19)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13462,plain,
% 2.00/2.18 (((~trans(s99, s19)) | (~always25(s99)) | always25(s19)) <=> ((~always25(s99)) | always25(s19) | (~trans(s99, s19)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13463,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s19)) | (~always25(s99)) | always25(s19))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s19) | (~trans(s99, s19))))),
% 2.00/2.18 inference(monotonicity,[status(thm)],[13462])).
% 2.00/2.18 tff(13464,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s19)) | (~always25(s99)) | always25(s19))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s19) | (~trans(s99, s19)))),
% 2.00/2.18 inference(transitivity,[status(thm)],[13463, 13461])).
% 2.00/2.18 tff(13465,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s19)) | (~always25(s99)) | always25(s19))),
% 2.00/2.18 inference(quant_inst,[status(thm)],[])).
% 2.00/2.18 tff(13466,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s19) | (~trans(s99, s19))),
% 2.00/2.18 inference(modus_ponens,[status(thm)],[13465, 13464])).
% 2.00/2.18 tff(13467,plain,
% 2.00/2.18 ($false),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13466, 11705, 3934, 13236, 8670])).
% 2.00/2.18 tff(13468,plain,((~trans(s99, s19)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.18 tff(13469,plain,
% 2.00/2.18 (~trans(s99, s19)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13468, 13016])).
% 2.00/2.18 tff(13470,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s63) | (~trans(s99, s63)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s63) | (~trans(s99, s63)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13471,plain,
% 2.00/2.18 (((~trans(s99, s63)) | (~always25(s99)) | always25(s63)) <=> ((~always25(s99)) | always25(s63) | (~trans(s99, s63)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13472,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s63)) | (~always25(s99)) | always25(s63))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s63) | (~trans(s99, s63))))),
% 2.00/2.18 inference(monotonicity,[status(thm)],[13471])).
% 2.00/2.18 tff(13473,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s63)) | (~always25(s99)) | always25(s63))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s63) | (~trans(s99, s63)))),
% 2.00/2.18 inference(transitivity,[status(thm)],[13472, 13470])).
% 2.00/2.18 tff(13474,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s63)) | (~always25(s99)) | always25(s63))),
% 2.00/2.18 inference(quant_inst,[status(thm)],[])).
% 2.00/2.18 tff(13475,plain,
% 2.00/2.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s63) | (~trans(s99, s63))),
% 2.00/2.18 inference(modus_ponens,[status(thm)],[13474, 13473])).
% 2.00/2.18 tff(13476,plain,
% 2.00/2.18 ($false),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13475, 11716, 3934, 13236, 8358])).
% 2.00/2.18 tff(13477,plain,((~trans(s99, s63)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.18 tff(13478,plain,
% 2.00/2.18 (~trans(s99, s63)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[13477, 13016])).
% 2.00/2.18 tff(13479,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s50) | (~trans(s99, s50)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s50) | (~trans(s99, s50)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13480,plain,
% 2.00/2.18 (((~trans(s99, s50)) | (~always25(s99)) | always25(s50)) <=> ((~always25(s99)) | always25(s50) | (~trans(s99, s50)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(13481,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s50)) | (~always25(s99)) | always25(s50))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s50) | (~trans(s99, s50))))),
% 2.00/2.18 inference(monotonicity,[status(thm)],[13480])).
% 2.00/2.18 tff(13482,plain,
% 2.00/2.18 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s50)) | (~always25(s99)) | always25(s50))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s50) | (~trans(s99, s50)))),
% 2.00/2.19 inference(transitivity,[status(thm)],[13481, 13479])).
% 2.00/2.19 tff(13483,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s50)) | (~always25(s99)) | always25(s50))),
% 2.00/2.19 inference(quant_inst,[status(thm)],[])).
% 2.00/2.19 tff(13484,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s50) | (~trans(s99, s50))),
% 2.00/2.19 inference(modus_ponens,[status(thm)],[13483, 13482])).
% 2.00/2.19 tff(13485,plain,
% 2.00/2.19 ($false),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13484, 11727, 3934, 13236, 8454])).
% 2.00/2.19 tff(13486,plain,((~trans(s99, s50)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.19 tff(13487,plain,
% 2.00/2.19 (~trans(s99, s50)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13486, 13016])).
% 2.00/2.19 tff(13488,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s66) | (~trans(s99, s66)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s66) | (~trans(s99, s66)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13489,plain,
% 2.00/2.19 (((~trans(s99, s66)) | (~always25(s99)) | always25(s66)) <=> ((~always25(s99)) | always25(s66) | (~trans(s99, s66)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13490,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s66)) | (~always25(s99)) | always25(s66))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s66) | (~trans(s99, s66))))),
% 2.00/2.19 inference(monotonicity,[status(thm)],[13489])).
% 2.00/2.19 tff(13491,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s66)) | (~always25(s99)) | always25(s66))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s66) | (~trans(s99, s66)))),
% 2.00/2.19 inference(transitivity,[status(thm)],[13490, 13488])).
% 2.00/2.19 tff(13492,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s66)) | (~always25(s99)) | always25(s66))),
% 2.00/2.19 inference(quant_inst,[status(thm)],[])).
% 2.00/2.19 tff(13493,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s66) | (~trans(s99, s66))),
% 2.00/2.19 inference(modus_ponens,[status(thm)],[13492, 13491])).
% 2.00/2.19 tff(13494,plain,
% 2.00/2.19 ($false),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13493, 11738, 3934, 13236, 8338])).
% 2.00/2.19 tff(13495,plain,((~trans(s99, s66)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.19 tff(13496,plain,
% 2.00/2.19 (~trans(s99, s66)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13495, 13016])).
% 2.00/2.19 tff(13497,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s58) | (~trans(s99, s58)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s58) | (~trans(s99, s58)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13498,plain,
% 2.00/2.19 (((~trans(s99, s58)) | (~always25(s99)) | always25(s58)) <=> ((~always25(s99)) | always25(s58) | (~trans(s99, s58)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13499,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s58)) | (~always25(s99)) | always25(s58))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s58) | (~trans(s99, s58))))),
% 2.00/2.19 inference(monotonicity,[status(thm)],[13498])).
% 2.00/2.19 tff(13500,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s58)) | (~always25(s99)) | always25(s58))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s58) | (~trans(s99, s58)))),
% 2.00/2.19 inference(transitivity,[status(thm)],[13499, 13497])).
% 2.00/2.19 tff(13501,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s58)) | (~always25(s99)) | always25(s58))),
% 2.00/2.19 inference(quant_inst,[status(thm)],[])).
% 2.00/2.19 tff(13502,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s58) | (~trans(s99, s58))),
% 2.00/2.19 inference(modus_ponens,[status(thm)],[13501, 13500])).
% 2.00/2.19 tff(13503,plain,
% 2.00/2.19 ($false),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13502, 11749, 3934, 13236, 8396])).
% 2.00/2.19 tff(13504,plain,((~trans(s99, s58)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.19 tff(13505,plain,
% 2.00/2.19 (~trans(s99, s58)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13504, 13016])).
% 2.00/2.19 tff(13506,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s87) | (~trans(s99, s87)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s87) | (~trans(s99, s87)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13507,plain,
% 2.00/2.19 (((~trans(s99, s87)) | (~always25(s99)) | always25(s87)) <=> ((~always25(s99)) | always25(s87) | (~trans(s99, s87)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13508,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s87)) | (~always25(s99)) | always25(s87))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s87) | (~trans(s99, s87))))),
% 2.00/2.19 inference(monotonicity,[status(thm)],[13507])).
% 2.00/2.19 tff(13509,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s87)) | (~always25(s99)) | always25(s87))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s87) | (~trans(s99, s87)))),
% 2.00/2.19 inference(transitivity,[status(thm)],[13508, 13506])).
% 2.00/2.19 tff(13510,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s87)) | (~always25(s99)) | always25(s87))),
% 2.00/2.19 inference(quant_inst,[status(thm)],[])).
% 2.00/2.19 tff(13511,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s87) | (~trans(s99, s87))),
% 2.00/2.19 inference(modus_ponens,[status(thm)],[13510, 13509])).
% 2.00/2.19 tff(13512,plain,
% 2.00/2.19 ($false),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13511, 11760, 3934, 13236, 8184])).
% 2.00/2.19 tff(13513,plain,((~trans(s99, s87)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.19 tff(13514,plain,
% 2.00/2.19 (~trans(s99, s87)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13513, 13016])).
% 2.00/2.19 tff(13515,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s80) | (~trans(s99, s80)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s80) | (~trans(s99, s80)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13516,plain,
% 2.00/2.19 (((~trans(s99, s80)) | (~always25(s99)) | always25(s80)) <=> ((~always25(s99)) | always25(s80) | (~trans(s99, s80)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13517,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s80)) | (~always25(s99)) | always25(s80))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s80) | (~trans(s99, s80))))),
% 2.00/2.19 inference(monotonicity,[status(thm)],[13516])).
% 2.00/2.19 tff(13518,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s80)) | (~always25(s99)) | always25(s80))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s80) | (~trans(s99, s80)))),
% 2.00/2.19 inference(transitivity,[status(thm)],[13517, 13515])).
% 2.00/2.19 tff(13519,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s80)) | (~always25(s99)) | always25(s80))),
% 2.00/2.19 inference(quant_inst,[status(thm)],[])).
% 2.00/2.19 tff(13520,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s80) | (~trans(s99, s80))),
% 2.00/2.19 inference(modus_ponens,[status(thm)],[13519, 13518])).
% 2.00/2.19 tff(13521,plain,
% 2.00/2.19 ($false),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13520, 11771, 3934, 13236, 8237])).
% 2.00/2.19 tff(13522,plain,((~trans(s99, s80)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.19 tff(13523,plain,
% 2.00/2.19 (~trans(s99, s80)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13522, 13016])).
% 2.00/2.19 tff(13524,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s16) | (~trans(s99, s16)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s16) | (~trans(s99, s16)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13525,plain,
% 2.00/2.19 (((~trans(s99, s16)) | (~always25(s99)) | always25(s16)) <=> ((~always25(s99)) | always25(s16) | (~trans(s99, s16)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13526,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s16)) | (~always25(s99)) | always25(s16))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s16) | (~trans(s99, s16))))),
% 2.00/2.19 inference(monotonicity,[status(thm)],[13525])).
% 2.00/2.19 tff(13527,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s16)) | (~always25(s99)) | always25(s16))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s16) | (~trans(s99, s16)))),
% 2.00/2.19 inference(transitivity,[status(thm)],[13526, 13524])).
% 2.00/2.19 tff(13528,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s16)) | (~always25(s99)) | always25(s16))),
% 2.00/2.19 inference(quant_inst,[status(thm)],[])).
% 2.00/2.19 tff(13529,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s16) | (~trans(s99, s16))),
% 2.00/2.19 inference(modus_ponens,[status(thm)],[13528, 13527])).
% 2.00/2.19 tff(13530,plain,
% 2.00/2.19 ($false),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13529, 11782, 3934, 13236, 8694])).
% 2.00/2.19 tff(13531,plain,((~trans(s99, s16)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.19 tff(13532,plain,
% 2.00/2.19 (~trans(s99, s16)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13531, 13016])).
% 2.00/2.19 tff(13533,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s49, s50)) | (~always25(s49)) | always25(s50))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s49, s50)) | (~always25(s49)) | always25(s50))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13534,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s49, s50)) | (~always25(s49)) | always25(s50))),
% 2.00/2.19 inference(quant_inst,[status(thm)],[])).
% 2.00/2.19 tff(13535,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s49, s50)) | (~always25(s49)) | always25(s50)),
% 2.00/2.19 inference(modus_ponens,[status(thm)],[13534, 13533])).
% 2.00/2.19 tff(13536,plain,
% 2.00/2.19 ((~always25(s49)) | always25(s50)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13535, 3934, 4414])).
% 2.00/2.19 tff(13537,plain,
% 2.00/2.19 (~always25(s49)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13536, 8454])).
% 2.00/2.19 tff(13538,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s49) | (~trans(s99, s49)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s49) | (~trans(s99, s49)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13539,plain,
% 2.00/2.19 (((~trans(s99, s49)) | (~always25(s99)) | always25(s49)) <=> ((~always25(s99)) | always25(s49) | (~trans(s99, s49)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13540,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s49)) | (~always25(s99)) | always25(s49))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s49) | (~trans(s99, s49))))),
% 2.00/2.19 inference(monotonicity,[status(thm)],[13539])).
% 2.00/2.19 tff(13541,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s49)) | (~always25(s99)) | always25(s49))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s49) | (~trans(s99, s49)))),
% 2.00/2.19 inference(transitivity,[status(thm)],[13540, 13538])).
% 2.00/2.19 tff(13542,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s49)) | (~always25(s99)) | always25(s49))),
% 2.00/2.19 inference(quant_inst,[status(thm)],[])).
% 2.00/2.19 tff(13543,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s49) | (~trans(s99, s49))),
% 2.00/2.19 inference(modus_ponens,[status(thm)],[13542, 13541])).
% 2.00/2.19 tff(13544,plain,
% 2.00/2.19 ($false),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13543, 11793, 3934, 13236, 13537])).
% 2.00/2.19 tff(13545,plain,((~trans(s99, s49)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.19 tff(13546,plain,
% 2.00/2.19 (~trans(s99, s49)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13545, 13016])).
% 2.00/2.19 tff(13547,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s33, s34)) | (~always25(s33)) | always25(s34))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s33, s34)) | (~always25(s33)) | always25(s34))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13548,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s33, s34)) | (~always25(s33)) | always25(s34))),
% 2.00/2.19 inference(quant_inst,[status(thm)],[])).
% 2.00/2.19 tff(13549,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s33, s34)) | (~always25(s33)) | always25(s34)),
% 2.00/2.19 inference(modus_ponens,[status(thm)],[13548, 13547])).
% 2.00/2.19 tff(13550,plain,
% 2.00/2.19 ((~always25(s33)) | always25(s34)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13549, 3934, 3087])).
% 2.00/2.19 tff(13551,plain,
% 2.00/2.19 (~always25(s33)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13550, 8563])).
% 2.00/2.19 tff(13552,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s33) | (~trans(s99, s33)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s33) | (~trans(s99, s33)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13553,plain,
% 2.00/2.19 (((~trans(s99, s33)) | (~always25(s99)) | always25(s33)) <=> ((~always25(s99)) | always25(s33) | (~trans(s99, s33)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13554,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s33)) | (~always25(s99)) | always25(s33))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s33) | (~trans(s99, s33))))),
% 2.00/2.19 inference(monotonicity,[status(thm)],[13553])).
% 2.00/2.19 tff(13555,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s33)) | (~always25(s99)) | always25(s33))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s33) | (~trans(s99, s33)))),
% 2.00/2.19 inference(transitivity,[status(thm)],[13554, 13552])).
% 2.00/2.19 tff(13556,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s33)) | (~always25(s99)) | always25(s33))),
% 2.00/2.19 inference(quant_inst,[status(thm)],[])).
% 2.00/2.19 tff(13557,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s33) | (~trans(s99, s33))),
% 2.00/2.19 inference(modus_ponens,[status(thm)],[13556, 13555])).
% 2.00/2.19 tff(13558,plain,
% 2.00/2.19 ($false),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13557, 11804, 3934, 13236, 13551])).
% 2.00/2.19 tff(13559,plain,((~trans(s99, s33)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.19 tff(13560,plain,
% 2.00/2.19 (~trans(s99, s33)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13559, 13016])).
% 2.00/2.19 tff(13561,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s13, s14)) | (~always25(s13)) | always25(s14))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s13, s14)) | (~always25(s13)) | always25(s14))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13562,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s13, s14)) | (~always25(s13)) | always25(s14))),
% 2.00/2.19 inference(quant_inst,[status(thm)],[])).
% 2.00/2.19 tff(13563,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s13, s14)) | (~always25(s13)) | always25(s14)),
% 2.00/2.19 inference(modus_ponens,[status(thm)],[13562, 13561])).
% 2.00/2.19 tff(13564,plain,
% 2.00/2.19 ((~always25(s13)) | always25(s14)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13563, 3934, 1536])).
% 2.00/2.19 tff(13565,plain,
% 2.00/2.19 (~always25(s13)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13564, 8708])).
% 2.00/2.19 tff(13566,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s13) | (~trans(s99, s13)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s13) | (~trans(s99, s13)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13567,plain,
% 2.00/2.19 (((~trans(s99, s13)) | (~always25(s99)) | always25(s13)) <=> ((~always25(s99)) | always25(s13) | (~trans(s99, s13)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13568,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s13)) | (~always25(s99)) | always25(s13))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s13) | (~trans(s99, s13))))),
% 2.00/2.19 inference(monotonicity,[status(thm)],[13567])).
% 2.00/2.19 tff(13569,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s13)) | (~always25(s99)) | always25(s13))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s13) | (~trans(s99, s13)))),
% 2.00/2.19 inference(transitivity,[status(thm)],[13568, 13566])).
% 2.00/2.19 tff(13570,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s13)) | (~always25(s99)) | always25(s13))),
% 2.00/2.19 inference(quant_inst,[status(thm)],[])).
% 2.00/2.19 tff(13571,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s13) | (~trans(s99, s13))),
% 2.00/2.19 inference(modus_ponens,[status(thm)],[13570, 13569])).
% 2.00/2.19 tff(13572,plain,
% 2.00/2.19 ($false),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13571, 11815, 3934, 13236, 13565])).
% 2.00/2.19 tff(13573,plain,((~trans(s99, s13)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.19 tff(13574,plain,
% 2.00/2.19 (~trans(s99, s13)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13573, 13016])).
% 2.00/2.19 tff(13575,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s77, s78)) | (~always25(s77)) | always25(s78))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s77, s78)) | (~always25(s77)) | always25(s78))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13576,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s77, s78)) | (~always25(s77)) | always25(s78))),
% 2.00/2.19 inference(quant_inst,[status(thm)],[])).
% 2.00/2.19 tff(13577,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s77, s78)) | (~always25(s77)) | always25(s78)),
% 2.00/2.19 inference(modus_ponens,[status(thm)],[13576, 13575])).
% 2.00/2.19 tff(13578,plain,
% 2.00/2.19 ((~always25(s77)) | always25(s78)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13577, 3934, 6593])).
% 2.00/2.19 tff(13579,plain,
% 2.00/2.19 (~always25(s77)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13578, 8251])).
% 2.00/2.19 tff(13580,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s77) | (~trans(s99, s77)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s77) | (~trans(s99, s77)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13581,plain,
% 2.00/2.19 (((~trans(s99, s77)) | (~always25(s99)) | always25(s77)) <=> ((~always25(s99)) | always25(s77) | (~trans(s99, s77)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13582,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s77)) | (~always25(s99)) | always25(s77))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s77) | (~trans(s99, s77))))),
% 2.00/2.19 inference(monotonicity,[status(thm)],[13581])).
% 2.00/2.19 tff(13583,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s77)) | (~always25(s99)) | always25(s77))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s77) | (~trans(s99, s77)))),
% 2.00/2.19 inference(transitivity,[status(thm)],[13582, 13580])).
% 2.00/2.19 tff(13584,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s77)) | (~always25(s99)) | always25(s77))),
% 2.00/2.19 inference(quant_inst,[status(thm)],[])).
% 2.00/2.19 tff(13585,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s77) | (~trans(s99, s77))),
% 2.00/2.19 inference(modus_ponens,[status(thm)],[13584, 13583])).
% 2.00/2.19 tff(13586,plain,
% 2.00/2.19 ($false),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13585, 11826, 3934, 13236, 13579])).
% 2.00/2.19 tff(13587,plain,((~trans(s99, s77)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.19 tff(13588,plain,
% 2.00/2.19 (~trans(s99, s77)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13587, 13016])).
% 2.00/2.19 tff(13589,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s46) | (~trans(s99, s46)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s46) | (~trans(s99, s46)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13590,plain,
% 2.00/2.19 (((~trans(s99, s46)) | (~always25(s99)) | always25(s46)) <=> ((~always25(s99)) | always25(s46) | (~trans(s99, s46)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13591,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s46)) | (~always25(s99)) | always25(s46))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s46) | (~trans(s99, s46))))),
% 2.00/2.19 inference(monotonicity,[status(thm)],[13590])).
% 2.00/2.19 tff(13592,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s46)) | (~always25(s99)) | always25(s46))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s46) | (~trans(s99, s46)))),
% 2.00/2.19 inference(transitivity,[status(thm)],[13591, 13589])).
% 2.00/2.19 tff(13593,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s46)) | (~always25(s99)) | always25(s46))),
% 2.00/2.19 inference(quant_inst,[status(thm)],[])).
% 2.00/2.19 tff(13594,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s46) | (~trans(s99, s46))),
% 2.00/2.19 inference(modus_ponens,[status(thm)],[13593, 13592])).
% 2.00/2.19 tff(13595,plain,
% 2.00/2.19 ($false),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13594, 11837, 3934, 13236, 8483])).
% 2.00/2.19 tff(13596,plain,((~trans(s99, s46)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.19 tff(13597,plain,
% 2.00/2.19 (~trans(s99, s46)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13596, 13016])).
% 2.00/2.19 tff(13598,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s47) | (~trans(s99, s47)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s47) | (~trans(s99, s47)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13599,plain,
% 2.00/2.19 (((~trans(s99, s47)) | (~always25(s99)) | always25(s47)) <=> ((~always25(s99)) | always25(s47) | (~trans(s99, s47)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13600,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s47)) | (~always25(s99)) | always25(s47))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s47) | (~trans(s99, s47))))),
% 2.00/2.19 inference(monotonicity,[status(thm)],[13599])).
% 2.00/2.19 tff(13601,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s47)) | (~always25(s99)) | always25(s47))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s47) | (~trans(s99, s47)))),
% 2.00/2.19 inference(transitivity,[status(thm)],[13600, 13598])).
% 2.00/2.19 tff(13602,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s47)) | (~always25(s99)) | always25(s47))),
% 2.00/2.19 inference(quant_inst,[status(thm)],[])).
% 2.00/2.19 tff(13603,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s47) | (~trans(s99, s47))),
% 2.00/2.19 inference(modus_ponens,[status(thm)],[13602, 13601])).
% 2.00/2.19 tff(13604,plain,
% 2.00/2.19 ($false),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13603, 11848, 3934, 13236, 8474])).
% 2.00/2.19 tff(13605,plain,((~trans(s99, s47)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.19 tff(13606,plain,
% 2.00/2.19 (~trans(s99, s47)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13605, 13016])).
% 2.00/2.19 tff(13607,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s89, s90)) | (~always25(s89)) | always25(s90))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s89, s90)) | (~always25(s89)) | always25(s90))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13608,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s89, s90)) | (~always25(s89)) | always25(s90))),
% 2.00/2.19 inference(quant_inst,[status(thm)],[])).
% 2.00/2.19 tff(13609,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s89, s90)) | (~always25(s89)) | always25(s90)),
% 2.00/2.19 inference(modus_ponens,[status(thm)],[13608, 13607])).
% 2.00/2.19 tff(13610,plain,
% 2.00/2.19 ((~always25(s89)) | always25(s90)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13609, 3934, 7554])).
% 2.00/2.19 tff(13611,plain,
% 2.00/2.19 (~always25(s89)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13610, 8164])).
% 2.00/2.19 tff(13612,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s89) | (~trans(s99, s89)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s89) | (~trans(s99, s89)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13613,plain,
% 2.00/2.19 (((~trans(s99, s89)) | (~always25(s99)) | always25(s89)) <=> ((~always25(s99)) | always25(s89) | (~trans(s99, s89)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13614,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s89)) | (~always25(s99)) | always25(s89))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s89) | (~trans(s99, s89))))),
% 2.00/2.19 inference(monotonicity,[status(thm)],[13613])).
% 2.00/2.19 tff(13615,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s89)) | (~always25(s99)) | always25(s89))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s89) | (~trans(s99, s89)))),
% 2.00/2.19 inference(transitivity,[status(thm)],[13614, 13612])).
% 2.00/2.19 tff(13616,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s89)) | (~always25(s99)) | always25(s89))),
% 2.00/2.19 inference(quant_inst,[status(thm)],[])).
% 2.00/2.19 tff(13617,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s89) | (~trans(s99, s89))),
% 2.00/2.19 inference(modus_ponens,[status(thm)],[13616, 13615])).
% 2.00/2.19 tff(13618,plain,
% 2.00/2.19 ($false),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13617, 11859, 3934, 13236, 13611])).
% 2.00/2.19 tff(13619,plain,((~trans(s99, s89)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.19 tff(13620,plain,
% 2.00/2.19 (~trans(s99, s89)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13619, 13016])).
% 2.00/2.19 tff(13621,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s88) | (~trans(s99, s88)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s88) | (~trans(s99, s88)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13622,plain,
% 2.00/2.19 (((~trans(s99, s88)) | (~always25(s99)) | always25(s88)) <=> ((~always25(s99)) | always25(s88) | (~trans(s99, s88)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13623,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s88)) | (~always25(s99)) | always25(s88))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s88) | (~trans(s99, s88))))),
% 2.00/2.19 inference(monotonicity,[status(thm)],[13622])).
% 2.00/2.19 tff(13624,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s88)) | (~always25(s99)) | always25(s88))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s88) | (~trans(s99, s88)))),
% 2.00/2.19 inference(transitivity,[status(thm)],[13623, 13621])).
% 2.00/2.19 tff(13625,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s88)) | (~always25(s99)) | always25(s88))),
% 2.00/2.19 inference(quant_inst,[status(thm)],[])).
% 2.00/2.19 tff(13626,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s88) | (~trans(s99, s88))),
% 2.00/2.19 inference(modus_ponens,[status(thm)],[13625, 13624])).
% 2.00/2.19 tff(13627,plain,
% 2.00/2.19 ($false),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13626, 11870, 3934, 13236, 8179])).
% 2.00/2.19 tff(13628,plain,((~trans(s99, s88)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.19 tff(13629,plain,
% 2.00/2.19 (~trans(s99, s88)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13628, 13016])).
% 2.00/2.19 tff(13630,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s60) | (~trans(s99, s60)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s60) | (~trans(s99, s60)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13631,plain,
% 2.00/2.19 (((~trans(s99, s60)) | (~always25(s99)) | always25(s60)) <=> ((~always25(s99)) | always25(s60) | (~trans(s99, s60)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13632,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s60)) | (~always25(s99)) | always25(s60))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s60) | (~trans(s99, s60))))),
% 2.00/2.19 inference(monotonicity,[status(thm)],[13631])).
% 2.00/2.19 tff(13633,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s60)) | (~always25(s99)) | always25(s60))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s60) | (~trans(s99, s60)))),
% 2.00/2.19 inference(transitivity,[status(thm)],[13632, 13630])).
% 2.00/2.19 tff(13634,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s60)) | (~always25(s99)) | always25(s60))),
% 2.00/2.19 inference(quant_inst,[status(thm)],[])).
% 2.00/2.19 tff(13635,plain,
% 2.00/2.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s60) | (~trans(s99, s60))),
% 2.00/2.19 inference(modus_ponens,[status(thm)],[13634, 13633])).
% 2.00/2.19 tff(13636,plain,
% 2.00/2.19 ($false),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13635, 11881, 3934, 13236, 8382])).
% 2.00/2.19 tff(13637,plain,((~trans(s99, s60)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.19 tff(13638,plain,
% 2.00/2.19 (~trans(s99, s60)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[13637, 13016])).
% 2.00/2.19 tff(13639,plain,
% 2.00/2.19 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s52) | (~trans(s99, s52)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s52) | (~trans(s99, s52)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(13640,plain,
% 2.00/2.19 (((~trans(s99, s52)) | (~always25(s99)) | always25(s52)) <=> ((~always25(s99)) | always25(s52) | (~trans(s99, s52)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(13641,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s52)) | (~always25(s99)) | always25(s52))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s52) | (~trans(s99, s52))))),
% 2.00/2.20 inference(monotonicity,[status(thm)],[13640])).
% 2.00/2.20 tff(13642,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s52)) | (~always25(s99)) | always25(s52))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s52) | (~trans(s99, s52)))),
% 2.00/2.20 inference(transitivity,[status(thm)],[13641, 13639])).
% 2.00/2.20 tff(13643,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s52)) | (~always25(s99)) | always25(s52))),
% 2.00/2.20 inference(quant_inst,[status(thm)],[])).
% 2.00/2.20 tff(13644,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s52) | (~trans(s99, s52))),
% 2.00/2.20 inference(modus_ponens,[status(thm)],[13643, 13642])).
% 2.00/2.20 tff(13645,plain,
% 2.00/2.20 ($false),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13644, 11892, 3934, 13236, 8440])).
% 2.00/2.20 tff(13646,plain,((~trans(s99, s52)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.20 tff(13647,plain,
% 2.00/2.20 (~trans(s99, s52)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13646, 13016])).
% 2.00/2.20 tff(13648,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s64) | (~trans(s99, s64)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s64) | (~trans(s99, s64)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(13649,plain,
% 2.00/2.20 (((~trans(s99, s64)) | (~always25(s99)) | always25(s64)) <=> ((~always25(s99)) | always25(s64) | (~trans(s99, s64)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(13650,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s64)) | (~always25(s99)) | always25(s64))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s64) | (~trans(s99, s64))))),
% 2.00/2.20 inference(monotonicity,[status(thm)],[13649])).
% 2.00/2.20 tff(13651,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s64)) | (~always25(s99)) | always25(s64))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s64) | (~trans(s99, s64)))),
% 2.00/2.20 inference(transitivity,[status(thm)],[13650, 13648])).
% 2.00/2.20 tff(13652,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s64)) | (~always25(s99)) | always25(s64))),
% 2.00/2.20 inference(quant_inst,[status(thm)],[])).
% 2.00/2.20 tff(13653,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s64) | (~trans(s99, s64))),
% 2.00/2.20 inference(modus_ponens,[status(thm)],[13652, 13651])).
% 2.00/2.20 tff(13654,plain,
% 2.00/2.20 ($false),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13653, 11903, 3934, 13236, 8353])).
% 2.00/2.20 tff(13655,plain,((~trans(s99, s64)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.20 tff(13656,plain,
% 2.00/2.20 (~trans(s99, s64)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13655, 13016])).
% 2.00/2.20 tff(13657,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s67) | (~trans(s99, s67)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s67) | (~trans(s99, s67)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(13658,plain,
% 2.00/2.20 (((~trans(s99, s67)) | (~always25(s99)) | always25(s67)) <=> ((~always25(s99)) | always25(s67) | (~trans(s99, s67)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(13659,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s67)) | (~always25(s99)) | always25(s67))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s67) | (~trans(s99, s67))))),
% 2.00/2.20 inference(monotonicity,[status(thm)],[13658])).
% 2.00/2.20 tff(13660,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s67)) | (~always25(s99)) | always25(s67))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s67) | (~trans(s99, s67)))),
% 2.00/2.20 inference(transitivity,[status(thm)],[13659, 13657])).
% 2.00/2.20 tff(13661,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s67)) | (~always25(s99)) | always25(s67))),
% 2.00/2.20 inference(quant_inst,[status(thm)],[])).
% 2.00/2.20 tff(13662,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s67) | (~trans(s99, s67))),
% 2.00/2.20 inference(modus_ponens,[status(thm)],[13661, 13660])).
% 2.00/2.20 tff(13663,plain,
% 2.00/2.20 ($false),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13662, 11914, 3934, 13236, 8329])).
% 2.00/2.20 tff(13664,plain,((~trans(s99, s67)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.20 tff(13665,plain,
% 2.00/2.20 (~trans(s99, s67)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13664, 13016])).
% 2.00/2.20 tff(13666,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s22) | (~trans(s99, s22)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s22) | (~trans(s99, s22)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(13667,plain,
% 2.00/2.20 (((~trans(s99, s22)) | (~always25(s99)) | always25(s22)) <=> ((~always25(s99)) | always25(s22) | (~trans(s99, s22)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(13668,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s22)) | (~always25(s99)) | always25(s22))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s22) | (~trans(s99, s22))))),
% 2.00/2.20 inference(monotonicity,[status(thm)],[13667])).
% 2.00/2.20 tff(13669,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s22)) | (~always25(s99)) | always25(s22))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s22) | (~trans(s99, s22)))),
% 2.00/2.20 inference(transitivity,[status(thm)],[13668, 13666])).
% 2.00/2.20 tff(13670,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s22)) | (~always25(s99)) | always25(s22))),
% 2.00/2.20 inference(quant_inst,[status(thm)],[])).
% 2.00/2.20 tff(13671,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s22) | (~trans(s99, s22))),
% 2.00/2.20 inference(modus_ponens,[status(thm)],[13670, 13669])).
% 2.00/2.20 tff(13672,plain,
% 2.00/2.20 ($false),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13671, 11925, 3934, 13236, 8650])).
% 2.00/2.20 tff(13673,plain,((~trans(s99, s22)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.20 tff(13674,plain,
% 2.00/2.20 (~trans(s99, s22)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13673, 13016])).
% 2.00/2.20 tff(13675,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s43) | (~trans(s99, s43)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s43) | (~trans(s99, s43)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(13676,plain,
% 2.00/2.20 (((~trans(s99, s43)) | (~always25(s99)) | always25(s43)) <=> ((~always25(s99)) | always25(s43) | (~trans(s99, s43)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(13677,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s43)) | (~always25(s99)) | always25(s43))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s43) | (~trans(s99, s43))))),
% 2.00/2.20 inference(monotonicity,[status(thm)],[13676])).
% 2.00/2.20 tff(13678,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s43)) | (~always25(s99)) | always25(s43))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s43) | (~trans(s99, s43)))),
% 2.00/2.20 inference(transitivity,[status(thm)],[13677, 13675])).
% 2.00/2.20 tff(13679,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s43)) | (~always25(s99)) | always25(s43))),
% 2.00/2.20 inference(quant_inst,[status(thm)],[])).
% 2.00/2.20 tff(13680,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s43) | (~trans(s99, s43))),
% 2.00/2.20 inference(modus_ponens,[status(thm)],[13679, 13678])).
% 2.00/2.20 tff(13681,plain,
% 2.00/2.20 ($false),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13680, 11936, 3934, 13236, 8496])).
% 2.00/2.20 tff(13682,plain,((~trans(s99, s43)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.20 tff(13683,plain,
% 2.00/2.20 (~trans(s99, s43)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13682, 13016])).
% 2.00/2.20 tff(13684,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s34) | (~trans(s99, s34)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s34) | (~trans(s99, s34)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(13685,plain,
% 2.00/2.20 (((~trans(s99, s34)) | (~always25(s99)) | always25(s34)) <=> ((~always25(s99)) | always25(s34) | (~trans(s99, s34)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(13686,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s34)) | (~always25(s99)) | always25(s34))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s34) | (~trans(s99, s34))))),
% 2.00/2.20 inference(monotonicity,[status(thm)],[13685])).
% 2.00/2.20 tff(13687,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s34)) | (~always25(s99)) | always25(s34))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s34) | (~trans(s99, s34)))),
% 2.00/2.20 inference(transitivity,[status(thm)],[13686, 13684])).
% 2.00/2.20 tff(13688,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s34)) | (~always25(s99)) | always25(s34))),
% 2.00/2.20 inference(quant_inst,[status(thm)],[])).
% 2.00/2.20 tff(13689,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s34) | (~trans(s99, s34))),
% 2.00/2.20 inference(modus_ponens,[status(thm)],[13688, 13687])).
% 2.00/2.20 tff(13690,plain,
% 2.00/2.20 ($false),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13689, 11947, 3934, 13236, 8563])).
% 2.00/2.20 tff(13691,plain,((~trans(s99, s34)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.20 tff(13692,plain,
% 2.00/2.20 (~trans(s99, s34)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13691, 13016])).
% 2.00/2.20 tff(13693,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s21, s22)) | (~always25(s21)) | always25(s22))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s21, s22)) | (~always25(s21)) | always25(s22))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(13694,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s21, s22)) | (~always25(s21)) | always25(s22))),
% 2.00/2.20 inference(quant_inst,[status(thm)],[])).
% 2.00/2.20 tff(13695,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s21, s22)) | (~always25(s21)) | always25(s22)),
% 2.00/2.20 inference(modus_ponens,[status(thm)],[13694, 13693])).
% 2.00/2.20 tff(13696,plain,
% 2.00/2.20 ((~always25(s21)) | always25(s22)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13695, 3934, 2164])).
% 2.00/2.20 tff(13697,plain,
% 2.00/2.20 (~always25(s21)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13696, 8650])).
% 2.00/2.20 tff(13698,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s21) | (~trans(s99, s21)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s21) | (~trans(s99, s21)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(13699,plain,
% 2.00/2.20 (((~trans(s99, s21)) | (~always25(s99)) | always25(s21)) <=> ((~always25(s99)) | always25(s21) | (~trans(s99, s21)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(13700,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s21)) | (~always25(s99)) | always25(s21))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s21) | (~trans(s99, s21))))),
% 2.00/2.20 inference(monotonicity,[status(thm)],[13699])).
% 2.00/2.20 tff(13701,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s21)) | (~always25(s99)) | always25(s21))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s21) | (~trans(s99, s21)))),
% 2.00/2.20 inference(transitivity,[status(thm)],[13700, 13698])).
% 2.00/2.20 tff(13702,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s21)) | (~always25(s99)) | always25(s21))),
% 2.00/2.20 inference(quant_inst,[status(thm)],[])).
% 2.00/2.20 tff(13703,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s21) | (~trans(s99, s21))),
% 2.00/2.20 inference(modus_ponens,[status(thm)],[13702, 13701])).
% 2.00/2.20 tff(13704,plain,
% 2.00/2.20 ($false),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13703, 11958, 3934, 13236, 13697])).
% 2.00/2.20 tff(13705,plain,((~trans(s99, s21)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.20 tff(13706,plain,
% 2.00/2.20 (~trans(s99, s21)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13705, 13016])).
% 2.00/2.20 tff(13707,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s29, s30)) | (~always25(s29)) | always25(s30))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s29, s30)) | (~always25(s29)) | always25(s30))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(13708,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s29, s30)) | (~always25(s29)) | always25(s30))),
% 2.00/2.20 inference(quant_inst,[status(thm)],[])).
% 2.00/2.20 tff(13709,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s29, s30)) | (~always25(s29)) | always25(s30)),
% 2.00/2.20 inference(modus_ponens,[status(thm)],[13708, 13707])).
% 2.00/2.20 tff(13710,plain,
% 2.00/2.20 ((~always25(s29)) | always25(s30)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13709, 3934, 2792])).
% 2.00/2.20 tff(13711,plain,
% 2.00/2.20 (~always25(s29)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13710, 8592])).
% 2.00/2.20 tff(13712,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s29) | (~trans(s99, s29)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s29) | (~trans(s99, s29)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(13713,plain,
% 2.00/2.20 (((~trans(s99, s29)) | (~always25(s99)) | always25(s29)) <=> ((~always25(s99)) | always25(s29) | (~trans(s99, s29)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(13714,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s29)) | (~always25(s99)) | always25(s29))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s29) | (~trans(s99, s29))))),
% 2.00/2.20 inference(monotonicity,[status(thm)],[13713])).
% 2.00/2.20 tff(13715,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s29)) | (~always25(s99)) | always25(s29))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s29) | (~trans(s99, s29)))),
% 2.00/2.20 inference(transitivity,[status(thm)],[13714, 13712])).
% 2.00/2.20 tff(13716,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s29)) | (~always25(s99)) | always25(s29))),
% 2.00/2.20 inference(quant_inst,[status(thm)],[])).
% 2.00/2.20 tff(13717,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s29) | (~trans(s99, s29))),
% 2.00/2.20 inference(modus_ponens,[status(thm)],[13716, 13715])).
% 2.00/2.20 tff(13718,plain,
% 2.00/2.20 ($false),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13717, 11969, 3934, 13236, 13711])).
% 2.00/2.20 tff(13719,plain,((~trans(s99, s29)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.20 tff(13720,plain,
% 2.00/2.20 (~trans(s99, s29)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13719, 13016])).
% 2.00/2.20 tff(13721,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s17, s18)) | (~always25(s17)) | always25(s18))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s17, s18)) | (~always25(s17)) | always25(s18))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(13722,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s17, s18)) | (~always25(s17)) | always25(s18))),
% 2.00/2.20 inference(quant_inst,[status(thm)],[])).
% 2.00/2.20 tff(13723,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s17, s18)) | (~always25(s17)) | always25(s18)),
% 2.00/2.20 inference(modus_ponens,[status(thm)],[13722, 13721])).
% 2.00/2.20 tff(13724,plain,
% 2.00/2.20 ((~always25(s17)) | always25(s18)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13723, 3934, 1831])).
% 2.00/2.20 tff(13725,plain,
% 2.00/2.20 (~always25(s17)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13724, 8679])).
% 2.00/2.20 tff(13726,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s17) | (~trans(s99, s17)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s17) | (~trans(s99, s17)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(13727,plain,
% 2.00/2.20 (((~trans(s99, s17)) | (~always25(s99)) | always25(s17)) <=> ((~always25(s99)) | always25(s17) | (~trans(s99, s17)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(13728,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s17)) | (~always25(s99)) | always25(s17))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s17) | (~trans(s99, s17))))),
% 2.00/2.20 inference(monotonicity,[status(thm)],[13727])).
% 2.00/2.20 tff(13729,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s17)) | (~always25(s99)) | always25(s17))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s17) | (~trans(s99, s17)))),
% 2.00/2.20 inference(transitivity,[status(thm)],[13728, 13726])).
% 2.00/2.20 tff(13730,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s17)) | (~always25(s99)) | always25(s17))),
% 2.00/2.20 inference(quant_inst,[status(thm)],[])).
% 2.00/2.20 tff(13731,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s17) | (~trans(s99, s17))),
% 2.00/2.20 inference(modus_ponens,[status(thm)],[13730, 13729])).
% 2.00/2.20 tff(13732,plain,
% 2.00/2.20 ($false),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13731, 11980, 3934, 13236, 13725])).
% 2.00/2.20 tff(13733,plain,((~trans(s99, s17)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.20 tff(13734,plain,
% 2.00/2.20 (~trans(s99, s17)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13733, 13016])).
% 2.00/2.20 tff(13735,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s14) | (~trans(s99, s14)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s14) | (~trans(s99, s14)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(13736,plain,
% 2.00/2.20 (((~trans(s99, s14)) | (~always25(s99)) | always25(s14)) <=> ((~always25(s99)) | always25(s14) | (~trans(s99, s14)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(13737,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s14)) | (~always25(s99)) | always25(s14))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s14) | (~trans(s99, s14))))),
% 2.00/2.20 inference(monotonicity,[status(thm)],[13736])).
% 2.00/2.20 tff(13738,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s14)) | (~always25(s99)) | always25(s14))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s14) | (~trans(s99, s14)))),
% 2.00/2.20 inference(transitivity,[status(thm)],[13737, 13735])).
% 2.00/2.20 tff(13739,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s14)) | (~always25(s99)) | always25(s14))),
% 2.00/2.20 inference(quant_inst,[status(thm)],[])).
% 2.00/2.20 tff(13740,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s14) | (~trans(s99, s14))),
% 2.00/2.20 inference(modus_ponens,[status(thm)],[13739, 13738])).
% 2.00/2.20 tff(13741,plain,
% 2.00/2.20 ($false),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13740, 11991, 3934, 13236, 8708])).
% 2.00/2.20 tff(13742,plain,((~trans(s99, s14)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.20 tff(13743,plain,
% 2.00/2.20 (~trans(s99, s14)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13742, 13016])).
% 2.00/2.20 tff(13744,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s25, s26)) | (~always25(s25)) | always25(s26))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s25, s26)) | (~always25(s25)) | always25(s26))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(13745,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s25, s26)) | (~always25(s25)) | always25(s26))),
% 2.00/2.20 inference(quant_inst,[status(thm)],[])).
% 2.00/2.20 tff(13746,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s25, s26)) | (~always25(s25)) | always25(s26)),
% 2.00/2.20 inference(modus_ponens,[status(thm)],[13745, 13744])).
% 2.00/2.20 tff(13747,plain,
% 2.00/2.20 ((~always25(s25)) | always25(s26)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13746, 3934, 2459])).
% 2.00/2.20 tff(13748,plain,
% 2.00/2.20 (~always25(s25)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13747, 8621])).
% 2.00/2.20 tff(13749,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s25) | (~trans(s99, s25)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s25) | (~trans(s99, s25)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(13750,plain,
% 2.00/2.20 (((~trans(s99, s25)) | (~always25(s99)) | always25(s25)) <=> ((~always25(s99)) | always25(s25) | (~trans(s99, s25)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(13751,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s25)) | (~always25(s99)) | always25(s25))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s25) | (~trans(s99, s25))))),
% 2.00/2.20 inference(monotonicity,[status(thm)],[13750])).
% 2.00/2.20 tff(13752,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s25)) | (~always25(s99)) | always25(s25))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s25) | (~trans(s99, s25)))),
% 2.00/2.20 inference(transitivity,[status(thm)],[13751, 13749])).
% 2.00/2.20 tff(13753,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s25)) | (~always25(s99)) | always25(s25))),
% 2.00/2.20 inference(quant_inst,[status(thm)],[])).
% 2.00/2.20 tff(13754,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s25) | (~trans(s99, s25))),
% 2.00/2.20 inference(modus_ponens,[status(thm)],[13753, 13752])).
% 2.00/2.20 tff(13755,plain,
% 2.00/2.20 ($false),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13754, 12002, 3934, 13236, 13748])).
% 2.00/2.20 tff(13756,plain,((~trans(s99, s25)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.20 tff(13757,plain,
% 2.00/2.20 (~trans(s99, s25)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13756, 13016])).
% 2.00/2.20 tff(13758,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s31) | (~trans(s99, s31)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s31) | (~trans(s99, s31)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(13759,plain,
% 2.00/2.20 (((~trans(s99, s31)) | (~always25(s99)) | always25(s31)) <=> ((~always25(s99)) | always25(s31) | (~trans(s99, s31)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(13760,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s31)) | (~always25(s99)) | always25(s31))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s31) | (~trans(s99, s31))))),
% 2.00/2.20 inference(monotonicity,[status(thm)],[13759])).
% 2.00/2.20 tff(13761,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s31)) | (~always25(s99)) | always25(s31))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s31) | (~trans(s99, s31)))),
% 2.00/2.20 inference(transitivity,[status(thm)],[13760, 13758])).
% 2.00/2.20 tff(13762,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s31)) | (~always25(s99)) | always25(s31))),
% 2.00/2.20 inference(quant_inst,[status(thm)],[])).
% 2.00/2.20 tff(13763,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s31) | (~trans(s99, s31))),
% 2.00/2.20 inference(modus_ponens,[status(thm)],[13762, 13761])).
% 2.00/2.20 tff(13764,plain,
% 2.00/2.20 ($false),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13763, 12013, 3934, 13236, 8583])).
% 2.00/2.20 tff(13765,plain,((~trans(s99, s31)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.20 tff(13766,plain,
% 2.00/2.20 (~trans(s99, s31)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13765, 13016])).
% 2.00/2.20 tff(13767,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s38) | (~trans(s99, s38)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s38) | (~trans(s99, s38)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(13768,plain,
% 2.00/2.20 (((~trans(s99, s38)) | (~always25(s99)) | always25(s38)) <=> ((~always25(s99)) | always25(s38) | (~trans(s99, s38)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(13769,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s38)) | (~always25(s99)) | always25(s38))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s38) | (~trans(s99, s38))))),
% 2.00/2.20 inference(monotonicity,[status(thm)],[13768])).
% 2.00/2.20 tff(13770,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s38)) | (~always25(s99)) | always25(s38))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s38) | (~trans(s99, s38)))),
% 2.00/2.20 inference(transitivity,[status(thm)],[13769, 13767])).
% 2.00/2.20 tff(13771,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s38)) | (~always25(s99)) | always25(s38))),
% 2.00/2.20 inference(quant_inst,[status(thm)],[])).
% 2.00/2.20 tff(13772,plain,
% 2.00/2.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s38) | (~trans(s99, s38))),
% 2.00/2.20 inference(modus_ponens,[status(thm)],[13771, 13770])).
% 2.00/2.20 tff(13773,plain,
% 2.00/2.20 ($false),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13772, 12024, 3934, 13236, 8534])).
% 2.00/2.20 tff(13774,plain,((~trans(s99, s38)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.20 tff(13775,plain,
% 2.00/2.20 (~trans(s99, s38)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[13774, 13016])).
% 2.00/2.20 tff(13776,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s3) | (~trans(s99, s3)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s3) | (~trans(s99, s3)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(13777,plain,
% 2.00/2.20 (((~trans(s99, s3)) | (~always25(s99)) | always25(s3)) <=> ((~always25(s99)) | always25(s3) | (~trans(s99, s3)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(13778,plain,
% 2.00/2.20 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s3)) | (~always25(s99)) | always25(s3))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s3) | (~trans(s99, s3))))),
% 2.00/2.21 inference(monotonicity,[status(thm)],[13777])).
% 2.00/2.21 tff(13779,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s3)) | (~always25(s99)) | always25(s3))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s3) | (~trans(s99, s3)))),
% 2.00/2.21 inference(transitivity,[status(thm)],[13778, 13776])).
% 2.00/2.21 tff(13780,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s3)) | (~always25(s99)) | always25(s3))),
% 2.00/2.21 inference(quant_inst,[status(thm)],[])).
% 2.00/2.21 tff(13781,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s3) | (~trans(s99, s3))),
% 2.00/2.21 inference(modus_ponens,[status(thm)],[13780, 13779])).
% 2.00/2.21 tff(13782,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13781, 12035, 3934, 13236, 8786])).
% 2.00/2.21 tff(13783,plain,((~trans(s99, s3)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(13784,plain,
% 2.00/2.21 (~trans(s99, s3)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13783, 13016])).
% 2.00/2.21 tff(13785,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s15) | (~trans(s99, s15)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s15) | (~trans(s99, s15)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(13786,plain,
% 2.00/2.21 (((~trans(s99, s15)) | (~always25(s99)) | always25(s15)) <=> ((~always25(s99)) | always25(s15) | (~trans(s99, s15)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(13787,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s15)) | (~always25(s99)) | always25(s15))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s15) | (~trans(s99, s15))))),
% 2.00/2.21 inference(monotonicity,[status(thm)],[13786])).
% 2.00/2.21 tff(13788,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s15)) | (~always25(s99)) | always25(s15))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s15) | (~trans(s99, s15)))),
% 2.00/2.21 inference(transitivity,[status(thm)],[13787, 13785])).
% 2.00/2.21 tff(13789,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s15)) | (~always25(s99)) | always25(s15))),
% 2.00/2.21 inference(quant_inst,[status(thm)],[])).
% 2.00/2.21 tff(13790,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s15) | (~trans(s99, s15))),
% 2.00/2.21 inference(modus_ponens,[status(thm)],[13789, 13788])).
% 2.00/2.21 tff(13791,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13790, 12046, 3934, 13236, 8699])).
% 2.00/2.21 tff(13792,plain,((~trans(s99, s15)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(13793,plain,
% 2.00/2.21 (~trans(s99, s15)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13792, 13016])).
% 2.00/2.21 tff(13794,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s27) | (~trans(s99, s27)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s27) | (~trans(s99, s27)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(13795,plain,
% 2.00/2.21 (((~trans(s99, s27)) | (~always25(s99)) | always25(s27)) <=> ((~always25(s99)) | always25(s27) | (~trans(s99, s27)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(13796,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s27)) | (~always25(s99)) | always25(s27))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s27) | (~trans(s99, s27))))),
% 2.00/2.21 inference(monotonicity,[status(thm)],[13795])).
% 2.00/2.21 tff(13797,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s27)) | (~always25(s99)) | always25(s27))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s27) | (~trans(s99, s27)))),
% 2.00/2.21 inference(transitivity,[status(thm)],[13796, 13794])).
% 2.00/2.21 tff(13798,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s27)) | (~always25(s99)) | always25(s27))),
% 2.00/2.21 inference(quant_inst,[status(thm)],[])).
% 2.00/2.21 tff(13799,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s27) | (~trans(s99, s27))),
% 2.00/2.21 inference(modus_ponens,[status(thm)],[13798, 13797])).
% 2.00/2.21 tff(13800,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13799, 12057, 3934, 13236, 8612])).
% 2.00/2.21 tff(13801,plain,((~trans(s99, s27)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(13802,plain,
% 2.00/2.21 (~trans(s99, s27)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13801, 13016])).
% 2.00/2.21 tff(13803,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s7) | (~trans(s99, s7)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s7) | (~trans(s99, s7)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(13804,plain,
% 2.00/2.21 (((~trans(s99, s7)) | (~always25(s99)) | always25(s7)) <=> ((~always25(s99)) | always25(s7) | (~trans(s99, s7)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(13805,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s7)) | (~always25(s99)) | always25(s7))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s7) | (~trans(s99, s7))))),
% 2.00/2.21 inference(monotonicity,[status(thm)],[13804])).
% 2.00/2.21 tff(13806,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s7)) | (~always25(s99)) | always25(s7))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s7) | (~trans(s99, s7)))),
% 2.00/2.21 inference(transitivity,[status(thm)],[13805, 13803])).
% 2.00/2.21 tff(13807,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s7)) | (~always25(s99)) | always25(s7))),
% 2.00/2.21 inference(quant_inst,[status(thm)],[])).
% 2.00/2.21 tff(13808,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s7) | (~trans(s99, s7))),
% 2.00/2.21 inference(modus_ponens,[status(thm)],[13807, 13806])).
% 2.00/2.21 tff(13809,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13808, 12068, 3934, 13236, 8757])).
% 2.00/2.21 tff(13810,plain,((~trans(s99, s7)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(13811,plain,
% 2.00/2.21 (~trans(s99, s7)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13810, 13016])).
% 2.00/2.21 tff(13812,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s23) | (~trans(s99, s23)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s23) | (~trans(s99, s23)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(13813,plain,
% 2.00/2.21 (((~trans(s99, s23)) | (~always25(s99)) | always25(s23)) <=> ((~always25(s99)) | always25(s23) | (~trans(s99, s23)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(13814,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s23)) | (~always25(s99)) | always25(s23))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s23) | (~trans(s99, s23))))),
% 2.00/2.21 inference(monotonicity,[status(thm)],[13813])).
% 2.00/2.21 tff(13815,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s23)) | (~always25(s99)) | always25(s23))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s23) | (~trans(s99, s23)))),
% 2.00/2.21 inference(transitivity,[status(thm)],[13814, 13812])).
% 2.00/2.21 tff(13816,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s23)) | (~always25(s99)) | always25(s23))),
% 2.00/2.21 inference(quant_inst,[status(thm)],[])).
% 2.00/2.21 tff(13817,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s23) | (~trans(s99, s23))),
% 2.00/2.21 inference(modus_ponens,[status(thm)],[13816, 13815])).
% 2.00/2.21 tff(13818,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13817, 12079, 3934, 13236, 8641])).
% 2.00/2.21 tff(13819,plain,((~trans(s99, s23)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(13820,plain,
% 2.00/2.21 (~trans(s99, s23)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13819, 13016])).
% 2.00/2.21 tff(13821,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s6) | (~trans(s99, s6)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s6) | (~trans(s99, s6)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(13822,plain,
% 2.00/2.21 (((~trans(s99, s6)) | (~always25(s99)) | always25(s6)) <=> ((~always25(s99)) | always25(s6) | (~trans(s99, s6)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(13823,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s6)) | (~always25(s99)) | always25(s6))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s6) | (~trans(s99, s6))))),
% 2.00/2.21 inference(monotonicity,[status(thm)],[13822])).
% 2.00/2.21 tff(13824,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s6)) | (~always25(s99)) | always25(s6))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s6) | (~trans(s99, s6)))),
% 2.00/2.21 inference(transitivity,[status(thm)],[13823, 13821])).
% 2.00/2.21 tff(13825,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s6)) | (~always25(s99)) | always25(s6))),
% 2.00/2.21 inference(quant_inst,[status(thm)],[])).
% 2.00/2.21 tff(13826,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s6) | (~trans(s99, s6))),
% 2.00/2.21 inference(modus_ponens,[status(thm)],[13825, 13824])).
% 2.00/2.21 tff(13827,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13826, 12090, 3934, 13236, 8766])).
% 2.00/2.21 tff(13828,plain,((~trans(s99, s6)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(13829,plain,
% 2.00/2.21 (~trans(s99, s6)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13828, 13016])).
% 2.00/2.21 tff(13830,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s9, s10)) | (~always25(s9)) | always25(s10))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s9, s10)) | (~always25(s9)) | always25(s10))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(13831,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s9, s10)) | (~always25(s9)) | always25(s10))),
% 2.00/2.21 inference(quant_inst,[status(thm)],[])).
% 2.00/2.21 tff(13832,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s9, s10)) | (~always25(s9)) | always25(s10)),
% 2.00/2.21 inference(modus_ponens,[status(thm)],[13831, 13830])).
% 2.00/2.21 tff(13833,plain,
% 2.00/2.21 ((~always25(s9)) | always25(s10)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13832, 3934, 1203])).
% 2.00/2.21 tff(13834,plain,
% 2.00/2.21 (~always25(s9)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13833, 8737])).
% 2.00/2.21 tff(13835,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s9) | (~trans(s99, s9)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s9) | (~trans(s99, s9)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(13836,plain,
% 2.00/2.21 (((~trans(s99, s9)) | (~always25(s99)) | always25(s9)) <=> ((~always25(s99)) | always25(s9) | (~trans(s99, s9)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(13837,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s9)) | (~always25(s99)) | always25(s9))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s9) | (~trans(s99, s9))))),
% 2.00/2.21 inference(monotonicity,[status(thm)],[13836])).
% 2.00/2.21 tff(13838,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s9)) | (~always25(s99)) | always25(s9))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s9) | (~trans(s99, s9)))),
% 2.00/2.21 inference(transitivity,[status(thm)],[13837, 13835])).
% 2.00/2.21 tff(13839,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s9)) | (~always25(s99)) | always25(s9))),
% 2.00/2.21 inference(quant_inst,[status(thm)],[])).
% 2.00/2.21 tff(13840,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s9) | (~trans(s99, s9))),
% 2.00/2.21 inference(modus_ponens,[status(thm)],[13839, 13838])).
% 2.00/2.21 tff(13841,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13840, 12101, 3934, 13236, 13834])).
% 2.00/2.21 tff(13842,plain,((~trans(s99, s9)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(13843,plain,
% 2.00/2.21 (~trans(s99, s9)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13842, 13016])).
% 2.00/2.21 tff(13844,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s5, s6)) | (~always25(s5)) | always25(s6))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s5, s6)) | (~always25(s5)) | always25(s6))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(13845,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s5, s6)) | (~always25(s5)) | always25(s6))),
% 2.00/2.21 inference(quant_inst,[status(thm)],[])).
% 2.00/2.21 tff(13846,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s5, s6)) | (~always25(s5)) | always25(s6)),
% 2.00/2.21 inference(modus_ponens,[status(thm)],[13845, 13844])).
% 2.00/2.21 tff(13847,plain,
% 2.00/2.21 ((~always25(s5)) | always25(s6)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13846, 3934, 878])).
% 2.00/2.21 tff(13848,plain,
% 2.00/2.21 (~always25(s5)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13847, 8766])).
% 2.00/2.21 tff(13849,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s5) | (~trans(s99, s5)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s5) | (~trans(s99, s5)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(13850,plain,
% 2.00/2.21 (((~trans(s99, s5)) | (~always25(s99)) | always25(s5)) <=> ((~always25(s99)) | always25(s5) | (~trans(s99, s5)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(13851,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s5)) | (~always25(s99)) | always25(s5))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s5) | (~trans(s99, s5))))),
% 2.00/2.21 inference(monotonicity,[status(thm)],[13850])).
% 2.00/2.21 tff(13852,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s5)) | (~always25(s99)) | always25(s5))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s5) | (~trans(s99, s5)))),
% 2.00/2.21 inference(transitivity,[status(thm)],[13851, 13849])).
% 2.00/2.21 tff(13853,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s5)) | (~always25(s99)) | always25(s5))),
% 2.00/2.21 inference(quant_inst,[status(thm)],[])).
% 2.00/2.21 tff(13854,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s5) | (~trans(s99, s5))),
% 2.00/2.21 inference(modus_ponens,[status(thm)],[13853, 13852])).
% 2.00/2.21 tff(13855,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13854, 12112, 3934, 13236, 13848])).
% 2.00/2.21 tff(13856,plain,((~trans(s99, s5)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(13857,plain,
% 2.00/2.21 (~trans(s99, s5)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13856, 13016])).
% 2.00/2.21 tff(13858,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s39) | (~trans(s99, s39)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s39) | (~trans(s99, s39)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(13859,plain,
% 2.00/2.21 (((~trans(s99, s39)) | (~always25(s99)) | always25(s39)) <=> ((~always25(s99)) | always25(s39) | (~trans(s99, s39)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(13860,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s39)) | (~always25(s99)) | always25(s39))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s39) | (~trans(s99, s39))))),
% 2.00/2.21 inference(monotonicity,[status(thm)],[13859])).
% 2.00/2.21 tff(13861,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s39)) | (~always25(s99)) | always25(s39))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s39) | (~trans(s99, s39)))),
% 2.00/2.21 inference(transitivity,[status(thm)],[13860, 13858])).
% 2.00/2.21 tff(13862,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s39)) | (~always25(s99)) | always25(s39))),
% 2.00/2.21 inference(quant_inst,[status(thm)],[])).
% 2.00/2.21 tff(13863,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s39) | (~trans(s99, s39))),
% 2.00/2.21 inference(modus_ponens,[status(thm)],[13862, 13861])).
% 2.00/2.21 tff(13864,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13863, 12123, 3934, 13236, 8525])).
% 2.00/2.21 tff(13865,plain,((~trans(s99, s39)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(13866,plain,
% 2.00/2.21 (~trans(s99, s39)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13865, 13016])).
% 2.00/2.21 tff(13867,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s8) | (~trans(s99, s8)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s8) | (~trans(s99, s8)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(13868,plain,
% 2.00/2.21 (((~trans(s99, s8)) | (~always25(s99)) | always25(s8)) <=> ((~always25(s99)) | always25(s8) | (~trans(s99, s8)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(13869,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s8)) | (~always25(s99)) | always25(s8))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s8) | (~trans(s99, s8))))),
% 2.00/2.21 inference(monotonicity,[status(thm)],[13868])).
% 2.00/2.21 tff(13870,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s8)) | (~always25(s99)) | always25(s8))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s8) | (~trans(s99, s8)))),
% 2.00/2.21 inference(transitivity,[status(thm)],[13869, 13867])).
% 2.00/2.21 tff(13871,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s8)) | (~always25(s99)) | always25(s8))),
% 2.00/2.21 inference(quant_inst,[status(thm)],[])).
% 2.00/2.21 tff(13872,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s8) | (~trans(s99, s8))),
% 2.00/2.21 inference(modus_ponens,[status(thm)],[13871, 13870])).
% 2.00/2.21 tff(13873,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13872, 12134, 3934, 13236, 8752])).
% 2.00/2.21 tff(13874,plain,((~trans(s99, s8)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(13875,plain,
% 2.00/2.21 (~trans(s99, s8)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13874, 13016])).
% 2.00/2.21 tff(13876,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s32) | (~trans(s99, s32)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s32) | (~trans(s99, s32)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(13877,plain,
% 2.00/2.21 (((~trans(s99, s32)) | (~always25(s99)) | always25(s32)) <=> ((~always25(s99)) | always25(s32) | (~trans(s99, s32)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(13878,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s32)) | (~always25(s99)) | always25(s32))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s32) | (~trans(s99, s32))))),
% 2.00/2.21 inference(monotonicity,[status(thm)],[13877])).
% 2.00/2.21 tff(13879,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s32)) | (~always25(s99)) | always25(s32))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s32) | (~trans(s99, s32)))),
% 2.00/2.21 inference(transitivity,[status(thm)],[13878, 13876])).
% 2.00/2.21 tff(13880,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s32)) | (~always25(s99)) | always25(s32))),
% 2.00/2.21 inference(quant_inst,[status(thm)],[])).
% 2.00/2.21 tff(13881,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s32) | (~trans(s99, s32))),
% 2.00/2.21 inference(modus_ponens,[status(thm)],[13880, 13879])).
% 2.00/2.21 tff(13882,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13881, 12145, 3934, 13236, 8578])).
% 2.00/2.21 tff(13883,plain,((~trans(s99, s32)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(13884,plain,
% 2.00/2.21 (~trans(s99, s32)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13883, 13016])).
% 2.00/2.21 tff(13885,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s24) | (~trans(s99, s24)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s24) | (~trans(s99, s24)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(13886,plain,
% 2.00/2.21 (((~trans(s99, s24)) | (~always25(s99)) | always25(s24)) <=> ((~always25(s99)) | always25(s24) | (~trans(s99, s24)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(13887,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s24)) | (~always25(s99)) | always25(s24))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s24) | (~trans(s99, s24))))),
% 2.00/2.21 inference(monotonicity,[status(thm)],[13886])).
% 2.00/2.21 tff(13888,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s24)) | (~always25(s99)) | always25(s24))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s24) | (~trans(s99, s24)))),
% 2.00/2.21 inference(transitivity,[status(thm)],[13887, 13885])).
% 2.00/2.21 tff(13889,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s24)) | (~always25(s99)) | always25(s24))),
% 2.00/2.21 inference(quant_inst,[status(thm)],[])).
% 2.00/2.21 tff(13890,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s24) | (~trans(s99, s24))),
% 2.00/2.21 inference(modus_ponens,[status(thm)],[13889, 13888])).
% 2.00/2.21 tff(13891,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13890, 12156, 3934, 13236, 8636])).
% 2.00/2.21 tff(13892,plain,((~trans(s99, s24)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(13893,plain,
% 2.00/2.21 (~trans(s99, s24)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13892, 13016])).
% 2.00/2.21 tff(13894,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s20) | (~trans(s99, s20)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s20) | (~trans(s99, s20)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(13895,plain,
% 2.00/2.21 (((~trans(s99, s20)) | (~always25(s99)) | always25(s20)) <=> ((~always25(s99)) | always25(s20) | (~trans(s99, s20)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(13896,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s20)) | (~always25(s99)) | always25(s20))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s20) | (~trans(s99, s20))))),
% 2.00/2.21 inference(monotonicity,[status(thm)],[13895])).
% 2.00/2.21 tff(13897,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s20)) | (~always25(s99)) | always25(s20))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s20) | (~trans(s99, s20)))),
% 2.00/2.21 inference(transitivity,[status(thm)],[13896, 13894])).
% 2.00/2.21 tff(13898,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s20)) | (~always25(s99)) | always25(s20))),
% 2.00/2.21 inference(quant_inst,[status(thm)],[])).
% 2.00/2.21 tff(13899,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s20) | (~trans(s99, s20))),
% 2.00/2.21 inference(modus_ponens,[status(thm)],[13898, 13897])).
% 2.00/2.21 tff(13900,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13899, 12167, 3934, 13236, 8665])).
% 2.00/2.21 tff(13901,plain,((~trans(s99, s20)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(13902,plain,
% 2.00/2.21 (~trans(s99, s20)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13901, 13016])).
% 2.00/2.21 tff(13903,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s83) | (~trans(s99, s83)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s83) | (~trans(s99, s83)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(13904,plain,
% 2.00/2.21 (((~trans(s99, s83)) | (~always25(s99)) | always25(s83)) <=> ((~always25(s99)) | always25(s83) | (~trans(s99, s83)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(13905,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s83)) | (~always25(s99)) | always25(s83))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s83) | (~trans(s99, s83))))),
% 2.00/2.21 inference(monotonicity,[status(thm)],[13904])).
% 2.00/2.21 tff(13906,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s83)) | (~always25(s99)) | always25(s83))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s83) | (~trans(s99, s83)))),
% 2.00/2.21 inference(transitivity,[status(thm)],[13905, 13903])).
% 2.00/2.21 tff(13907,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s83)) | (~always25(s99)) | always25(s83))),
% 2.00/2.21 inference(quant_inst,[status(thm)],[])).
% 2.00/2.21 tff(13908,plain,
% 2.00/2.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s83) | (~trans(s99, s83))),
% 2.00/2.21 inference(modus_ponens,[status(thm)],[13907, 13906])).
% 2.00/2.21 tff(13909,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13908, 12178, 3934, 13236, 8213])).
% 2.00/2.21 tff(13910,plain,((~trans(s99, s83)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(13911,plain,
% 2.00/2.21 (~trans(s99, s83)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[13910, 13016])).
% 2.00/2.21 tff(13912,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s71) | (~trans(s99, s71)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s71) | (~trans(s99, s71)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(13913,plain,
% 2.00/2.21 (((~trans(s99, s71)) | (~always25(s99)) | always25(s71)) <=> ((~always25(s99)) | always25(s71) | (~trans(s99, s71)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(13914,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s71)) | (~always25(s99)) | always25(s71))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s71) | (~trans(s99, s71))))),
% 2.00/2.21 inference(monotonicity,[status(thm)],[13913])).
% 2.00/2.21 tff(13915,plain,
% 2.00/2.21 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s71)) | (~always25(s99)) | always25(s71))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s71) | (~trans(s99, s71)))),
% 2.00/2.22 inference(transitivity,[status(thm)],[13914, 13912])).
% 2.00/2.22 tff(13916,plain,
% 2.00/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s71)) | (~always25(s99)) | always25(s71))),
% 2.00/2.22 inference(quant_inst,[status(thm)],[])).
% 2.00/2.22 tff(13917,plain,
% 2.00/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s71) | (~trans(s99, s71))),
% 2.00/2.22 inference(modus_ponens,[status(thm)],[13916, 13915])).
% 2.00/2.22 tff(13918,plain,
% 2.00/2.22 ($false),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[13917, 12189, 3934, 13236, 8300])).
% 2.00/2.22 tff(13919,plain,((~trans(s99, s71)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.22 tff(13920,plain,
% 2.00/2.22 (~trans(s99, s71)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[13919, 13016])).
% 2.00/2.22 tff(13921,plain,
% 2.00/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s28) | (~trans(s99, s28)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s28) | (~trans(s99, s28)))),
% 2.00/2.22 inference(rewrite,[status(thm)],[])).
% 2.00/2.22 tff(13922,plain,
% 2.00/2.22 (((~trans(s99, s28)) | (~always25(s99)) | always25(s28)) <=> ((~always25(s99)) | always25(s28) | (~trans(s99, s28)))),
% 2.00/2.22 inference(rewrite,[status(thm)],[])).
% 2.00/2.22 tff(13923,plain,
% 2.00/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s28)) | (~always25(s99)) | always25(s28))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s28) | (~trans(s99, s28))))),
% 2.00/2.22 inference(monotonicity,[status(thm)],[13922])).
% 2.00/2.22 tff(13924,plain,
% 2.00/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s28)) | (~always25(s99)) | always25(s28))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s28) | (~trans(s99, s28)))),
% 2.00/2.22 inference(transitivity,[status(thm)],[13923, 13921])).
% 2.00/2.22 tff(13925,plain,
% 2.00/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s28)) | (~always25(s99)) | always25(s28))),
% 2.00/2.22 inference(quant_inst,[status(thm)],[])).
% 2.00/2.22 tff(13926,plain,
% 2.00/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s28) | (~trans(s99, s28))),
% 2.00/2.22 inference(modus_ponens,[status(thm)],[13925, 13924])).
% 2.00/2.22 tff(13927,plain,
% 2.00/2.22 ($false),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[13926, 12200, 3934, 13236, 8607])).
% 2.00/2.22 tff(13928,plain,((~trans(s99, s28)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.22 tff(13929,plain,
% 2.00/2.22 (~trans(s99, s28)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[13928, 13016])).
% 2.00/2.22 tff(13930,plain,
% 2.00/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s48) | (~trans(s99, s48)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s48) | (~trans(s99, s48)))),
% 2.00/2.22 inference(rewrite,[status(thm)],[])).
% 2.00/2.22 tff(13931,plain,
% 2.00/2.22 (((~trans(s99, s48)) | (~always25(s99)) | always25(s48)) <=> ((~always25(s99)) | always25(s48) | (~trans(s99, s48)))),
% 2.00/2.22 inference(rewrite,[status(thm)],[])).
% 2.00/2.22 tff(13932,plain,
% 2.00/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s48)) | (~always25(s99)) | always25(s48))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s48) | (~trans(s99, s48))))),
% 2.00/2.22 inference(monotonicity,[status(thm)],[13931])).
% 2.00/2.22 tff(13933,plain,
% 2.00/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s48)) | (~always25(s99)) | always25(s48))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s48) | (~trans(s99, s48)))),
% 2.00/2.22 inference(transitivity,[status(thm)],[13932, 13930])).
% 2.00/2.22 tff(13934,plain,
% 2.00/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s48)) | (~always25(s99)) | always25(s48))),
% 2.00/2.22 inference(quant_inst,[status(thm)],[])).
% 2.00/2.22 tff(13935,plain,
% 2.00/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s48) | (~trans(s99, s48))),
% 2.00/2.22 inference(modus_ponens,[status(thm)],[13934, 13933])).
% 2.00/2.22 tff(13936,plain,
% 2.00/2.22 ($false),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[13935, 12211, 3934, 13236, 8469])).
% 2.00/2.22 tff(13937,plain,((~trans(s99, s48)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.22 tff(13938,plain,
% 2.00/2.22 (~trans(s99, s48)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[13937, 13016])).
% 2.00/2.22 tff(13939,plain,
% 2.00/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s79) | (~trans(s99, s79)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s79) | (~trans(s99, s79)))),
% 2.00/2.22 inference(rewrite,[status(thm)],[])).
% 2.00/2.22 tff(13940,plain,
% 2.00/2.22 (((~trans(s99, s79)) | (~always25(s99)) | always25(s79)) <=> ((~always25(s99)) | always25(s79) | (~trans(s99, s79)))),
% 2.00/2.22 inference(rewrite,[status(thm)],[])).
% 2.00/2.22 tff(13941,plain,
% 2.00/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s79)) | (~always25(s99)) | always25(s79))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s79) | (~trans(s99, s79))))),
% 2.00/2.22 inference(monotonicity,[status(thm)],[13940])).
% 2.00/2.22 tff(13942,plain,
% 2.00/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s79)) | (~always25(s99)) | always25(s79))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s79) | (~trans(s99, s79)))),
% 2.00/2.22 inference(transitivity,[status(thm)],[13941, 13939])).
% 2.00/2.22 tff(13943,plain,
% 2.00/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s79)) | (~always25(s99)) | always25(s79))),
% 2.00/2.22 inference(quant_inst,[status(thm)],[])).
% 2.00/2.22 tff(13944,plain,
% 2.00/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s79) | (~trans(s99, s79))),
% 2.00/2.22 inference(modus_ponens,[status(thm)],[13943, 13942])).
% 2.00/2.22 tff(13945,plain,
% 2.00/2.22 ($false),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[13944, 12222, 3934, 13236, 8242])).
% 2.00/2.22 tff(13946,plain,((~trans(s99, s79)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.22 tff(13947,plain,
% 2.00/2.22 (~trans(s99, s79)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[13946, 13016])).
% 2.00/2.22 tff(13948,plain,
% 2.00/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s42) | (~trans(s99, s42)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s42) | (~trans(s99, s42)))),
% 2.00/2.22 inference(rewrite,[status(thm)],[])).
% 2.00/2.22 tff(13949,plain,
% 2.00/2.22 (((~trans(s99, s42)) | (~always25(s99)) | always25(s42)) <=> ((~always25(s99)) | always25(s42) | (~trans(s99, s42)))),
% 2.00/2.22 inference(rewrite,[status(thm)],[])).
% 2.00/2.22 tff(13950,plain,
% 2.00/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s42)) | (~always25(s99)) | always25(s42))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s42) | (~trans(s99, s42))))),
% 2.00/2.22 inference(monotonicity,[status(thm)],[13949])).
% 2.00/2.22 tff(13951,plain,
% 2.00/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s42)) | (~always25(s99)) | always25(s42))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s42) | (~trans(s99, s42)))),
% 2.00/2.22 inference(transitivity,[status(thm)],[13950, 13948])).
% 2.00/2.22 tff(13952,plain,
% 2.00/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s42)) | (~always25(s99)) | always25(s42))),
% 2.00/2.22 inference(quant_inst,[status(thm)],[])).
% 2.00/2.22 tff(13953,plain,
% 2.00/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s42) | (~trans(s99, s42))),
% 2.00/2.22 inference(modus_ponens,[status(thm)],[13952, 13951])).
% 2.00/2.22 tff(13954,plain,
% 2.00/2.22 ($false),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[13953, 12233, 3934, 13236, 8505])).
% 2.00/2.22 tff(13955,plain,((~trans(s99, s42)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.22 tff(13956,plain,
% 2.00/2.22 (~trans(s99, s42)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[13955, 13016])).
% 2.00/2.22 tff(13957,plain,
% 2.00/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s85, s86)) | (~always25(s85)) | always25(s86))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s85, s86)) | (~always25(s85)) | always25(s86))),
% 2.00/2.22 inference(rewrite,[status(thm)],[])).
% 2.00/2.22 tff(13958,plain,
% 2.00/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s85, s86)) | (~always25(s85)) | always25(s86))),
% 2.00/2.22 inference(quant_inst,[status(thm)],[])).
% 2.00/2.22 tff(13959,plain,
% 2.00/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~trans(s85, s86)) | (~always25(s85)) | always25(s86)),
% 2.00/2.22 inference(modus_ponens,[status(thm)],[13958, 13957])).
% 2.00/2.22 tff(13960,plain,
% 2.00/2.22 ((~always25(s85)) | always25(s86)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[13959, 3934, 7221])).
% 2.00/2.22 tff(13961,plain,
% 2.00/2.22 (~always25(s85)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[13960, 8193])).
% 2.00/2.22 tff(13962,plain,
% 2.00/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s85) | (~trans(s99, s85)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s85) | (~trans(s99, s85)))),
% 2.00/2.22 inference(rewrite,[status(thm)],[])).
% 2.00/2.22 tff(13963,plain,
% 2.00/2.22 (((~trans(s99, s85)) | (~always25(s99)) | always25(s85)) <=> ((~always25(s99)) | always25(s85) | (~trans(s99, s85)))),
% 2.00/2.22 inference(rewrite,[status(thm)],[])).
% 2.00/2.22 tff(13964,plain,
% 2.00/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s85)) | (~always25(s99)) | always25(s85))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s85) | (~trans(s99, s85))))),
% 2.00/2.22 inference(monotonicity,[status(thm)],[13963])).
% 2.00/2.22 tff(13965,plain,
% 2.00/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s85)) | (~always25(s99)) | always25(s85))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s85) | (~trans(s99, s85)))),
% 2.00/2.22 inference(transitivity,[status(thm)],[13964, 13962])).
% 2.00/2.22 tff(13966,plain,
% 2.00/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s85)) | (~always25(s99)) | always25(s85))),
% 2.00/2.22 inference(quant_inst,[status(thm)],[])).
% 2.00/2.22 tff(13967,plain,
% 2.00/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s85) | (~trans(s99, s85))),
% 2.00/2.22 inference(modus_ponens,[status(thm)],[13966, 13965])).
% 2.00/2.22 tff(13968,plain,
% 2.00/2.22 ($false),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[13967, 12255, 3934, 13236, 13961])).
% 2.00/2.22 tff(13969,plain,((~trans(s99, s85)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.22 tff(13970,plain,
% 2.00/2.22 (~trans(s99, s85)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[13969, 13016])).
% 2.00/2.22 tff(13971,plain,
% 2.00/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s95) | (~trans(s99, s95)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s95) | (~trans(s99, s95)))),
% 2.00/2.22 inference(rewrite,[status(thm)],[])).
% 2.00/2.22 tff(13972,plain,
% 2.00/2.22 (((~trans(s99, s95)) | (~always25(s99)) | always25(s95)) <=> ((~always25(s99)) | always25(s95) | (~trans(s99, s95)))),
% 2.00/2.22 inference(rewrite,[status(thm)],[])).
% 2.00/2.22 tff(13973,plain,
% 2.00/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s95)) | (~always25(s99)) | always25(s95))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s95) | (~trans(s99, s95))))),
% 2.00/2.22 inference(monotonicity,[status(thm)],[13972])).
% 2.00/2.22 tff(13974,plain,
% 2.00/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s95)) | (~always25(s99)) | always25(s95))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s95) | (~trans(s99, s95)))),
% 2.00/2.22 inference(transitivity,[status(thm)],[13973, 13971])).
% 2.00/2.22 tff(13975,plain,
% 2.00/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s95)) | (~always25(s99)) | always25(s95))),
% 2.00/2.22 inference(quant_inst,[status(thm)],[])).
% 2.00/2.22 tff(13976,plain,
% 2.00/2.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s95) | (~trans(s99, s95))),
% 2.00/2.22 inference(modus_ponens,[status(thm)],[13975, 13974])).
% 2.00/2.22 tff(13977,plain,
% 2.00/2.22 ($false),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[13976, 12365, 3934, 13236, 8126])).
% 2.00/2.22 tff(13978,plain,((~trans(s99, s95)) | (~always25(s99))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.22 tff(13979,plain,
% 2.00/2.22 (~trans(s99, s95)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[13978, 13016])).
% 2.00/2.22 tff(13980,plain,
% 2.00/2.22 (trans(s99, s0) | trans(s99, s2) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s35) | trans(s99, s37) | trans(s99, s40) | trans(s99, s41) | trans(s99, s44) | trans(s99, s51) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s62) | trans(s99, s65) | trans(s99, s68) | trans(s99, s72) | trans(s99, s73) | trans(s99, s76) | trans(s99, s81) | trans(s99, s82) | trans(s99, s92)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[12992, 13979, 13970, 13956, 13947, 13938, 13929, 13920, 13911, 13902, 13893, 13884, 13875, 13866, 13857, 13843, 13829, 13820, 13811, 13802, 13793, 13784, 13775, 13766, 13757, 13743, 13734, 13720, 13706, 13692, 13683, 13674, 13665, 13656, 13647, 13638, 13629, 13620, 13606, 13597, 13588, 13574, 13560, 13546, 13532, 13523, 13514, 13505, 13496, 13487, 13478, 13469, 13460, 13451, 13442, 13433, 13424, 13410, 13396, 13382, 13373, 13359, 13350, 13341, 13332, 13322, 13313, 13304, 13295, 13281, 13272, 13263, 13254, 13245])).
% 2.00/2.22 tff(13981,plain,
% 2.00/2.22 (trans(s99, s0) | trans(s99, s2) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s35) | trans(s99, s37) | trans(s99, s40) | trans(s99, s41) | trans(s99, s44) | trans(s99, s51) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s62) | trans(s99, s68) | trans(s99, s73) | trans(s99, s76) | trans(s99, s82)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[13980, 13235, 13227, 13214, 13206])).
% 2.00/2.22 tff(13982,plain,
% 2.00/2.22 (trans(s99, s0) | trans(s99, s2) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s35) | trans(s99, s37) | trans(s99, s41) | trans(s99, s44) | trans(s99, s55) | trans(s99, s56) | trans(s99, s62) | trans(s99, s68) | trans(s99, s73) | trans(s99, s76) | trans(s99, s82)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[13981, 13193, 13185, 13177, 13164])).
% 2.00/2.22 tff(13983,plain,
% 2.00/2.22 (trans(s99, s0) | trans(s99, s2) | trans(s99, s10) | trans(s99, s12) | trans(s99, s35) | trans(s99, s37) | trans(s99, s41) | trans(s99, s44) | trans(s99, s55) | trans(s99, s68) | trans(s99, s73) | trans(s99, s82)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[13982, 13156, 13148, 13140, 13132])).
% 2.00/2.22 tff(13984,plain,
% 2.00/2.22 (trans(s99, s0) | trans(s99, s2) | trans(s99, s10) | trans(s99, s35) | trans(s99, s37) | trans(s99, s44) | trans(s99, s68) | trans(s99, s82)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[13983, 13124, 13116, 13108, 13095])).
% 2.00/2.22 tff(13985,plain,
% 2.00/2.22 (trans(s99, s10) | trans(s99, s35) | trans(s99, s44) | trans(s99, s68)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[13984, 13082, 13074, 13061, 13053])).
% 2.00/2.22 tff(13986,plain,
% 2.00/2.22 (trans(s99, s44)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[13985, 13040, 13032, 13024])).
% 2.00/2.22 tff(13987,plain,
% 2.00/2.22 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s44) | (~trans(s99, s44)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s44) | (~trans(s99, s44)))),
% 2.00/2.23 inference(rewrite,[status(thm)],[])).
% 2.00/2.23 tff(13988,plain,
% 2.00/2.23 (((~trans(s99, s44)) | (~always25(s99)) | always25(s44)) <=> ((~always25(s99)) | always25(s44) | (~trans(s99, s44)))),
% 2.00/2.23 inference(rewrite,[status(thm)],[])).
% 2.00/2.23 tff(13989,plain,
% 2.00/2.23 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s44)) | (~always25(s99)) | always25(s44))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~always25(s99)) | always25(s44) | (~trans(s99, s44))))),
% 2.00/2.23 inference(monotonicity,[status(thm)],[13988])).
% 2.00/2.23 tff(13990,plain,
% 2.00/2.23 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s44)) | (~always25(s99)) | always25(s44))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s44) | (~trans(s99, s44)))),
% 2.00/2.23 inference(transitivity,[status(thm)],[13989, 13987])).
% 2.00/2.23 tff(13991,plain,
% 2.00/2.23 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | ((~trans(s99, s44)) | (~always25(s99)) | always25(s44))),
% 2.00/2.23 inference(quant_inst,[status(thm)],[])).
% 2.00/2.23 tff(13992,plain,
% 2.00/2.23 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always25(X)) | always25(Y))) | (~always25(s99)) | always25(s44) | (~trans(s99, s44))),
% 2.00/2.23 inference(modus_ponens,[status(thm)],[13991, 13990])).
% 2.00/2.23 tff(13993,plain,
% 2.00/2.23 ($false),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[13992, 13986, 3934, 13016, 3915])).
% 2.00/2.23 % SZS output end Proof
% 2.00/2.23 % E exiting
%------------------------------------------------------------------------------