TSTP Solution File: SYN036-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN036-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 23:53:14 EDT 2022
% Result : Unsatisfiable 0.19s 0.53s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN036-3 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 01:06:30 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.53 % SZS status Unsatisfiable
% 0.19/0.53 % SZS output start Proof
% 0.19/0.53 tff(n5_type, type, (
% 0.19/0.53 n5: $i > $o)).
% 0.19/0.53 tff(s4_type, type, (
% 0.19/0.53 s4: $i)).
% 0.19/0.53 tff(n4_type, type, (
% 0.19/0.53 n4: $o)).
% 0.19/0.53 tff(q_type, type, (
% 0.19/0.53 q: $i > $o)).
% 0.19/0.53 tff(s6_type, type, (
% 0.19/0.53 s6: $i)).
% 0.19/0.53 tff(n6_type, type, (
% 0.19/0.53 n6: $o)).
% 0.19/0.53 tff(n10_type, type, (
% 0.19/0.53 n10: $o)).
% 0.19/0.53 tff(p_type, type, (
% 0.19/0.53 p: $i > $o)).
% 0.19/0.53 tff(s2_type, type, (
% 0.19/0.53 s2: $i)).
% 0.19/0.53 tff(s1_type, type, (
% 0.19/0.53 s1: $i > $i)).
% 0.19/0.53 tff(s7_type, type, (
% 0.19/0.53 s7: $i)).
% 0.19/0.53 tff(n1_type, type, (
% 0.19/0.53 n1: $i > $o)).
% 0.19/0.53 tff(n7_type, type, (
% 0.19/0.53 n7: $o)).
% 0.19/0.53 tff(n8_type, type, (
% 0.19/0.53 n8: $o)).
% 0.19/0.53 tff(s8_type, type, (
% 0.19/0.53 s8: $i)).
% 0.19/0.53 tff(n2_type, type, (
% 0.19/0.53 n2: $o)).
% 0.19/0.53 tff(s5_type, type, (
% 0.19/0.53 s5: $i > $i)).
% 0.19/0.53 tff(n9_type, type, (
% 0.19/0.53 n9: $o)).
% 0.19/0.53 tff(n3_type, type, (
% 0.19/0.53 n3: $o)).
% 0.19/0.53 tff(s3_type, type, (
% 0.19/0.53 s3: $i)).
% 0.19/0.53 tff(1,assumption,(~n10), introduced(assumption)).
% 0.19/0.53 tff(2,assumption,(~n7), introduced(assumption)).
% 0.19/0.53 tff(3,plain,
% 0.19/0.53 ((n10 | n8 | n7) <=> (n10 | n8 | n7)),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(4,plain,
% 0.19/0.53 (((n7 | n8) | n10) <=> (n10 | n8 | n7)),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(5,axiom,((n7 | n8) | n10), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_34')).
% 0.19/0.53 tff(6,plain,
% 0.19/0.53 (n10 | n8 | n7),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.53 tff(7,plain,
% 0.19/0.53 (n10 | n8 | n7),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[6, 3])).
% 0.19/0.53 tff(8,plain,
% 0.19/0.53 (n10 | n8 | n7),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.53 tff(9,plain,
% 0.19/0.53 (n10 | n8 | n7),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.19/0.53 tff(10,plain,
% 0.19/0.53 (n10 | n8 | n7),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[9, 3])).
% 0.19/0.53 tff(11,plain,
% 0.19/0.53 (n10 | n8 | n7),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.19/0.53 tff(12,plain,
% 0.19/0.53 (n10 | n8 | n7),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[11, 3])).
% 0.19/0.53 tff(13,plain,
% 0.19/0.53 (n10 | n8 | n7),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[12, 3])).
% 0.19/0.53 tff(14,plain,
% 0.19/0.53 (n8),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[13, 2, 1])).
% 0.19/0.53 tff(15,assumption,(~p(s2)), introduced(assumption)).
% 0.19/0.53 tff(16,plain,
% 0.19/0.53 (^[X8: $i] : refl(((~n8) | p(X8)) <=> ((~n8) | p(X8)))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(17,plain,
% 0.19/0.53 (![X8: $i] : ((~n8) | p(X8)) <=> ![X8: $i] : ((~n8) | p(X8))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.53 tff(18,plain,
% 0.19/0.53 (![X8: $i] : ((~n8) | p(X8)) <=> ![X8: $i] : ((~n8) | p(X8))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(19,axiom,(![X8: $i] : ((~n8) | p(X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_10')).
% 0.19/0.53 tff(20,plain,
% 0.19/0.53 (![X8: $i] : ((~n8) | p(X8))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.53 tff(21,plain,(
% 0.19/0.53 ![X8: $i] : ((~n8) | p(X8))),
% 0.19/0.53 inference(skolemize,[status(sab)],[20])).
% 0.19/0.53 tff(22,plain,
% 0.19/0.53 (![X8: $i] : ((~n8) | p(X8))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.19/0.53 tff(23,assumption,(n8), introduced(assumption)).
% 0.19/0.53 tff(24,plain,
% 0.19/0.53 (((~![X8: $i] : ((~n8) | p(X8))) | ((~n8) | p(s2))) <=> ((~![X8: $i] : ((~n8) | p(X8))) | (~n8) | p(s2))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(25,plain,
% 0.19/0.53 ((~![X8: $i] : ((~n8) | p(X8))) | ((~n8) | p(s2))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(26,plain,
% 0.19/0.53 ((~![X8: $i] : ((~n8) | p(X8))) | (~n8) | p(s2)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.19/0.53 tff(27,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[26, 23, 22, 15])).
% 0.19/0.53 tff(28,plain,(p(s2) | (~n8)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.53 tff(29,plain,
% 0.19/0.53 (p(s2)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[28, 14])).
% 0.19/0.53 tff(30,plain,
% 0.19/0.53 (^[X7: $i] : refl((n7 | (~p(X7))) <=> (n7 | (~p(X7))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(31,plain,
% 0.19/0.53 (![X7: $i] : (n7 | (~p(X7))) <=> ![X7: $i] : (n7 | (~p(X7)))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[30])).
% 0.19/0.53 tff(32,plain,
% 0.19/0.53 (![X7: $i] : (n7 | (~p(X7))) <=> ![X7: $i] : (n7 | (~p(X7)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(33,plain,
% 0.19/0.53 (^[X7: $i] : rewrite(((~p(X7)) | n7) <=> (n7 | (~p(X7))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(34,plain,
% 0.19/0.53 (![X7: $i] : ((~p(X7)) | n7) <=> ![X7: $i] : (n7 | (~p(X7)))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[33])).
% 0.19/0.53 tff(35,axiom,(![X7: $i] : ((~p(X7)) | n7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_11')).
% 0.19/0.53 tff(36,plain,
% 0.19/0.53 (![X7: $i] : (n7 | (~p(X7)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.53 tff(37,plain,
% 0.19/0.53 (![X7: $i] : (n7 | (~p(X7)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.19/0.53 tff(38,plain,(
% 0.19/0.53 ![X7: $i] : (n7 | (~p(X7)))),
% 0.19/0.53 inference(skolemize,[status(sab)],[37])).
% 0.19/0.53 tff(39,plain,
% 0.19/0.53 (![X7: $i] : (n7 | (~p(X7)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.19/0.53 tff(40,plain,
% 0.19/0.53 (((~![X7: $i] : (n7 | (~p(X7)))) | (n7 | (~p(s2)))) <=> ((~![X7: $i] : (n7 | (~p(X7)))) | n7 | (~p(s2)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(41,plain,
% 0.19/0.53 ((~![X7: $i] : (n7 | (~p(X7)))) | (n7 | (~p(s2)))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(42,plain,
% 0.19/0.53 ((~![X7: $i] : (n7 | (~p(X7)))) | n7 | (~p(s2))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.19/0.53 tff(43,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[42, 39, 2, 29])).
% 0.19/0.53 tff(44,plain,(n7 | n10), inference(lemma,lemma(discharge,[]))).
% 0.19/0.53 tff(45,plain,
% 0.19/0.53 (n7),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[44, 1])).
% 0.19/0.53 tff(46,plain,
% 0.19/0.53 (((~n7) | p(s7)) <=> ((~n7) | p(s7))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(47,axiom,((~n7) | p(s7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_12')).
% 0.19/0.53 tff(48,plain,
% 0.19/0.53 ((~n7) | p(s7)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.19/0.53 tff(49,plain,
% 0.19/0.53 (p(s7)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[48, 45])).
% 0.19/0.53 tff(50,plain,
% 0.19/0.53 (^[X: $i, X1: $i] : refl((p(X1) | (~p(X)) | (~n1(X))) <=> (p(X1) | (~p(X)) | (~n1(X))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(51,plain,
% 0.19/0.53 (![X: $i, X1: $i] : (p(X1) | (~p(X)) | (~n1(X))) <=> ![X: $i, X1: $i] : (p(X1) | (~p(X)) | (~n1(X)))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.53 tff(52,plain,
% 0.19/0.53 (![X: $i, X1: $i] : (p(X1) | (~p(X)) | (~n1(X))) <=> ![X: $i, X1: $i] : (p(X1) | (~p(X)) | (~n1(X)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(53,plain,
% 0.19/0.53 (^[X: $i, X1: $i] : rewrite((((~n1(X)) | (~p(X))) | p(X1)) <=> (p(X1) | (~p(X)) | (~n1(X))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(54,plain,
% 0.19/0.53 (![X: $i, X1: $i] : (((~n1(X)) | (~p(X))) | p(X1)) <=> ![X: $i, X1: $i] : (p(X1) | (~p(X)) | (~n1(X)))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.53 tff(55,axiom,(![X: $i, X1: $i] : (((~n1(X)) | (~p(X))) | p(X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_27')).
% 0.19/0.53 tff(56,plain,
% 0.19/0.53 (![X: $i, X1: $i] : (p(X1) | (~p(X)) | (~n1(X)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.53 tff(57,plain,
% 0.19/0.53 (![X: $i, X1: $i] : (p(X1) | (~p(X)) | (~n1(X)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.19/0.53 tff(58,plain,(
% 0.19/0.53 ![X: $i, X1: $i] : (p(X1) | (~p(X)) | (~n1(X)))),
% 0.19/0.53 inference(skolemize,[status(sab)],[57])).
% 0.19/0.53 tff(59,plain,
% 0.19/0.53 (![X: $i, X1: $i] : (p(X1) | (~p(X)) | (~n1(X)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.19/0.53 tff(60,plain,
% 0.19/0.53 ((n10 | (~n7) | (~n8)) <=> (n10 | (~n7) | (~n8))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(61,plain,
% 0.19/0.53 ((((~n7) | (~n8)) | n10) <=> (n10 | (~n7) | (~n8))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(62,axiom,(((~n7) | (~n8)) | n10), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_33')).
% 0.19/0.53 tff(63,plain,
% 0.19/0.53 (n10 | (~n7) | (~n8)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.53 tff(64,plain,
% 0.19/0.53 (n10 | (~n7) | (~n8)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[63, 60])).
% 0.19/0.53 tff(65,plain,
% 0.19/0.53 (~n8),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[64, 45, 1])).
% 0.19/0.53 tff(66,plain,
% 0.19/0.53 (((~p(s8)) | n8) <=> ((~p(s8)) | n8)),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(67,axiom,((~p(s8)) | n8), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_9')).
% 0.19/0.53 tff(68,plain,
% 0.19/0.53 ((~p(s8)) | n8),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.53 tff(69,plain,
% 0.19/0.53 ((~p(s8)) | n8),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[68, 66])).
% 0.19/0.53 tff(70,plain,
% 0.19/0.53 ((~p(s8)) | n8),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[69, 66])).
% 0.19/0.53 tff(71,plain,
% 0.19/0.53 ((~p(s8)) | n8),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.19/0.53 tff(72,plain,
% 0.19/0.53 ((~p(s8)) | n8),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[71, 66])).
% 0.19/0.53 tff(73,plain,
% 0.19/0.53 ((~p(s8)) | n8),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[72, 66])).
% 0.19/0.53 tff(74,plain,
% 0.19/0.53 ((~p(s8)) | n8),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.19/0.53 tff(75,plain,
% 0.19/0.53 ((~p(s8)) | n8),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[74, 66])).
% 0.19/0.53 tff(76,plain,
% 0.19/0.53 (~p(s8)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[75, 65])).
% 0.19/0.53 tff(77,plain,
% 0.19/0.53 (((~![X: $i, X1: $i] : (p(X1) | (~p(X)) | (~n1(X)))) | (p(s8) | (~p(s7)) | (~n1(s7)))) <=> ((~![X: $i, X1: $i] : (p(X1) | (~p(X)) | (~n1(X)))) | p(s8) | (~p(s7)) | (~n1(s7)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(78,plain,
% 0.19/0.53 ((~![X: $i, X1: $i] : (p(X1) | (~p(X)) | (~n1(X)))) | (p(s8) | (~p(s7)) | (~n1(s7)))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(79,plain,
% 0.19/0.53 ((~![X: $i, X1: $i] : (p(X1) | (~p(X)) | (~n1(X)))) | p(s8) | (~p(s7)) | (~n1(s7))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.19/0.53 tff(80,plain,
% 0.19/0.53 (~n1(s7)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[79, 76, 49, 59])).
% 0.19/0.53 tff(81,plain,
% 0.19/0.53 (^[X: $i] : refl(((~p(X)) | n1(X) | (~p(s1(X)))) <=> ((~p(X)) | n1(X) | (~p(s1(X)))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(82,plain,
% 0.19/0.53 (![X: $i] : ((~p(X)) | n1(X) | (~p(s1(X)))) <=> ![X: $i] : ((~p(X)) | n1(X) | (~p(s1(X))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[81])).
% 0.19/0.53 tff(83,plain,
% 0.19/0.53 (![X: $i] : ((~p(X)) | n1(X) | (~p(s1(X)))) <=> ![X: $i] : ((~p(X)) | n1(X) | (~p(s1(X))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(84,plain,
% 0.19/0.53 (^[X: $i] : rewrite((((~p(X)) | (~p(s1(X)))) | n1(X)) <=> ((~p(X)) | n1(X) | (~p(s1(X)))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(85,plain,
% 0.19/0.53 (![X: $i] : (((~p(X)) | (~p(s1(X)))) | n1(X)) <=> ![X: $i] : ((~p(X)) | n1(X) | (~p(s1(X))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[84])).
% 0.19/0.53 tff(86,axiom,(![X: $i] : (((~p(X)) | (~p(s1(X)))) | n1(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_25')).
% 0.19/0.53 tff(87,plain,
% 0.19/0.53 (![X: $i] : ((~p(X)) | n1(X) | (~p(s1(X))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.53 tff(88,plain,
% 0.19/0.53 (![X: $i] : ((~p(X)) | n1(X) | (~p(s1(X))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.19/0.53 tff(89,plain,(
% 0.19/0.53 ![X: $i] : ((~p(X)) | n1(X) | (~p(s1(X))))),
% 0.19/0.53 inference(skolemize,[status(sab)],[88])).
% 0.19/0.53 tff(90,plain,
% 0.19/0.53 (![X: $i] : ((~p(X)) | n1(X) | (~p(s1(X))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.19/0.53 tff(91,plain,
% 0.19/0.53 (((~![X: $i] : ((~p(X)) | n1(X) | (~p(s1(X))))) | ((~p(s7)) | n1(s7) | (~p(s1(s7))))) <=> ((~![X: $i] : ((~p(X)) | n1(X) | (~p(s1(X))))) | (~p(s7)) | n1(s7) | (~p(s1(s7))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(92,plain,
% 0.19/0.53 ((~![X: $i] : ((~p(X)) | n1(X) | (~p(s1(X))))) | ((~p(s7)) | n1(s7) | (~p(s1(s7))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(93,plain,
% 0.19/0.53 ((~![X: $i] : ((~p(X)) | n1(X) | (~p(s1(X))))) | (~p(s7)) | n1(s7) | (~p(s1(s7)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.53 tff(94,plain,
% 0.19/0.53 ((~p(s7)) | n1(s7) | (~p(s1(s7)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[93, 90])).
% 0.19/0.53 tff(95,plain,
% 0.19/0.53 (~p(s1(s7))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[94, 80, 49])).
% 0.19/0.53 tff(96,plain,
% 0.19/0.53 (^[X: $i, X1: $i] : refl(((~p(X1)) | p(X) | (~n1(X))) <=> ((~p(X1)) | p(X) | (~n1(X))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(97,plain,
% 0.19/0.53 (![X: $i, X1: $i] : ((~p(X1)) | p(X) | (~n1(X))) <=> ![X: $i, X1: $i] : ((~p(X1)) | p(X) | (~n1(X)))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[96])).
% 0.19/0.53 tff(98,plain,
% 0.19/0.53 (![X: $i, X1: $i] : ((~p(X1)) | p(X) | (~n1(X))) <=> ![X: $i, X1: $i] : ((~p(X1)) | p(X) | (~n1(X)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(99,plain,
% 0.19/0.53 (^[X: $i, X1: $i] : trans(monotonicity(rewrite(((~n1(X)) | p(X)) <=> (p(X) | (~n1(X)))), ((((~n1(X)) | p(X)) | (~p(X1))) <=> ((p(X) | (~n1(X))) | (~p(X1))))), rewrite(((p(X) | (~n1(X))) | (~p(X1))) <=> ((~p(X1)) | p(X) | (~n1(X)))), ((((~n1(X)) | p(X)) | (~p(X1))) <=> ((~p(X1)) | p(X) | (~n1(X)))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(100,plain,
% 0.19/0.53 (![X: $i, X1: $i] : (((~n1(X)) | p(X)) | (~p(X1))) <=> ![X: $i, X1: $i] : ((~p(X1)) | p(X) | (~n1(X)))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[99])).
% 0.19/0.53 tff(101,axiom,(![X: $i, X1: $i] : (((~n1(X)) | p(X)) | (~p(X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_28')).
% 0.19/0.53 tff(102,plain,
% 0.19/0.53 (![X: $i, X1: $i] : ((~p(X1)) | p(X) | (~n1(X)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.19/0.53 tff(103,plain,
% 0.19/0.53 (![X: $i, X1: $i] : ((~p(X1)) | p(X) | (~n1(X)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.19/0.53 tff(104,plain,(
% 0.19/0.53 ![X: $i, X1: $i] : ((~p(X1)) | p(X) | (~n1(X)))),
% 0.19/0.53 inference(skolemize,[status(sab)],[103])).
% 0.19/0.53 tff(105,plain,
% 0.19/0.53 (![X: $i, X1: $i] : ((~p(X1)) | p(X) | (~n1(X)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.19/0.53 tff(106,plain,
% 0.19/0.53 (((~![X: $i, X1: $i] : ((~p(X1)) | p(X) | (~n1(X)))) | ((~p(s7)) | p(s1(s7)) | (~n1(s1(s7))))) <=> ((~![X: $i, X1: $i] : ((~p(X1)) | p(X) | (~n1(X)))) | (~p(s7)) | p(s1(s7)) | (~n1(s1(s7))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(107,plain,
% 0.19/0.53 ((~![X: $i, X1: $i] : ((~p(X1)) | p(X) | (~n1(X)))) | ((~p(s7)) | p(s1(s7)) | (~n1(s1(s7))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(108,plain,
% 0.19/0.53 ((~![X: $i, X1: $i] : ((~p(X1)) | p(X) | (~n1(X)))) | (~p(s7)) | p(s1(s7)) | (~n1(s1(s7)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.19/0.53 tff(109,plain,
% 0.19/0.53 (~n1(s1(s7))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[108, 49, 105, 95])).
% 0.19/0.53 tff(110,plain,
% 0.19/0.53 (^[X: $i] : refl((p(X) | n1(X) | p(s1(X))) <=> (p(X) | n1(X) | p(s1(X))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(111,plain,
% 0.19/0.53 (![X: $i] : (p(X) | n1(X) | p(s1(X))) <=> ![X: $i] : (p(X) | n1(X) | p(s1(X)))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[110])).
% 0.19/0.53 tff(112,plain,
% 0.19/0.53 (![X: $i] : (p(X) | n1(X) | p(s1(X))) <=> ![X: $i] : (p(X) | n1(X) | p(s1(X)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(113,plain,
% 0.19/0.53 (^[X: $i] : rewrite(((p(X) | p(s1(X))) | n1(X)) <=> (p(X) | n1(X) | p(s1(X))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(114,plain,
% 0.19/0.53 (![X: $i] : ((p(X) | p(s1(X))) | n1(X)) <=> ![X: $i] : (p(X) | n1(X) | p(s1(X)))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[113])).
% 0.19/0.53 tff(115,axiom,(![X: $i] : ((p(X) | p(s1(X))) | n1(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_26')).
% 0.19/0.53 tff(116,plain,
% 0.19/0.53 (![X: $i] : (p(X) | n1(X) | p(s1(X)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.19/0.53 tff(117,plain,
% 0.19/0.53 (![X: $i] : (p(X) | n1(X) | p(s1(X)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.19/0.53 tff(118,plain,(
% 0.19/0.53 ![X: $i] : (p(X) | n1(X) | p(s1(X)))),
% 0.19/0.53 inference(skolemize,[status(sab)],[117])).
% 0.19/0.53 tff(119,plain,
% 0.19/0.53 (![X: $i] : (p(X) | n1(X) | p(s1(X)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[118, 111])).
% 0.19/0.53 tff(120,plain,
% 0.19/0.53 (((~![X: $i] : (p(X) | n1(X) | p(s1(X)))) | (p(s1(s7)) | n1(s1(s7)) | p(s1(s1(s7))))) <=> ((~![X: $i] : (p(X) | n1(X) | p(s1(X)))) | p(s1(s7)) | n1(s1(s7)) | p(s1(s1(s7))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(121,plain,
% 0.19/0.53 ((~![X: $i] : (p(X) | n1(X) | p(s1(X)))) | (p(s1(s7)) | n1(s1(s7)) | p(s1(s1(s7))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(122,plain,
% 0.19/0.53 ((~![X: $i] : (p(X) | n1(X) | p(s1(X)))) | p(s1(s7)) | n1(s1(s7)) | p(s1(s1(s7)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.19/0.53 tff(123,plain,
% 0.19/0.53 (p(s1(s1(s7)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[122, 119, 95, 109])).
% 0.19/0.53 tff(124,assumption,(~n2), introduced(assumption)).
% 0.19/0.53 tff(125,assumption,(n1(s2)), introduced(assumption)).
% 0.19/0.53 tff(126,plain,
% 0.19/0.53 (^[X2: $i] : refl((n2 | (~n1(X2))) <=> (n2 | (~n1(X2))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(127,plain,
% 0.19/0.53 (![X2: $i] : (n2 | (~n1(X2))) <=> ![X2: $i] : (n2 | (~n1(X2)))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[126])).
% 0.19/0.53 tff(128,plain,
% 0.19/0.53 (![X2: $i] : (n2 | (~n1(X2))) <=> ![X2: $i] : (n2 | (~n1(X2)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(129,plain,
% 0.19/0.53 (^[X2: $i] : rewrite(((~n1(X2)) | n2) <=> (n2 | (~n1(X2))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(130,plain,
% 0.19/0.53 (![X2: $i] : ((~n1(X2)) | n2) <=> ![X2: $i] : (n2 | (~n1(X2)))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[129])).
% 0.19/0.53 tff(131,axiom,(![X2: $i] : ((~n1(X2)) | n2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_23')).
% 0.19/0.53 tff(132,plain,
% 0.19/0.53 (![X2: $i] : (n2 | (~n1(X2)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.19/0.53 tff(133,plain,
% 0.19/0.53 (![X2: $i] : (n2 | (~n1(X2)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.19/0.53 tff(134,plain,(
% 0.19/0.53 ![X2: $i] : (n2 | (~n1(X2)))),
% 0.19/0.53 inference(skolemize,[status(sab)],[133])).
% 0.19/0.53 tff(135,plain,
% 0.19/0.53 (![X2: $i] : (n2 | (~n1(X2)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[134, 127])).
% 0.19/0.53 tff(136,plain,
% 0.19/0.53 (((~![X2: $i] : (n2 | (~n1(X2)))) | (n2 | (~n1(s2)))) <=> ((~![X2: $i] : (n2 | (~n1(X2)))) | n2 | (~n1(s2)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(137,plain,
% 0.19/0.53 ((~![X2: $i] : (n2 | (~n1(X2)))) | (n2 | (~n1(s2)))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(138,plain,
% 0.19/0.53 ((~![X2: $i] : (n2 | (~n1(X2)))) | n2 | (~n1(s2))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.19/0.53 tff(139,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[138, 124, 135, 125])).
% 0.19/0.53 tff(140,plain,((~n1(s2)) | n2), inference(lemma,lemma(discharge,[]))).
% 0.19/0.53 tff(141,plain,
% 0.19/0.53 (~n1(s2)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[140, 124])).
% 0.19/0.53 tff(142,assumption,(p(s1(s2))), introduced(assumption)).
% 0.19/0.53 tff(143,plain,
% 0.19/0.53 (((~![X7: $i] : (n7 | (~p(X7)))) | (n7 | (~p(s1(s2))))) <=> ((~![X7: $i] : (n7 | (~p(X7)))) | n7 | (~p(s1(s2))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(144,plain,
% 0.19/0.53 ((~![X7: $i] : (n7 | (~p(X7)))) | (n7 | (~p(s1(s2))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(145,plain,
% 0.19/0.53 ((~![X7: $i] : (n7 | (~p(X7)))) | n7 | (~p(s1(s2)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.19/0.53 tff(146,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[145, 39, 2, 142])).
% 0.19/0.53 tff(147,plain,((~p(s1(s2))) | n7), inference(lemma,lemma(discharge,[]))).
% 0.19/0.53 tff(148,plain,
% 0.19/0.53 (~p(s1(s2))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[147, 2])).
% 0.19/0.53 tff(149,assumption,(~n1(s2)), introduced(assumption)).
% 0.19/0.53 tff(150,plain,
% 0.19/0.53 (((~![X: $i] : (p(X) | n1(X) | p(s1(X)))) | (n1(s2) | p(s2) | p(s1(s2)))) <=> ((~![X: $i] : (p(X) | n1(X) | p(s1(X)))) | n1(s2) | p(s2) | p(s1(s2)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(151,plain,
% 0.19/0.53 ((p(s2) | n1(s2) | p(s1(s2))) <=> (n1(s2) | p(s2) | p(s1(s2)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(152,plain,
% 0.19/0.53 (((~![X: $i] : (p(X) | n1(X) | p(s1(X)))) | (p(s2) | n1(s2) | p(s1(s2)))) <=> ((~![X: $i] : (p(X) | n1(X) | p(s1(X)))) | (n1(s2) | p(s2) | p(s1(s2))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[151])).
% 0.19/0.53 tff(153,plain,
% 0.19/0.53 (((~![X: $i] : (p(X) | n1(X) | p(s1(X)))) | (p(s2) | n1(s2) | p(s1(s2)))) <=> ((~![X: $i] : (p(X) | n1(X) | p(s1(X)))) | n1(s2) | p(s2) | p(s1(s2)))),
% 0.19/0.53 inference(transitivity,[status(thm)],[152, 150])).
% 0.19/0.53 tff(154,plain,
% 0.19/0.53 ((~![X: $i] : (p(X) | n1(X) | p(s1(X)))) | (p(s2) | n1(s2) | p(s1(s2)))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(155,plain,
% 0.19/0.53 ((~![X: $i] : (p(X) | n1(X) | p(s1(X)))) | n1(s2) | p(s2) | p(s1(s2))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.19/0.53 tff(156,plain,
% 0.19/0.53 (p(s2) | p(s1(s2))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[155, 149, 119])).
% 0.19/0.53 tff(157,plain,
% 0.19/0.53 (p(s2)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[156, 148])).
% 0.19/0.53 tff(158,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[42, 39, 2, 157])).
% 0.19/0.53 tff(159,plain,(n7 | n1(s2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.53 tff(160,plain,
% 0.19/0.53 (n7),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[159, 141])).
% 0.19/0.53 tff(161,plain,
% 0.19/0.53 (p(s2)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[28, 23])).
% 0.19/0.53 tff(162,plain,
% 0.19/0.53 (((~![X: $i] : ((~p(X)) | n1(X) | (~p(s1(X))))) | (n1(s2) | (~p(s2)) | (~p(s1(s2))))) <=> ((~![X: $i] : ((~p(X)) | n1(X) | (~p(s1(X))))) | n1(s2) | (~p(s2)) | (~p(s1(s2))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(163,plain,
% 0.19/0.53 (((~p(s2)) | n1(s2) | (~p(s1(s2)))) <=> (n1(s2) | (~p(s2)) | (~p(s1(s2))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(164,plain,
% 0.19/0.53 (((~![X: $i] : ((~p(X)) | n1(X) | (~p(s1(X))))) | ((~p(s2)) | n1(s2) | (~p(s1(s2))))) <=> ((~![X: $i] : ((~p(X)) | n1(X) | (~p(s1(X))))) | (n1(s2) | (~p(s2)) | (~p(s1(s2)))))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[163])).
% 0.19/0.54 tff(165,plain,
% 0.19/0.54 (((~![X: $i] : ((~p(X)) | n1(X) | (~p(s1(X))))) | ((~p(s2)) | n1(s2) | (~p(s1(s2))))) <=> ((~![X: $i] : ((~p(X)) | n1(X) | (~p(s1(X))))) | n1(s2) | (~p(s2)) | (~p(s1(s2))))),
% 0.19/0.54 inference(transitivity,[status(thm)],[164, 162])).
% 0.19/0.54 tff(166,plain,
% 0.19/0.54 ((~![X: $i] : ((~p(X)) | n1(X) | (~p(s1(X))))) | ((~p(s2)) | n1(s2) | (~p(s1(s2))))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(167,plain,
% 0.19/0.54 ((~![X: $i] : ((~p(X)) | n1(X) | (~p(s1(X))))) | n1(s2) | (~p(s2)) | (~p(s1(s2)))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.19/0.54 tff(168,plain,
% 0.19/0.54 (n1(s2) | (~p(s2)) | (~p(s1(s2)))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[167, 90])).
% 0.19/0.54 tff(169,plain,
% 0.19/0.54 (~p(s1(s2))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[168, 161, 149])).
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% 0.19/0.54 inference(unit_resolution,[status(thm)],[377, 373])).
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% 0.19/0.55 inference(unit_resolution,[status(thm)],[542, 432, 532, 536])).
% 0.19/0.55 tff(544,plain,
% 0.19/0.55 (((~![X: $i, X5: $i] : ((~q(X5)) | q(X) | (~n5(X)))) | ((~q(s3)) | q(s5(s5(s5(s5(s4))))) | (~n5(s5(s5(s5(s5(s4)))))))) <=> ((~![X: $i, X5: $i] : ((~q(X5)) | q(X) | (~n5(X)))) | (~q(s3)) | q(s5(s5(s5(s5(s4))))) | (~n5(s5(s5(s5(s5(s4)))))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(545,plain,
% 0.19/0.55 ((~![X: $i, X5: $i] : ((~q(X5)) | q(X) | (~n5(X)))) | ((~q(s3)) | q(s5(s5(s5(s5(s4))))) | (~n5(s5(s5(s5(s5(s4)))))))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(546,plain,
% 0.19/0.55 ((~![X: $i, X5: $i] : ((~q(X5)) | q(X) | (~n5(X)))) | (~q(s3)) | q(s5(s5(s5(s5(s4))))) | (~n5(s5(s5(s5(s5(s4))))))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[545, 544])).
% 0.19/0.55 tff(547,plain,
% 0.19/0.55 (~n5(s5(s5(s5(s5(s4)))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[546, 491, 481, 543])).
% 0.19/0.55 tff(548,plain,
% 0.19/0.55 (((~![X: $i] : (n5(X) | q(s5(X)) | q(X))) | (n5(s5(s5(s5(s5(s4))))) | q(s5(s5(s5(s5(s4))))) | q(s5(s5(s5(s5(s5(s4)))))))) <=> ((~![X: $i] : (n5(X) | q(s5(X)) | q(X))) | n5(s5(s5(s5(s5(s4))))) | q(s5(s5(s5(s5(s4))))) | q(s5(s5(s5(s5(s5(s4)))))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(549,plain,
% 0.19/0.55 ((n5(s5(s5(s5(s5(s4))))) | q(s5(s5(s5(s5(s5(s4)))))) | q(s5(s5(s5(s5(s4)))))) <=> (n5(s5(s5(s5(s5(s4))))) | q(s5(s5(s5(s5(s4))))) | q(s5(s5(s5(s5(s5(s4)))))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(550,plain,
% 0.19/0.55 (((~![X: $i] : (n5(X) | q(s5(X)) | q(X))) | (n5(s5(s5(s5(s5(s4))))) | q(s5(s5(s5(s5(s5(s4)))))) | q(s5(s5(s5(s5(s4))))))) <=> ((~![X: $i] : (n5(X) | q(s5(X)) | q(X))) | (n5(s5(s5(s5(s5(s4))))) | q(s5(s5(s5(s5(s4))))) | q(s5(s5(s5(s5(s5(s4))))))))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[549])).
% 0.19/0.55 tff(551,plain,
% 0.19/0.55 (((~![X: $i] : (n5(X) | q(s5(X)) | q(X))) | (n5(s5(s5(s5(s5(s4))))) | q(s5(s5(s5(s5(s5(s4)))))) | q(s5(s5(s5(s5(s4))))))) <=> ((~![X: $i] : (n5(X) | q(s5(X)) | q(X))) | n5(s5(s5(s5(s5(s4))))) | q(s5(s5(s5(s5(s4))))) | q(s5(s5(s5(s5(s5(s4)))))))),
% 0.19/0.55 inference(transitivity,[status(thm)],[550, 548])).
% 0.19/0.55 tff(552,plain,
% 0.19/0.55 ((~![X: $i] : (n5(X) | q(s5(X)) | q(X))) | (n5(s5(s5(s5(s5(s4))))) | q(s5(s5(s5(s5(s5(s4)))))) | q(s5(s5(s5(s5(s4))))))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(553,plain,
% 0.19/0.55 ((~![X: $i] : (n5(X) | q(s5(X)) | q(X))) | n5(s5(s5(s5(s5(s4))))) | q(s5(s5(s5(s5(s4))))) | q(s5(s5(s5(s5(s5(s4))))))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[552, 551])).
% 0.19/0.55 tff(554,plain,
% 0.19/0.55 (q(s5(s5(s5(s5(s5(s4))))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[553, 241, 543, 547])).
% 0.19/0.55 tff(555,plain,
% 0.19/0.55 (((~![X: $i, X5: $i] : ((~q(X5)) | q(X) | (~n5(X)))) | (q(s6) | (~n5(s6)) | (~q(s5(s5(s5(s5(s5(s4))))))))) <=> ((~![X: $i, X5: $i] : ((~q(X5)) | q(X) | (~n5(X)))) | q(s6) | (~n5(s6)) | (~q(s5(s5(s5(s5(s5(s4))))))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(556,plain,
% 0.19/0.55 (((~q(s5(s5(s5(s5(s5(s4))))))) | q(s6) | (~n5(s6))) <=> (q(s6) | (~n5(s6)) | (~q(s5(s5(s5(s5(s5(s4))))))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(557,plain,
% 0.19/0.55 (((~![X: $i, X5: $i] : ((~q(X5)) | q(X) | (~n5(X)))) | ((~q(s5(s5(s5(s5(s5(s4))))))) | q(s6) | (~n5(s6)))) <=> ((~![X: $i, X5: $i] : ((~q(X5)) | q(X) | (~n5(X)))) | (q(s6) | (~n5(s6)) | (~q(s5(s5(s5(s5(s5(s4)))))))))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[556])).
% 0.19/0.55 tff(558,plain,
% 0.19/0.55 (((~![X: $i, X5: $i] : ((~q(X5)) | q(X) | (~n5(X)))) | ((~q(s5(s5(s5(s5(s5(s4))))))) | q(s6) | (~n5(s6)))) <=> ((~![X: $i, X5: $i] : ((~q(X5)) | q(X) | (~n5(X)))) | q(s6) | (~n5(s6)) | (~q(s5(s5(s5(s5(s5(s4))))))))),
% 0.19/0.55 inference(transitivity,[status(thm)],[557, 555])).
% 0.19/0.55 tff(559,plain,
% 0.19/0.55 ((~![X: $i, X5: $i] : ((~q(X5)) | q(X) | (~n5(X)))) | ((~q(s5(s5(s5(s5(s5(s4))))))) | q(s6) | (~n5(s6)))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(560,plain,
% 0.19/0.55 ((~![X: $i, X5: $i] : ((~q(X5)) | q(X) | (~n5(X)))) | q(s6) | (~n5(s6)) | (~q(s5(s5(s5(s5(s5(s4)))))))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[559, 558])).
% 0.19/0.55 tff(561,plain,
% 0.19/0.55 (q(s6) | (~n5(s6)) | (~q(s5(s5(s5(s5(s5(s4)))))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[560, 491])).
% 0.19/0.55 tff(562,plain,
% 0.19/0.55 (q(s6)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[561, 554, 452])).
% 0.19/0.55 tff(563,plain,
% 0.19/0.55 (((~![X: $i, X5: $i] : (q(X5) | (~q(X)) | (~n5(X)))) | (q(s4) | (~n5(s6)) | (~q(s6)))) <=> ((~![X: $i, X5: $i] : (q(X5) | (~q(X)) | (~n5(X)))) | q(s4) | (~n5(s6)) | (~q(s6)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(564,plain,
% 0.19/0.55 ((q(s4) | (~q(s6)) | (~n5(s6))) <=> (q(s4) | (~n5(s6)) | (~q(s6)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(565,plain,
% 0.19/0.55 (((~![X: $i, X5: $i] : (q(X5) | (~q(X)) | (~n5(X)))) | (q(s4) | (~q(s6)) | (~n5(s6)))) <=> ((~![X: $i, X5: $i] : (q(X5) | (~q(X)) | (~n5(X)))) | (q(s4) | (~n5(s6)) | (~q(s6))))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[564])).
% 0.19/0.55 tff(566,plain,
% 0.19/0.55 (((~![X: $i, X5: $i] : (q(X5) | (~q(X)) | (~n5(X)))) | (q(s4) | (~q(s6)) | (~n5(s6)))) <=> ((~![X: $i, X5: $i] : (q(X5) | (~q(X)) | (~n5(X)))) | q(s4) | (~n5(s6)) | (~q(s6)))),
% 0.19/0.55 inference(transitivity,[status(thm)],[565, 563])).
% 0.19/0.55 tff(567,plain,
% 0.19/0.55 ((~![X: $i, X5: $i] : (q(X5) | (~q(X)) | (~n5(X)))) | (q(s4) | (~q(s6)) | (~n5(s6)))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(568,plain,
% 0.19/0.55 ((~![X: $i, X5: $i] : (q(X5) | (~q(X)) | (~n5(X)))) | q(s4) | (~n5(s6)) | (~q(s6))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[567, 566])).
% 0.19/0.55 tff(569,plain,
% 0.19/0.55 ($false),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[568, 452, 509, 477, 562])).
% 0.19/0.55 tff(570,plain,(n2), inference(lemma,lemma(discharge,[]))).
% 0.19/0.55 tff(571,plain,
% 0.19/0.55 (n1(s2)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[337, 570])).
% 0.19/0.55 tff(572,plain,
% 0.19/0.55 ((~p(s1(s1(s7)))) | p(s2)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[363, 571])).
% 0.19/0.55 tff(573,plain,
% 0.19/0.55 (p(s2)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[572, 123])).
% 0.19/0.55 tff(574,plain,
% 0.19/0.55 ($false),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[370, 76, 571, 59, 573])).
% 0.19/0.55 tff(575,plain,(n10), inference(lemma,lemma(discharge,[]))).
% 0.19/0.55 tff(576,assumption,(~n4), introduced(assumption)).
% 0.19/0.55 tff(577,plain,
% 0.19/0.55 (~n9),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[408, 576])).
% 0.19/0.55 tff(578,plain,
% 0.19/0.55 (((~n2) | n9 | n6 | (~n10)) <=> ((~n2) | n9 | n6 | (~n10))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(579,plain,
% 0.19/0.55 ((((~n2) | n9 | n6) | (~n10)) <=> ((~n2) | n9 | n6 | (~n10))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(580,plain,
% 0.19/0.55 ((((~n2) | n9) | n6) <=> ((~n2) | n9 | n6)),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(581,plain,
% 0.19/0.56 (((~n2) | n9) <=> ((~n2) | n9)),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(582,plain,
% 0.19/0.56 ((((~n2) | n9) | n6) <=> (((~n2) | n9) | n6)),
% 0.19/0.56 inference(monotonicity,[status(thm)],[581])).
% 0.19/0.56 tff(583,plain,
% 0.19/0.56 ((((~n2) | n9) | n6) <=> ((~n2) | n9 | n6)),
% 0.19/0.56 inference(transitivity,[status(thm)],[582, 580])).
% 0.19/0.56 tff(584,plain,
% 0.19/0.56 (((((~n2) | n9) | n6) | (~n10)) <=> (((~n2) | n9 | n6) | (~n10))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[583])).
% 0.19/0.56 tff(585,plain,
% 0.19/0.56 (((((~n2) | n9) | n6) | (~n10)) <=> ((~n2) | n9 | n6 | (~n10))),
% 0.19/0.56 inference(transitivity,[status(thm)],[584, 579])).
% 0.19/0.56 tff(586,axiom,((((~n2) | n9) | n6) | (~n10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_6')).
% 0.19/0.56 tff(587,plain,
% 0.19/0.56 ((~n2) | n9 | n6 | (~n10)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[586, 585])).
% 0.19/0.56 tff(588,plain,
% 0.19/0.56 ((~n2) | n9 | n6 | (~n10)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[587, 578])).
% 0.19/0.56 tff(589,plain,
% 0.19/0.56 ((~n2) | n9 | n6 | (~n10)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[588, 578])).
% 0.19/0.56 tff(590,plain,
% 0.19/0.56 ((~n2) | n9 | n6 | (~n10)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[589, 578])).
% 0.19/0.56 tff(591,plain,
% 0.19/0.56 ((~n2) | n9 | n6 | (~n10)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[590, 578])).
% 0.19/0.56 tff(592,plain,
% 0.19/0.56 ((~n2) | n9 | n6 | (~n10)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[591, 578])).
% 0.19/0.56 tff(593,plain,
% 0.19/0.56 ((~n2) | n9 | n6 | (~n10)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[592, 578])).
% 0.19/0.56 tff(594,plain,
% 0.19/0.56 ((~n2) | n9 | n6 | (~n10)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[593, 578])).
% 0.19/0.56 tff(595,plain,
% 0.19/0.56 (n9 | n6 | (~n10)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[594, 570])).
% 0.19/0.56 tff(596,plain,
% 0.19/0.56 (n6),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[595, 577, 575])).
% 0.19/0.56 tff(597,plain,
% 0.19/0.56 (n5(s6)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[451, 596])).
% 0.19/0.56 tff(598,plain,
% 0.19/0.56 (~q(s4)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[476, 576])).
% 0.19/0.56 tff(599,plain,
% 0.19/0.56 (~n5(s4)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[497, 491, 598, 481])).
% 0.19/0.56 tff(600,plain,
% 0.19/0.56 (q(s5(s4))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[248, 599, 598])).
% 0.19/0.56 tff(601,plain,
% 0.19/0.56 (~n5(s5(s4))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[512, 509, 598, 600])).
% 0.19/0.56 tff(602,plain,
% 0.19/0.56 (~q(s5(s5(s4)))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[519, 432, 600, 601])).
% 0.19/0.56 tff(603,plain,
% 0.19/0.56 (~n5(s5(s5(s4)))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[523, 491, 481, 602])).
% 0.19/0.56 tff(604,plain,
% 0.19/0.56 (q(s5(s5(s5(s4))))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[531, 603, 602])).
% 0.19/0.56 tff(605,plain,
% 0.19/0.56 (~n5(s5(s5(s5(s4))))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[535, 509, 598, 604])).
% 0.19/0.56 tff(606,plain,
% 0.19/0.56 (~q(s5(s5(s5(s5(s4)))))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[542, 432, 604, 605])).
% 0.19/0.56 tff(607,plain,
% 0.19/0.56 (~n5(s5(s5(s5(s5(s4)))))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[546, 491, 481, 606])).
% 0.19/0.56 tff(608,plain,
% 0.19/0.56 (q(s5(s5(s5(s5(s5(s4))))))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[553, 241, 606, 607])).
% 0.19/0.56 tff(609,plain,
% 0.19/0.56 (q(s6)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[561, 608, 597])).
% 0.19/0.56 tff(610,plain,
% 0.19/0.56 ($false),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[568, 597, 509, 598, 609])).
% 0.19/0.56 tff(611,plain,(n4), inference(lemma,lemma(discharge,[]))).
% 0.19/0.56 tff(612,plain,
% 0.19/0.56 (q(s5(s4))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[416, 411])).
% 0.19/0.56 tff(613,assumption,(~n5(s4)), introduced(assumption)).
% 0.19/0.56 tff(614,plain,
% 0.19/0.56 (q(s4)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[421, 411])).
% 0.19/0.56 tff(615,plain,
% 0.19/0.56 ($false),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[438, 432, 614, 613, 612])).
% 0.19/0.56 tff(616,plain,((~n4) | n5(s4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.56 tff(617,plain,
% 0.19/0.56 (n5(s4)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[616, 611])).
% 0.19/0.56 tff(618,plain,
% 0.19/0.56 (n9),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[465, 611])).
% 0.19/0.56 tff(619,plain,
% 0.19/0.56 ((~n9) | (~n6) | (~n10)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[352, 570])).
% 0.19/0.56 tff(620,plain,
% 0.19/0.56 (~n6),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[619, 618, 575])).
% 0.19/0.56 tff(621,plain,
% 0.19/0.56 ($false),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[265, 620, 617])).
% 0.19/0.56 % SZS output end Proof
%------------------------------------------------------------------------------