TSTP Solution File: SYN006-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN006-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 23:53:08 EDT 2022
% Result : Unsatisfiable 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYN006-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n005.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 : Mon Sep 5 00:56:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(q3_type, type, (
% 0.19/0.40 q3: ( $i * $i ) > $o)).
% 0.19/0.40 tff(g_type, type, (
% 0.19/0.40 g: $i > $i)).
% 0.19/0.40 tff(f_type, type, (
% 0.19/0.40 f: $i > $i)).
% 0.19/0.40 tff(a_type, type, (
% 0.19/0.40 a: $i)).
% 0.19/0.40 tff(p2_type, type, (
% 0.19/0.40 p2: ( $i * $i ) > $o)).
% 0.19/0.40 tff(q1_type, type, (
% 0.19/0.40 q1: ( $i * $i ) > $o)).
% 0.19/0.40 tff(q2_type, type, (
% 0.19/0.40 q2: ( $i * $i ) > $o)).
% 0.19/0.40 tff(p1_type, type, (
% 0.19/0.40 p1: ( $i * $i ) > $o)).
% 0.19/0.40 tff(q4_type, type, (
% 0.19/0.40 q4: ( $i * $i ) > $o)).
% 0.19/0.40 tff(1,assumption,(q2(a, f(f(f(g(f(a))))))), introduced(assumption)).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 (^[Y: $i, X: $i] : refl((~q2(X, f(Y))) <=> (~q2(X, f(Y))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(3,plain,
% 0.19/0.40 (![Y: $i, X: $i] : (~q2(X, f(Y))) <=> ![Y: $i, X: $i] : (~q2(X, f(Y)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.40 tff(4,plain,
% 0.19/0.40 (![Y: $i, X: $i] : (~q2(X, f(Y))) <=> ![Y: $i, X: $i] : (~q2(X, f(Y)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(5,axiom,(![Y: $i, X: $i] : (~q2(X, f(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_3')).
% 0.19/0.40 tff(6,plain,
% 0.19/0.40 (![Y: $i, X: $i] : (~q2(X, f(Y)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.40 tff(7,plain,(
% 0.19/0.40 ![Y: $i, X: $i] : (~q2(X, f(Y)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[6])).
% 0.19/0.40 tff(8,plain,
% 0.19/0.40 (![Y: $i, X: $i] : (~q2(X, f(Y)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 ((~![Y: $i, X: $i] : (~q2(X, f(Y)))) | (~q2(a, f(f(f(g(f(a)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.19/0.40 tff(11,plain,(~q2(a, f(f(f(g(f(a))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(12,assumption,(~p1(a, f(f(f(g(f(a))))))), introduced(assumption)).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (^[Y: $i] : refl(p1(a, Y) <=> p1(a, Y))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 (![Y: $i] : p1(a, Y) <=> ![Y: $i] : p1(a, Y)),
% 0.19/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (![Y: $i] : p1(a, Y) <=> ![Y: $i] : p1(a, Y)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(16,axiom,(![Y: $i] : p1(a, Y)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_2')).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (![Y: $i] : p1(a, Y)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.40 tff(18,plain,(
% 0.19/0.40 ![Y: $i] : p1(a, Y)),
% 0.19/0.40 inference(skolemize,[status(sab)],[17])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (![Y: $i] : p1(a, Y)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 ((~![Y: $i] : p1(a, Y)) | p1(a, f(f(f(g(f(a))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[20, 19, 12])).
% 0.19/0.40 tff(22,plain,(p1(a, f(f(f(g(f(a))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (^[Y: $i, X: $i] : refl((q2(X, f(Y)) | q1(f(X), Y) | (~p1(X, f(Y)))) <=> (q2(X, f(Y)) | q1(f(X), Y) | (~p1(X, f(Y)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (![Y: $i, X: $i] : (q2(X, f(Y)) | q1(f(X), Y) | (~p1(X, f(Y)))) <=> ![Y: $i, X: $i] : (q2(X, f(Y)) | q1(f(X), Y) | (~p1(X, f(Y))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 (![Y: $i, X: $i] : (q2(X, f(Y)) | q1(f(X), Y) | (~p1(X, f(Y)))) <=> ![Y: $i, X: $i] : (q2(X, f(Y)) | q1(f(X), Y) | (~p1(X, f(Y))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 (^[Y: $i, X: $i] : rewrite((((~p1(X, f(Y))) | q1(f(X), Y)) | q2(X, f(Y))) <=> (q2(X, f(Y)) | q1(f(X), Y) | (~p1(X, f(Y)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 (![Y: $i, X: $i] : (((~p1(X, f(Y))) | q1(f(X), Y)) | q2(X, f(Y))) <=> ![Y: $i, X: $i] : (q2(X, f(Y)) | q1(f(X), Y) | (~p1(X, f(Y))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.40 tff(28,axiom,(![Y: $i, X: $i] : (((~p1(X, f(Y))) | q1(f(X), Y)) | q2(X, f(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_1')).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 (![Y: $i, X: $i] : (q2(X, f(Y)) | q1(f(X), Y) | (~p1(X, f(Y))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 (![Y: $i, X: $i] : (q2(X, f(Y)) | q1(f(X), Y) | (~p1(X, f(Y))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.19/0.40 tff(31,plain,(
% 0.19/0.40 ![Y: $i, X: $i] : (q2(X, f(Y)) | q1(f(X), Y) | (~p1(X, f(Y))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[30])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 (![Y: $i, X: $i] : (q2(X, f(Y)) | q1(f(X), Y) | (~p1(X, f(Y))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (((~![Y: $i, X: $i] : (q2(X, f(Y)) | q1(f(X), Y) | (~p1(X, f(Y))))) | ((~p1(a, f(f(f(g(f(a))))))) | q1(f(a), f(f(g(f(a))))) | q2(a, f(f(f(g(f(a)))))))) <=> ((~![Y: $i, X: $i] : (q2(X, f(Y)) | q1(f(X), Y) | (~p1(X, f(Y))))) | (~p1(a, f(f(f(g(f(a))))))) | q1(f(a), f(f(g(f(a))))) | q2(a, f(f(f(g(f(a)))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 ((q2(a, f(f(f(g(f(a)))))) | q1(f(a), f(f(g(f(a))))) | (~p1(a, f(f(f(g(f(a)))))))) <=> ((~p1(a, f(f(f(g(f(a))))))) | q1(f(a), f(f(g(f(a))))) | q2(a, f(f(f(g(f(a)))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 (((~![Y: $i, X: $i] : (q2(X, f(Y)) | q1(f(X), Y) | (~p1(X, f(Y))))) | (q2(a, f(f(f(g(f(a)))))) | q1(f(a), f(f(g(f(a))))) | (~p1(a, f(f(f(g(f(a))))))))) <=> ((~![Y: $i, X: $i] : (q2(X, f(Y)) | q1(f(X), Y) | (~p1(X, f(Y))))) | ((~p1(a, f(f(f(g(f(a))))))) | q1(f(a), f(f(g(f(a))))) | q2(a, f(f(f(g(f(a))))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[34])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 (((~![Y: $i, X: $i] : (q2(X, f(Y)) | q1(f(X), Y) | (~p1(X, f(Y))))) | (q2(a, f(f(f(g(f(a)))))) | q1(f(a), f(f(g(f(a))))) | (~p1(a, f(f(f(g(f(a))))))))) <=> ((~![Y: $i, X: $i] : (q2(X, f(Y)) | q1(f(X), Y) | (~p1(X, f(Y))))) | (~p1(a, f(f(f(g(f(a))))))) | q1(f(a), f(f(g(f(a))))) | q2(a, f(f(f(g(f(a)))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[35, 33])).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 ((~![Y: $i, X: $i] : (q2(X, f(Y)) | q1(f(X), Y) | (~p1(X, f(Y))))) | (q2(a, f(f(f(g(f(a)))))) | q1(f(a), f(f(g(f(a))))) | (~p1(a, f(f(f(g(f(a))))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 ((~![Y: $i, X: $i] : (q2(X, f(Y)) | q1(f(X), Y) | (~p1(X, f(Y))))) | (~p1(a, f(f(f(g(f(a))))))) | q1(f(a), f(f(g(f(a))))) | q2(a, f(f(f(g(f(a))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 (q1(f(a), f(f(g(f(a))))) | q2(a, f(f(f(g(f(a))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[38, 32, 22])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (q1(f(a), f(f(g(f(a)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[39, 11])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 (^[Y: $i, X: $i] : refl(((~q1(X, f(Y))) | p2(f(X), Y)) <=> ((~q1(X, f(Y))) | p2(f(X), Y)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 (![Y: $i, X: $i] : ((~q1(X, f(Y))) | p2(f(X), Y)) <=> ![Y: $i, X: $i] : ((~q1(X, f(Y))) | p2(f(X), Y))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[41])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 (![Y: $i, X: $i] : ((~q1(X, f(Y))) | p2(f(X), Y)) <=> ![Y: $i, X: $i] : ((~q1(X, f(Y))) | p2(f(X), Y))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(44,axiom,(![Y: $i, X: $i] : ((~q1(X, f(Y))) | p2(f(X), Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_7')).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 (![Y: $i, X: $i] : ((~q1(X, f(Y))) | p2(f(X), Y))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.40 tff(46,plain,(
% 0.19/0.40 ![Y: $i, X: $i] : ((~q1(X, f(Y))) | p2(f(X), Y))),
% 0.19/0.40 inference(skolemize,[status(sab)],[45])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (![Y: $i, X: $i] : ((~q1(X, f(Y))) | p2(f(X), Y))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (((~![Y: $i, X: $i] : ((~q1(X, f(Y))) | p2(f(X), Y))) | ((~q1(f(a), f(f(g(f(a)))))) | p2(f(f(a)), f(g(f(a)))))) <=> ((~![Y: $i, X: $i] : ((~q1(X, f(Y))) | p2(f(X), Y))) | (~q1(f(a), f(f(g(f(a)))))) | p2(f(f(a)), f(g(f(a)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 ((~![Y: $i, X: $i] : ((~q1(X, f(Y))) | p2(f(X), Y))) | ((~q1(f(a), f(f(g(f(a)))))) | p2(f(f(a)), f(g(f(a)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 ((~![Y: $i, X: $i] : ((~q1(X, f(Y))) | p2(f(X), Y))) | (~q1(f(a), f(f(g(f(a)))))) | p2(f(f(a)), f(g(f(a))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 (p2(f(f(a)), f(g(f(a))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[50, 47, 40])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (^[Y: $i, X: $i] : refl((~q4(f(f(X)), f(g(f(Y))))) <=> (~q4(f(f(X)), f(g(f(Y))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (![Y: $i, X: $i] : (~q4(f(f(X)), f(g(f(Y))))) <=> ![Y: $i, X: $i] : (~q4(f(f(X)), f(g(f(Y)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[52])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 (![Y: $i, X: $i] : (~q4(f(f(X)), f(g(f(Y))))) <=> ![Y: $i, X: $i] : (~q4(f(f(X)), f(g(f(Y)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(55,axiom,(![Y: $i, X: $i] : (~q4(f(f(X)), f(g(f(Y)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_6')).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 (![Y: $i, X: $i] : (~q4(f(f(X)), f(g(f(Y)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.40 tff(57,plain,(
% 0.19/0.40 ![Y: $i, X: $i] : (~q4(f(f(X)), f(g(f(Y)))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[56])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (![Y: $i, X: $i] : (~q4(f(f(X)), f(g(f(Y)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 ((~![Y: $i, X: $i] : (~q4(f(f(X)), f(g(f(Y)))))) | (~q4(f(f(a)), f(g(f(a)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 (~q4(f(f(a)), f(g(f(a))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 (^[Y: $i, X: $i] : refl((q4(X, f(Y)) | q3(f(X), Y) | (~p2(X, f(Y)))) <=> (q4(X, f(Y)) | q3(f(X), Y) | (~p2(X, f(Y)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 (![Y: $i, X: $i] : (q4(X, f(Y)) | q3(f(X), Y) | (~p2(X, f(Y)))) <=> ![Y: $i, X: $i] : (q4(X, f(Y)) | q3(f(X), Y) | (~p2(X, f(Y))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 (![Y: $i, X: $i] : (q4(X, f(Y)) | q3(f(X), Y) | (~p2(X, f(Y)))) <=> ![Y: $i, X: $i] : (q4(X, f(Y)) | q3(f(X), Y) | (~p2(X, f(Y))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (^[Y: $i, X: $i] : rewrite((((~p2(X, f(Y))) | q3(f(X), Y)) | q4(X, f(Y))) <=> (q4(X, f(Y)) | q3(f(X), Y) | (~p2(X, f(Y)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (![Y: $i, X: $i] : (((~p2(X, f(Y))) | q3(f(X), Y)) | q4(X, f(Y))) <=> ![Y: $i, X: $i] : (q4(X, f(Y)) | q3(f(X), Y) | (~p2(X, f(Y))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[64])).
% 0.19/0.40 tff(66,axiom,(![Y: $i, X: $i] : (((~p2(X, f(Y))) | q3(f(X), Y)) | q4(X, f(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_4')).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 (![Y: $i, X: $i] : (q4(X, f(Y)) | q3(f(X), Y) | (~p2(X, f(Y))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (![Y: $i, X: $i] : (q4(X, f(Y)) | q3(f(X), Y) | (~p2(X, f(Y))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.19/0.40 tff(69,plain,(
% 0.19/0.40 ![Y: $i, X: $i] : (q4(X, f(Y)) | q3(f(X), Y) | (~p2(X, f(Y))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[68])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (![Y: $i, X: $i] : (q4(X, f(Y)) | q3(f(X), Y) | (~p2(X, f(Y))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (((~![Y: $i, X: $i] : (q4(X, f(Y)) | q3(f(X), Y) | (~p2(X, f(Y))))) | (q4(f(f(a)), f(g(f(a)))) | q3(f(f(f(a))), g(f(a))) | (~p2(f(f(a)), f(g(f(a))))))) <=> ((~![Y: $i, X: $i] : (q4(X, f(Y)) | q3(f(X), Y) | (~p2(X, f(Y))))) | q4(f(f(a)), f(g(f(a)))) | q3(f(f(f(a))), g(f(a))) | (~p2(f(f(a)), f(g(f(a))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 ((~![Y: $i, X: $i] : (q4(X, f(Y)) | q3(f(X), Y) | (~p2(X, f(Y))))) | (q4(f(f(a)), f(g(f(a)))) | q3(f(f(f(a))), g(f(a))) | (~p2(f(f(a)), f(g(f(a))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 ((~![Y: $i, X: $i] : (q4(X, f(Y)) | q3(f(X), Y) | (~p2(X, f(Y))))) | q4(f(f(a)), f(g(f(a)))) | q3(f(f(f(a))), g(f(a))) | (~p2(f(f(a)), f(g(f(a)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 (q3(f(f(f(a))), g(f(a))) | (~p2(f(f(a)), f(g(f(a)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[73, 70, 60])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 (q3(f(f(f(a))), g(f(a)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[74, 51])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 (^[Y: $i, X: $i] : refl((~q3(X, g(Y))) <=> (~q3(X, g(Y))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 (![Y: $i, X: $i] : (~q3(X, g(Y))) <=> ![Y: $i, X: $i] : (~q3(X, g(Y)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[76])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 (![Y: $i, X: $i] : (~q3(X, g(Y))) <=> ![Y: $i, X: $i] : (~q3(X, g(Y)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(79,axiom,(![Y: $i, X: $i] : (~q3(X, g(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_5')).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 (![Y: $i, X: $i] : (~q3(X, g(Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.19/0.41 tff(81,plain,(
% 0.19/0.41 ![Y: $i, X: $i] : (~q3(X, g(Y)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[80])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (![Y: $i, X: $i] : (~q3(X, g(Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 ((~![Y: $i, X: $i] : (~q3(X, g(Y)))) | (~q3(f(f(f(a))), g(f(a))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[83, 82, 75])).
% 0.19/0.41 % SZS output end Proof
%------------------------------------------------------------------------------