TSTP Solution File: SYN728-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN728-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 23:57:07 EDT 2022
% Result : Unsatisfiable 0.17s 0.47s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN728-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.32 % Computer : n021.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Mon Sep 5 06:43:31 EDT 2022
% 0.13/0.32 % CPUTime :
% 0.13/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.33 Usage: tptp [options] [-file:]file
% 0.13/0.33 -h, -? prints this message.
% 0.13/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.33 -m, -model generate model.
% 0.13/0.33 -p, -proof generate proof.
% 0.13/0.33 -c, -core generate unsat core of named formulas.
% 0.13/0.33 -st, -statistics display statistics.
% 0.13/0.33 -t:timeout set timeout (in second).
% 0.13/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.33 -<param>:<value> configuration parameter and value.
% 0.13/0.33 -o:<output-file> file to place output in.
% 0.17/0.47 % SZS status Unsatisfiable
% 0.17/0.47 % SZS output start Proof
% 0.17/0.47 tff(p_type, type, (
% 0.17/0.47 p: ( $i * $i ) > $o)).
% 0.17/0.47 tff(g_type, type, (
% 0.17/0.47 g: $i > $i)).
% 0.17/0.47 tff(sk2_type, type, (
% 0.17/0.47 sk2: $i)).
% 0.17/0.47 tff(elem_0_type, type, (
% 0.17/0.47 elem_0: $i)).
% 0.17/0.47 tff(m_type, type, (
% 0.17/0.47 m: $i > $o)).
% 0.17/0.47 tff(f_type, type, (
% 0.17/0.47 f: ( $i * $i ) > $i)).
% 0.17/0.47 tff(sk1_type, type, (
% 0.17/0.47 sk1: $i > $i)).
% 0.17/0.47 tff(q_type, type, (
% 0.17/0.47 q: $i > $o)).
% 0.17/0.47 tff(1,assumption,(p(g(sk2), g(sk2))), introduced(assumption)).
% 0.17/0.47 tff(2,assumption,(~p(sk2, sk2)), introduced(assumption)).
% 0.17/0.47 tff(3,assumption,(~p(elem!0, elem!0)), introduced(assumption)).
% 0.17/0.47 tff(4,plain,
% 0.17/0.47 (^[B: $i, A: $i, C: $i] : refl(((~p(A, B)) | p(C, C)) <=> ((~p(A, B)) | p(C, C)))),
% 0.17/0.47 inference(bind,[status(th)],[])).
% 0.17/0.47 tff(5,plain,
% 0.17/0.47 (![B: $i, A: $i, C: $i] : ((~p(A, B)) | p(C, C)) <=> ![B: $i, A: $i, C: $i] : ((~p(A, B)) | p(C, C))),
% 0.17/0.47 inference(quant_intro,[status(thm)],[4])).
% 0.17/0.47 tff(6,plain,
% 0.17/0.47 (![B: $i, A: $i, C: $i] : ((~p(A, B)) | p(C, C)) <=> ![B: $i, A: $i, C: $i] : ((~p(A, B)) | p(C, C))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(7,plain,
% 0.17/0.47 (^[B: $i, A: $i, C: $i] : rewrite((p(C, C) | (~p(A, B))) <=> ((~p(A, B)) | p(C, C)))),
% 0.17/0.47 inference(bind,[status(th)],[])).
% 0.17/0.47 tff(8,plain,
% 0.17/0.47 (![B: $i, A: $i, C: $i] : (p(C, C) | (~p(A, B))) <=> ![B: $i, A: $i, C: $i] : ((~p(A, B)) | p(C, C))),
% 0.17/0.47 inference(quant_intro,[status(thm)],[7])).
% 0.17/0.47 tff(9,axiom,(![B: $i, A: $i, C: $i] : (p(C, C) | (~p(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm69_1')).
% 0.17/0.47 tff(10,plain,
% 0.17/0.47 (![B: $i, A: $i, C: $i] : ((~p(A, B)) | p(C, C))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.17/0.47 tff(11,plain,
% 0.17/0.47 (![B: $i, A: $i, C: $i] : ((~p(A, B)) | p(C, C))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.17/0.47 tff(12,plain,(
% 0.17/0.47 ![B: $i, A: $i, C: $i] : ((~p(A, B)) | p(C, C))),
% 0.17/0.47 inference(skolemize,[status(sab)],[11])).
% 0.17/0.47 tff(13,plain,
% 0.17/0.47 (![B: $i, A: $i, C: $i] : ((~p(A, B)) | p(C, C))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.17/0.47 tff(14,plain,
% 0.17/0.47 (((~![B: $i, A: $i, C: $i] : ((~p(A, B)) | p(C, C))) | ((~p(elem!0, sk1(elem!0))) | p(elem!0, elem!0))) <=> ((~![B: $i, A: $i, C: $i] : ((~p(A, B)) | p(C, C))) | (~p(elem!0, sk1(elem!0))) | p(elem!0, elem!0))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(15,plain,
% 0.17/0.47 ((~![B: $i, A: $i, C: $i] : ((~p(A, B)) | p(C, C))) | ((~p(elem!0, sk1(elem!0))) | p(elem!0, elem!0))),
% 0.17/0.47 inference(quant_inst,[status(thm)],[])).
% 0.17/0.47 tff(16,plain,
% 0.17/0.47 ((~![B: $i, A: $i, C: $i] : ((~p(A, B)) | p(C, C))) | (~p(elem!0, sk1(elem!0))) | p(elem!0, elem!0)),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.17/0.47 tff(17,plain,
% 0.17/0.47 ((~p(elem!0, sk1(elem!0))) | p(elem!0, elem!0)),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[16, 13])).
% 0.17/0.47 tff(18,plain,
% 0.17/0.47 (~p(elem!0, sk1(elem!0))),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[17, 3])).
% 0.17/0.47 tff(19,plain,
% 0.17/0.47 (^[A: $i] : refl((q(f(A, sk1(A))) | p(A, sk1(A))) <=> (q(f(A, sk1(A))) | p(A, sk1(A))))),
% 0.17/0.47 inference(bind,[status(th)],[])).
% 0.17/0.47 tff(20,plain,
% 0.17/0.47 (![A: $i] : (q(f(A, sk1(A))) | p(A, sk1(A))) <=> ![A: $i] : (q(f(A, sk1(A))) | p(A, sk1(A)))),
% 0.17/0.47 inference(quant_intro,[status(thm)],[19])).
% 0.17/0.47 tff(21,plain,
% 0.17/0.47 (![A: $i] : (q(f(A, sk1(A))) | p(A, sk1(A))) <=> ![A: $i] : (q(f(A, sk1(A))) | p(A, sk1(A)))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(22,axiom,(![A: $i] : (q(f(A, sk1(A))) | p(A, sk1(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm69_3')).
% 0.17/0.47 tff(23,plain,
% 0.17/0.47 (![A: $i] : (q(f(A, sk1(A))) | p(A, sk1(A)))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.17/0.47 tff(24,plain,(
% 0.17/0.47 ![A: $i] : (q(f(A, sk1(A))) | p(A, sk1(A)))),
% 0.17/0.47 inference(skolemize,[status(sab)],[23])).
% 0.17/0.47 tff(25,plain,
% 0.17/0.47 (![A: $i] : (q(f(A, sk1(A))) | p(A, sk1(A)))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.17/0.47 tff(26,plain,
% 0.17/0.47 (((~![A: $i] : (q(f(A, sk1(A))) | p(A, sk1(A)))) | (q(f(elem!0, sk1(elem!0))) | p(elem!0, sk1(elem!0)))) <=> ((~![A: $i] : (q(f(A, sk1(A))) | p(A, sk1(A)))) | q(f(elem!0, sk1(elem!0))) | p(elem!0, sk1(elem!0)))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(27,plain,
% 0.17/0.47 ((~![A: $i] : (q(f(A, sk1(A))) | p(A, sk1(A)))) | (q(f(elem!0, sk1(elem!0))) | p(elem!0, sk1(elem!0)))),
% 0.17/0.47 inference(quant_inst,[status(thm)],[])).
% 0.17/0.47 tff(28,plain,
% 0.17/0.47 ((~![A: $i] : (q(f(A, sk1(A))) | p(A, sk1(A)))) | q(f(elem!0, sk1(elem!0))) | p(elem!0, sk1(elem!0))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.17/0.47 tff(29,plain,
% 0.17/0.47 (q(f(elem!0, sk1(elem!0))) | p(elem!0, sk1(elem!0))),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[28, 25])).
% 0.17/0.47 tff(30,plain,
% 0.17/0.47 (q(f(elem!0, sk1(elem!0)))),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[29, 18])).
% 0.17/0.47 tff(31,plain,
% 0.17/0.47 (^[A: $i] : refl(((~q(A)) | (~m(g(A)))) <=> ((~q(A)) | (~m(g(A)))))),
% 0.17/0.47 inference(bind,[status(th)],[])).
% 0.17/0.47 tff(32,plain,
% 0.17/0.47 (![A: $i] : ((~q(A)) | (~m(g(A)))) <=> ![A: $i] : ((~q(A)) | (~m(g(A))))),
% 0.17/0.47 inference(quant_intro,[status(thm)],[31])).
% 0.17/0.47 tff(33,plain,
% 0.17/0.47 (![A: $i] : ((~q(A)) | (~m(g(A)))) <=> ![A: $i] : ((~q(A)) | (~m(g(A))))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(34,plain,
% 0.17/0.47 (^[A: $i] : rewrite(((~m(g(A))) | (~q(A))) <=> ((~q(A)) | (~m(g(A)))))),
% 0.17/0.47 inference(bind,[status(th)],[])).
% 0.17/0.47 tff(35,plain,
% 0.17/0.47 (![A: $i] : ((~m(g(A))) | (~q(A))) <=> ![A: $i] : ((~q(A)) | (~m(g(A))))),
% 0.17/0.47 inference(quant_intro,[status(thm)],[34])).
% 0.17/0.47 tff(36,axiom,(![A: $i] : ((~m(g(A))) | (~q(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm69_4')).
% 0.17/0.47 tff(37,plain,
% 0.17/0.47 (![A: $i] : ((~q(A)) | (~m(g(A))))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.17/0.47 tff(38,plain,
% 0.17/0.47 (![A: $i] : ((~q(A)) | (~m(g(A))))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.17/0.47 tff(39,plain,(
% 0.17/0.47 ![A: $i] : ((~q(A)) | (~m(g(A))))),
% 0.17/0.47 inference(skolemize,[status(sab)],[38])).
% 0.17/0.47 tff(40,plain,
% 0.17/0.47 (![A: $i] : ((~q(A)) | (~m(g(A))))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.17/0.47 tff(41,plain,
% 0.17/0.47 (((~![A: $i] : ((~q(A)) | (~m(g(A))))) | ((~q(f(elem!0, sk1(elem!0)))) | (~m(g(f(elem!0, sk1(elem!0))))))) <=> ((~![A: $i] : ((~q(A)) | (~m(g(A))))) | (~q(f(elem!0, sk1(elem!0)))) | (~m(g(f(elem!0, sk1(elem!0))))))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(42,plain,
% 0.17/0.47 ((~![A: $i] : ((~q(A)) | (~m(g(A))))) | ((~q(f(elem!0, sk1(elem!0)))) | (~m(g(f(elem!0, sk1(elem!0))))))),
% 0.17/0.47 inference(quant_inst,[status(thm)],[])).
% 0.17/0.47 tff(43,plain,
% 0.17/0.47 ((~![A: $i] : ((~q(A)) | (~m(g(A))))) | (~q(f(elem!0, sk1(elem!0)))) | (~m(g(f(elem!0, sk1(elem!0)))))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.17/0.47 tff(44,plain,
% 0.17/0.47 (~m(g(f(elem!0, sk1(elem!0))))),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[43, 40, 30])).
% 0.17/0.47 tff(45,plain,
% 0.17/0.47 (((~![B: $i, A: $i, C: $i] : ((~p(A, B)) | p(C, C))) | ((~p(g(f(elem!0, sk1(elem!0))), sk1(g(f(elem!0, sk1(elem!0)))))) | p(elem!0, elem!0))) <=> ((~![B: $i, A: $i, C: $i] : ((~p(A, B)) | p(C, C))) | (~p(g(f(elem!0, sk1(elem!0))), sk1(g(f(elem!0, sk1(elem!0)))))) | p(elem!0, elem!0))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(46,plain,
% 0.17/0.47 ((~![B: $i, A: $i, C: $i] : ((~p(A, B)) | p(C, C))) | ((~p(g(f(elem!0, sk1(elem!0))), sk1(g(f(elem!0, sk1(elem!0)))))) | p(elem!0, elem!0))),
% 0.17/0.47 inference(quant_inst,[status(thm)],[])).
% 0.17/0.47 tff(47,plain,
% 0.17/0.47 ((~![B: $i, A: $i, C: $i] : ((~p(A, B)) | p(C, C))) | (~p(g(f(elem!0, sk1(elem!0))), sk1(g(f(elem!0, sk1(elem!0)))))) | p(elem!0, elem!0)),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.17/0.47 tff(48,plain,
% 0.17/0.47 ((~p(g(f(elem!0, sk1(elem!0))), sk1(g(f(elem!0, sk1(elem!0)))))) | p(elem!0, elem!0)),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[47, 13])).
% 0.17/0.47 tff(49,plain,
% 0.17/0.47 (~p(g(f(elem!0, sk1(elem!0))), sk1(g(f(elem!0, sk1(elem!0)))))),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[48, 3])).
% 0.17/0.47 tff(50,plain,
% 0.17/0.47 (^[A: $i] : refl((m(A) | p(A, sk1(A))) <=> (m(A) | p(A, sk1(A))))),
% 0.17/0.47 inference(bind,[status(th)],[])).
% 0.17/0.47 tff(51,plain,
% 0.17/0.47 (![A: $i] : (m(A) | p(A, sk1(A))) <=> ![A: $i] : (m(A) | p(A, sk1(A)))),
% 0.17/0.47 inference(quant_intro,[status(thm)],[50])).
% 0.17/0.47 tff(52,plain,
% 0.17/0.47 (![A: $i] : (m(A) | p(A, sk1(A))) <=> ![A: $i] : (m(A) | p(A, sk1(A)))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(53,axiom,(![A: $i] : (m(A) | p(A, sk1(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm69_2')).
% 0.17/0.47 tff(54,plain,
% 0.17/0.47 (![A: $i] : (m(A) | p(A, sk1(A)))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.17/0.47 tff(55,plain,(
% 0.17/0.47 ![A: $i] : (m(A) | p(A, sk1(A)))),
% 0.17/0.47 inference(skolemize,[status(sab)],[54])).
% 0.17/0.47 tff(56,plain,
% 0.17/0.47 (![A: $i] : (m(A) | p(A, sk1(A)))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.17/0.47 tff(57,plain,
% 0.17/0.47 (((~![A: $i] : (m(A) | p(A, sk1(A)))) | (m(g(f(elem!0, sk1(elem!0)))) | p(g(f(elem!0, sk1(elem!0))), sk1(g(f(elem!0, sk1(elem!0))))))) <=> ((~![A: $i] : (m(A) | p(A, sk1(A)))) | m(g(f(elem!0, sk1(elem!0)))) | p(g(f(elem!0, sk1(elem!0))), sk1(g(f(elem!0, sk1(elem!0))))))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(58,plain,
% 0.17/0.47 ((~![A: $i] : (m(A) | p(A, sk1(A)))) | (m(g(f(elem!0, sk1(elem!0)))) | p(g(f(elem!0, sk1(elem!0))), sk1(g(f(elem!0, sk1(elem!0))))))),
% 0.17/0.47 inference(quant_inst,[status(thm)],[])).
% 0.17/0.47 tff(59,plain,
% 0.17/0.47 ((~![A: $i] : (m(A) | p(A, sk1(A)))) | m(g(f(elem!0, sk1(elem!0)))) | p(g(f(elem!0, sk1(elem!0))), sk1(g(f(elem!0, sk1(elem!0)))))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.17/0.47 tff(60,plain,
% 0.17/0.47 ($false),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[59, 56, 49, 44])).
% 0.17/0.47 tff(61,plain,(p(elem!0, elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.17/0.47 tff(62,plain,
% 0.17/0.47 (((~![B: $i, A: $i, C: $i] : ((~p(A, B)) | p(C, C))) | ((~p(elem!0, elem!0)) | p(sk2, sk2))) <=> ((~![B: $i, A: $i, C: $i] : ((~p(A, B)) | p(C, C))) | (~p(elem!0, elem!0)) | p(sk2, sk2))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(63,plain,
% 0.17/0.47 ((~![B: $i, A: $i, C: $i] : ((~p(A, B)) | p(C, C))) | ((~p(elem!0, elem!0)) | p(sk2, sk2))),
% 0.17/0.47 inference(quant_inst,[status(thm)],[])).
% 0.17/0.47 tff(64,plain,
% 0.17/0.47 ((~![B: $i, A: $i, C: $i] : ((~p(A, B)) | p(C, C))) | (~p(elem!0, elem!0)) | p(sk2, sk2)),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.17/0.47 tff(65,plain,
% 0.17/0.47 ($false),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[64, 13, 61, 2])).
% 0.17/0.47 tff(66,plain,(p(sk2, sk2)), inference(lemma,lemma(discharge,[]))).
% 0.17/0.47 tff(67,plain,
% 0.17/0.47 (^[A: $i] : refl(((~p(sk2, sk2)) | (~p(g(sk2), A))) <=> ((~p(sk2, sk2)) | (~p(g(sk2), A))))),
% 0.17/0.47 inference(bind,[status(th)],[])).
% 0.17/0.47 tff(68,plain,
% 0.17/0.47 (![A: $i] : ((~p(sk2, sk2)) | (~p(g(sk2), A))) <=> ![A: $i] : ((~p(sk2, sk2)) | (~p(g(sk2), A)))),
% 0.17/0.47 inference(quant_intro,[status(thm)],[67])).
% 0.17/0.47 tff(69,plain,
% 0.17/0.47 (![A: $i] : ((~p(sk2, sk2)) | (~p(g(sk2), A))) <=> ![A: $i] : ((~p(sk2, sk2)) | (~p(g(sk2), A)))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(70,axiom,(![A: $i] : ((~p(sk2, sk2)) | (~p(g(sk2), A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm69_5')).
% 0.17/0.47 tff(71,plain,
% 0.17/0.47 (![A: $i] : ((~p(sk2, sk2)) | (~p(g(sk2), A)))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.17/0.47 tff(72,plain,(
% 0.17/0.47 ![A: $i] : ((~p(sk2, sk2)) | (~p(g(sk2), A)))),
% 0.17/0.47 inference(skolemize,[status(sab)],[71])).
% 0.17/0.47 tff(73,plain,
% 0.17/0.47 (![A: $i] : ((~p(sk2, sk2)) | (~p(g(sk2), A)))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.17/0.47 tff(74,plain,
% 0.17/0.47 (((~![A: $i] : ((~p(sk2, sk2)) | (~p(g(sk2), A)))) | ((~p(sk2, sk2)) | (~p(g(sk2), g(sk2))))) <=> ((~![A: $i] : ((~p(sk2, sk2)) | (~p(g(sk2), A)))) | (~p(sk2, sk2)) | (~p(g(sk2), g(sk2))))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(75,plain,
% 0.17/0.47 ((~![A: $i] : ((~p(sk2, sk2)) | (~p(g(sk2), A)))) | ((~p(sk2, sk2)) | (~p(g(sk2), g(sk2))))),
% 0.17/0.47 inference(quant_inst,[status(thm)],[])).
% 0.17/0.47 tff(76,plain,
% 0.17/0.47 ((~![A: $i] : ((~p(sk2, sk2)) | (~p(g(sk2), A)))) | (~p(sk2, sk2)) | (~p(g(sk2), g(sk2)))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.17/0.47 tff(77,plain,
% 0.17/0.47 ($false),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[76, 73, 66, 1])).
% 0.17/0.47 tff(78,plain,(~p(g(sk2), g(sk2))), inference(lemma,lemma(discharge,[]))).
% 0.17/0.47 tff(79,plain,
% 0.17/0.47 (((~![B: $i, A: $i, C: $i] : ((~p(A, B)) | p(C, C))) | ((~p(elem!0, elem!0)) | p(g(sk2), g(sk2)))) <=> ((~![B: $i, A: $i, C: $i] : ((~p(A, B)) | p(C, C))) | (~p(elem!0, elem!0)) | p(g(sk2), g(sk2)))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(80,plain,
% 0.17/0.47 ((~![B: $i, A: $i, C: $i] : ((~p(A, B)) | p(C, C))) | ((~p(elem!0, elem!0)) | p(g(sk2), g(sk2)))),
% 0.17/0.47 inference(quant_inst,[status(thm)],[])).
% 0.17/0.47 tff(81,plain,
% 0.17/0.47 ((~![B: $i, A: $i, C: $i] : ((~p(A, B)) | p(C, C))) | (~p(elem!0, elem!0)) | p(g(sk2), g(sk2))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.17/0.48 tff(82,plain,
% 0.17/0.48 ($false),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[81, 13, 61, 78])).
% 0.17/0.48 % SZS output end Proof
%------------------------------------------------------------------------------