TSTP Solution File: SYN035-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN035-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 23:53:13 EDT 2022
% Result : Unsatisfiable 0.12s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN035-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Sep 5 01:16:19 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(p_type, type, (
% 0.12/0.39 p: ( $i * $i ) > $o)).
% 0.12/0.39 tff(f_type, type, (
% 0.12/0.39 f: ( $i * $i ) > $i)).
% 0.12/0.39 tff(elem_0_type, type, (
% 0.12/0.39 elem_0: $i)).
% 0.12/0.39 tff(q_type, type, (
% 0.12/0.39 q: ( $i * $i ) > $o)).
% 0.12/0.39 tff(1,assumption,(~p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))), introduced(assumption)).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (^[B: $i, A: $i] : refl(p(A, B) <=> p(A, B))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (![B: $i, A: $i] : p(A, B) <=> ![B: $i, A: $i] : p(A, B)),
% 0.12/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (![B: $i, A: $i] : p(A, B) <=> ![B: $i, A: $i] : p(A, B)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(5,axiom,(![B: $i, A: $i] : p(A, B)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 (![B: $i, A: $i] : p(A, B)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.39 tff(7,plain,(
% 0.12/0.39 ![B: $i, A: $i] : p(A, B)),
% 0.12/0.39 inference(skolemize,[status(sab)],[6])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (![B: $i, A: $i] : p(A, B)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 ((~![B: $i, A: $i] : p(A, B)) | p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.12/0.39 tff(11,plain,(p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(12,assumption,(~p(f(elem!0, elem!0), f(elem!0, f(elem!0, elem!0)))), introduced(assumption)).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 ((~![B: $i, A: $i] : p(A, B)) | p(f(elem!0, elem!0), f(elem!0, f(elem!0, elem!0)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[13, 8, 12])).
% 0.12/0.39 tff(15,plain,(p(f(elem!0, elem!0), f(elem!0, f(elem!0, elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(16,assumption,(~p(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0)))), introduced(assumption)).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 ((~![B: $i, A: $i] : p(A, B)) | p(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[17, 8, 16])).
% 0.12/0.39 tff(19,plain,(p(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (^[B: $i, A: $i] : refl((q(A, B) | (~p(B, f(A, B))) | (~p(f(A, B), f(A, B)))) <=> (q(A, B) | (~p(B, f(A, B))) | (~p(f(A, B), f(A, B)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (![B: $i, A: $i] : (q(A, B) | (~p(B, f(A, B))) | (~p(f(A, B), f(A, B)))) <=> ![B: $i, A: $i] : (q(A, B) | (~p(B, f(A, B))) | (~p(f(A, B), f(A, B))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[20])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (![B: $i, A: $i] : (q(A, B) | (~p(B, f(A, B))) | (~p(f(A, B), f(A, B)))) <=> ![B: $i, A: $i] : (q(A, B) | (~p(B, f(A, B))) | (~p(f(A, B), f(A, B))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 (^[B: $i, A: $i] : rewrite((((~p(f(A, B), f(A, B))) | (~p(B, f(A, B)))) | q(A, B)) <=> (q(A, B) | (~p(B, f(A, B))) | (~p(f(A, B), f(A, B)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (![B: $i, A: $i] : (((~p(f(A, B), f(A, B))) | (~p(B, f(A, B)))) | q(A, B)) <=> ![B: $i, A: $i] : (q(A, B) | (~p(B, f(A, B))) | (~p(f(A, B), f(A, B))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[23])).
% 0.12/0.39 tff(25,axiom,(![B: $i, A: $i] : (((~p(f(A, B), f(A, B))) | (~p(B, f(A, B)))) | q(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause2')).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (![B: $i, A: $i] : (q(A, B) | (~p(B, f(A, B))) | (~p(f(A, B), f(A, B))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (![B: $i, A: $i] : (q(A, B) | (~p(B, f(A, B))) | (~p(f(A, B), f(A, B))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.12/0.39 tff(28,plain,(
% 0.12/0.39 ![B: $i, A: $i] : (q(A, B) | (~p(B, f(A, B))) | (~p(f(A, B), f(A, B))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[27])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (![B: $i, A: $i] : (q(A, B) | (~p(B, f(A, B))) | (~p(f(A, B), f(A, B))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 (((~![B: $i, A: $i] : (q(A, B) | (~p(B, f(A, B))) | (~p(f(A, B), f(A, B))))) | (q(elem!0, f(elem!0, elem!0)) | (~p(f(elem!0, elem!0), f(elem!0, f(elem!0, elem!0)))) | (~p(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0)))))) <=> ((~![B: $i, A: $i] : (q(A, B) | (~p(B, f(A, B))) | (~p(f(A, B), f(A, B))))) | q(elem!0, f(elem!0, elem!0)) | (~p(f(elem!0, elem!0), f(elem!0, f(elem!0, elem!0)))) | (~p(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 ((~![B: $i, A: $i] : (q(A, B) | (~p(B, f(A, B))) | (~p(f(A, B), f(A, B))))) | (q(elem!0, f(elem!0, elem!0)) | (~p(f(elem!0, elem!0), f(elem!0, f(elem!0, elem!0)))) | (~p(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0)))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 ((~![B: $i, A: $i] : (q(A, B) | (~p(B, f(A, B))) | (~p(f(A, B), f(A, B))))) | q(elem!0, f(elem!0, elem!0)) | (~p(f(elem!0, elem!0), f(elem!0, f(elem!0, elem!0)))) | (~p(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 (q(elem!0, f(elem!0, elem!0)) | (~p(f(elem!0, elem!0), f(elem!0, f(elem!0, elem!0))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[32, 29, 19])).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 (q(elem!0, f(elem!0, elem!0))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[33, 15])).
% 0.20/0.39 tff(35,assumption,(~p(elem!0, f(elem!0, elem!0))), introduced(assumption)).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 ((~![B: $i, A: $i] : p(A, B)) | p(elem!0, f(elem!0, elem!0))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(37,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[36, 8, 35])).
% 0.20/0.39 tff(38,plain,(p(elem!0, f(elem!0, elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(39,assumption,(~p(f(elem!0, elem!0), f(elem!0, elem!0))), introduced(assumption)).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 ((~![B: $i, A: $i] : p(A, B)) | p(f(elem!0, elem!0), f(elem!0, elem!0))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[40, 8, 39])).
% 0.20/0.39 tff(42,plain,(p(f(elem!0, elem!0), f(elem!0, elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 (^[B: $i, A: $i] : refl(((~p(B, f(A, B))) | (~p(f(A, B), f(A, B))) | (~q(A, f(A, B))) | (~q(f(A, B), f(A, B)))) <=> ((~p(B, f(A, B))) | (~p(f(A, B), f(A, B))) | (~q(A, f(A, B))) | (~q(f(A, B), f(A, B)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 (![B: $i, A: $i] : ((~p(B, f(A, B))) | (~p(f(A, B), f(A, B))) | (~q(A, f(A, B))) | (~q(f(A, B), f(A, B)))) <=> ![B: $i, A: $i] : ((~p(B, f(A, B))) | (~p(f(A, B), f(A, B))) | (~q(A, f(A, B))) | (~q(f(A, B), f(A, B))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[43])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 (![B: $i, A: $i] : ((~p(B, f(A, B))) | (~p(f(A, B), f(A, B))) | (~q(A, f(A, B))) | (~q(f(A, B), f(A, B)))) <=> ![B: $i, A: $i] : ((~p(B, f(A, B))) | (~p(f(A, B), f(A, B))) | (~q(A, f(A, B))) | (~q(f(A, B), f(A, B))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 (^[B: $i, A: $i] : trans(monotonicity(rewrite((((~q(f(A, B), f(A, B))) | (~q(A, f(A, B)))) | (~p(f(A, B), f(A, B)))) <=> ((~p(f(A, B), f(A, B))) | (~q(A, f(A, B))) | (~q(f(A, B), f(A, B))))), (((((~q(f(A, B), f(A, B))) | (~q(A, f(A, B)))) | (~p(f(A, B), f(A, B)))) | (~p(B, f(A, B)))) <=> (((~p(f(A, B), f(A, B))) | (~q(A, f(A, B))) | (~q(f(A, B), f(A, B)))) | (~p(B, f(A, B)))))), rewrite((((~p(f(A, B), f(A, B))) | (~q(A, f(A, B))) | (~q(f(A, B), f(A, B)))) | (~p(B, f(A, B)))) <=> ((~p(B, f(A, B))) | (~p(f(A, B), f(A, B))) | (~q(A, f(A, B))) | (~q(f(A, B), f(A, B))))), (((((~q(f(A, B), f(A, B))) | (~q(A, f(A, B)))) | (~p(f(A, B), f(A, B)))) | (~p(B, f(A, B)))) <=> ((~p(B, f(A, B))) | (~p(f(A, B), f(A, B))) | (~q(A, f(A, B))) | (~q(f(A, B), f(A, B))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 (![B: $i, A: $i] : ((((~q(f(A, B), f(A, B))) | (~q(A, f(A, B)))) | (~p(f(A, B), f(A, B)))) | (~p(B, f(A, B)))) <=> ![B: $i, A: $i] : ((~p(B, f(A, B))) | (~p(f(A, B), f(A, B))) | (~q(A, f(A, B))) | (~q(f(A, B), f(A, B))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[46])).
% 0.20/0.40 tff(48,axiom,(![B: $i, A: $i] : ((((~q(f(A, B), f(A, B))) | (~q(A, f(A, B)))) | (~p(f(A, B), f(A, B)))) | (~p(B, f(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','theorem')).
% 0.20/0.40 tff(49,plain,
% 0.20/0.40 (![B: $i, A: $i] : ((~p(B, f(A, B))) | (~p(f(A, B), f(A, B))) | (~q(A, f(A, B))) | (~q(f(A, B), f(A, B))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.40 tff(50,plain,
% 0.20/0.40 (![B: $i, A: $i] : ((~p(B, f(A, B))) | (~p(f(A, B), f(A, B))) | (~q(A, f(A, B))) | (~q(f(A, B), f(A, B))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.20/0.40 tff(51,plain,(
% 0.20/0.40 ![B: $i, A: $i] : ((~p(B, f(A, B))) | (~p(f(A, B), f(A, B))) | (~q(A, f(A, B))) | (~q(f(A, B), f(A, B))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[50])).
% 0.20/0.40 tff(52,plain,
% 0.20/0.40 (![B: $i, A: $i] : ((~p(B, f(A, B))) | (~p(f(A, B), f(A, B))) | (~q(A, f(A, B))) | (~q(f(A, B), f(A, B))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.20/0.40 tff(53,plain,
% 0.20/0.40 (((~![B: $i, A: $i] : ((~p(B, f(A, B))) | (~p(f(A, B), f(A, B))) | (~q(A, f(A, B))) | (~q(f(A, B), f(A, B))))) | ((~p(elem!0, f(elem!0, elem!0))) | (~p(f(elem!0, elem!0), f(elem!0, elem!0))) | (~q(elem!0, f(elem!0, elem!0))) | (~q(f(elem!0, elem!0), f(elem!0, elem!0))))) <=> ((~![B: $i, A: $i] : ((~p(B, f(A, B))) | (~p(f(A, B), f(A, B))) | (~q(A, f(A, B))) | (~q(f(A, B), f(A, B))))) | (~p(elem!0, f(elem!0, elem!0))) | (~p(f(elem!0, elem!0), f(elem!0, elem!0))) | (~q(elem!0, f(elem!0, elem!0))) | (~q(f(elem!0, elem!0), f(elem!0, elem!0))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(54,plain,
% 0.20/0.40 ((~![B: $i, A: $i] : ((~p(B, f(A, B))) | (~p(f(A, B), f(A, B))) | (~q(A, f(A, B))) | (~q(f(A, B), f(A, B))))) | ((~p(elem!0, f(elem!0, elem!0))) | (~p(f(elem!0, elem!0), f(elem!0, elem!0))) | (~q(elem!0, f(elem!0, elem!0))) | (~q(f(elem!0, elem!0), f(elem!0, elem!0))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(55,plain,
% 0.20/0.40 ((~![B: $i, A: $i] : ((~p(B, f(A, B))) | (~p(f(A, B), f(A, B))) | (~q(A, f(A, B))) | (~q(f(A, B), f(A, B))))) | (~p(elem!0, f(elem!0, elem!0))) | (~p(f(elem!0, elem!0), f(elem!0, elem!0))) | (~q(elem!0, f(elem!0, elem!0))) | (~q(f(elem!0, elem!0), f(elem!0, elem!0)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.40 tff(56,plain,
% 0.20/0.40 ((~p(elem!0, f(elem!0, elem!0))) | (~q(elem!0, f(elem!0, elem!0))) | (~q(f(elem!0, elem!0), f(elem!0, elem!0)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[55, 52, 42])).
% 0.20/0.40 tff(57,plain,
% 0.20/0.40 ((~q(elem!0, f(elem!0, elem!0))) | (~q(f(elem!0, elem!0), f(elem!0, elem!0)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[56, 38])).
% 0.20/0.40 tff(58,plain,
% 0.20/0.40 (~q(f(elem!0, elem!0), f(elem!0, elem!0))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[57, 34])).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 (((~![B: $i, A: $i] : (q(A, B) | (~p(B, f(A, B))) | (~p(f(A, B), f(A, B))))) | (q(f(elem!0, elem!0), f(elem!0, elem!0)) | (~p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | (~p(f(f(elem!0, elem!0), f(elem!0, elem!0)), f(f(elem!0, elem!0), f(elem!0, elem!0)))))) <=> ((~![B: $i, A: $i] : (q(A, B) | (~p(B, f(A, B))) | (~p(f(A, B), f(A, B))))) | q(f(elem!0, elem!0), f(elem!0, elem!0)) | (~p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | (~p(f(f(elem!0, elem!0), f(elem!0, elem!0)), f(f(elem!0, elem!0), f(elem!0, elem!0)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(60,plain,
% 0.20/0.40 ((~![B: $i, A: $i] : (q(A, B) | (~p(B, f(A, B))) | (~p(f(A, B), f(A, B))))) | (q(f(elem!0, elem!0), f(elem!0, elem!0)) | (~p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | (~p(f(f(elem!0, elem!0), f(elem!0, elem!0)), f(f(elem!0, elem!0), f(elem!0, elem!0)))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 ((~![B: $i, A: $i] : (q(A, B) | (~p(B, f(A, B))) | (~p(f(A, B), f(A, B))))) | q(f(elem!0, elem!0), f(elem!0, elem!0)) | (~p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | (~p(f(f(elem!0, elem!0), f(elem!0, elem!0)), f(f(elem!0, elem!0), f(elem!0, elem!0))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 ((~p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | (~p(f(f(elem!0, elem!0), f(elem!0, elem!0)), f(f(elem!0, elem!0), f(elem!0, elem!0))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[61, 29, 58])).
% 0.20/0.40 tff(63,plain,
% 0.20/0.40 (~p(f(f(elem!0, elem!0), f(elem!0, elem!0)), f(f(elem!0, elem!0), f(elem!0, elem!0)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[62, 11])).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 ((~![B: $i, A: $i] : p(A, B)) | p(f(f(elem!0, elem!0), f(elem!0, elem!0)), f(f(elem!0, elem!0), f(elem!0, elem!0)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(65,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[64, 8, 63])).
% 0.20/0.40 % SZS output end Proof
%------------------------------------------------------------------------------