TSTP Solution File: SYN347-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN347-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 23:54:53 EDT 2022
% Result : Unsatisfiable 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN347-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n004.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 02:42:34 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Unsatisfiable
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(f_type, type, (
% 0.20/0.40 f: ( $i * $i ) > $o)).
% 0.20/0.40 tff(b_type, type, (
% 0.20/0.40 b: $i)).
% 0.20/0.40 tff(a_type, type, (
% 0.20/0.40 a: $i)).
% 0.20/0.40 tff(y_type, type, (
% 0.20/0.40 y: ( $i * $i ) > $i)).
% 0.20/0.40 tff(1,assumption,(~f(a, b)), introduced(assumption)).
% 0.20/0.40 tff(2,assumption,(~f(a, y(a, b))), introduced(assumption)).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (^[X2: $i, X1: $i] : refl((f(a, y(X1, X2)) | f(b, y(X1, X2))) <=> (f(a, y(X1, X2)) | f(b, y(X1, X2))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (![X2: $i, X1: $i] : (f(a, y(X1, X2)) | f(b, y(X1, X2))) <=> ![X2: $i, X1: $i] : (f(a, y(X1, X2)) | f(b, y(X1, X2)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (![X2: $i, X1: $i] : (f(a, y(X1, X2)) | f(b, y(X1, X2))) <=> ![X2: $i, X1: $i] : (f(a, y(X1, X2)) | f(b, y(X1, X2)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(6,axiom,(![X2: $i, X1: $i] : (f(a, y(X1, X2)) | f(b, y(X1, X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause5')).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (![X2: $i, X1: $i] : (f(a, y(X1, X2)) | f(b, y(X1, X2)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.40 tff(8,plain,(
% 0.20/0.40 ![X2: $i, X1: $i] : (f(a, y(X1, X2)) | f(b, y(X1, X2)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[7])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (![X2: $i, X1: $i] : (f(a, y(X1, X2)) | f(b, y(X1, X2)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (((~![X2: $i, X1: $i] : (f(a, y(X1, X2)) | f(b, y(X1, X2)))) | (f(a, y(a, b)) | f(b, y(a, b)))) <=> ((~![X2: $i, X1: $i] : (f(a, y(X1, X2)) | f(b, y(X1, X2)))) | f(a, y(a, b)) | f(b, y(a, b)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 ((~![X2: $i, X1: $i] : (f(a, y(X1, X2)) | f(b, y(X1, X2)))) | (f(a, y(a, b)) | f(b, y(a, b)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 ((~![X2: $i, X1: $i] : (f(a, y(X1, X2)) | f(b, y(X1, X2)))) | f(a, y(a, b)) | f(b, y(a, b))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (f(a, y(a, b)) | f(b, y(a, b))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[12, 9])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (f(b, y(a, b))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[13, 2])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (^[X2: $i, X1: $i] : refl((f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2))) <=> (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (![X2: $i, X1: $i] : (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2))) <=> ![X2: $i, X1: $i] : (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (![X2: $i, X1: $i] : (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2))) <=> ![X2: $i, X1: $i] : (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (^[X2: $i, X1: $i] : trans(monotonicity(rewrite((f(X1, y(X1, X2)) | (~f(X2, y(X1, X2)))) <=> ((~f(X2, y(X1, X2))) | f(X1, y(X1, X2)))), (((f(X1, y(X1, X2)) | (~f(X2, y(X1, X2)))) | f(a, b)) <=> (((~f(X2, y(X1, X2))) | f(X1, y(X1, X2))) | f(a, b)))), rewrite((((~f(X2, y(X1, X2))) | f(X1, y(X1, X2))) | f(a, b)) <=> (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2)))), (((f(X1, y(X1, X2)) | (~f(X2, y(X1, X2)))) | f(a, b)) <=> (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (![X2: $i, X1: $i] : ((f(X1, y(X1, X2)) | (~f(X2, y(X1, X2)))) | f(a, b)) <=> ![X2: $i, X1: $i] : (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.40 tff(20,axiom,(![X2: $i, X1: $i] : ((f(X1, y(X1, X2)) | (~f(X2, y(X1, X2)))) | f(a, b))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (![X2: $i, X1: $i] : (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (![X2: $i, X1: $i] : (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.20/0.40 tff(23,plain,(
% 0.20/0.40 ![X2: $i, X1: $i] : (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[22])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 (![X2: $i, X1: $i] : (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (((~![X2: $i, X1: $i] : (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2)))) | (f(a, b) | f(a, y(a, b)) | (~f(b, y(a, b))))) <=> ((~![X2: $i, X1: $i] : (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2)))) | f(a, b) | f(a, y(a, b)) | (~f(b, y(a, b))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 ((f(a, b) | (~f(b, y(a, b))) | f(a, y(a, b))) <=> (f(a, b) | f(a, y(a, b)) | (~f(b, y(a, b))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 (((~![X2: $i, X1: $i] : (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2)))) | (f(a, b) | (~f(b, y(a, b))) | f(a, y(a, b)))) <=> ((~![X2: $i, X1: $i] : (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2)))) | (f(a, b) | f(a, y(a, b)) | (~f(b, y(a, b)))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[26])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (((~![X2: $i, X1: $i] : (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2)))) | (f(a, b) | (~f(b, y(a, b))) | f(a, y(a, b)))) <=> ((~![X2: $i, X1: $i] : (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2)))) | f(a, b) | f(a, y(a, b)) | (~f(b, y(a, b))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[27, 25])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 ((~![X2: $i, X1: $i] : (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2)))) | (f(a, b) | (~f(b, y(a, b))) | f(a, y(a, b)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 ((~![X2: $i, X1: $i] : (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2)))) | f(a, b) | f(a, y(a, b)) | (~f(b, y(a, b)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[30, 24, 2, 14, 1])).
% 0.20/0.40 tff(32,plain,(f(a, y(a, b)) | f(a, b)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (f(a, y(a, b))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[32, 1])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 (^[X2: $i, X1: $i] : refl(((~f(a, y(X1, X2))) | (~f(b, y(X1, X2)))) <=> ((~f(a, y(X1, X2))) | (~f(b, y(X1, X2)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 (![X2: $i, X1: $i] : ((~f(a, y(X1, X2))) | (~f(b, y(X1, X2)))) <=> ![X2: $i, X1: $i] : ((~f(a, y(X1, X2))) | (~f(b, y(X1, X2))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 (![X2: $i, X1: $i] : ((~f(a, y(X1, X2))) | (~f(b, y(X1, X2)))) <=> ![X2: $i, X1: $i] : ((~f(a, y(X1, X2))) | (~f(b, y(X1, X2))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(37,axiom,(![X2: $i, X1: $i] : ((~f(a, y(X1, X2))) | (~f(b, y(X1, X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause6')).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 (![X2: $i, X1: $i] : ((~f(a, y(X1, X2))) | (~f(b, y(X1, X2))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.40 tff(39,plain,(
% 0.20/0.40 ![X2: $i, X1: $i] : ((~f(a, y(X1, X2))) | (~f(b, y(X1, X2))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[38])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 (![X2: $i, X1: $i] : ((~f(a, y(X1, X2))) | (~f(b, y(X1, X2))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 (((~![X2: $i, X1: $i] : ((~f(a, y(X1, X2))) | (~f(b, y(X1, X2))))) | ((~f(a, y(a, b))) | (~f(b, y(a, b))))) <=> ((~![X2: $i, X1: $i] : ((~f(a, y(X1, X2))) | (~f(b, y(X1, X2))))) | (~f(a, y(a, b))) | (~f(b, y(a, b))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 ((~![X2: $i, X1: $i] : ((~f(a, y(X1, X2))) | (~f(b, y(X1, X2))))) | ((~f(a, y(a, b))) | (~f(b, y(a, b))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 ((~![X2: $i, X1: $i] : ((~f(a, y(X1, X2))) | (~f(b, y(X1, X2))))) | (~f(a, y(a, b))) | (~f(b, y(a, b)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.40 tff(44,plain,
% 0.20/0.40 (~f(b, y(a, b))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[43, 40, 33])).
% 0.20/0.40 tff(45,plain,
% 0.20/0.40 (^[X2: $i, X1: $i] : refl((f(a, b) | f(X2, y(X1, X2)) | (~f(X1, y(X1, X2)))) <=> (f(a, b) | f(X2, y(X1, X2)) | (~f(X1, y(X1, X2)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 (![X2: $i, X1: $i] : (f(a, b) | f(X2, y(X1, X2)) | (~f(X1, y(X1, X2)))) <=> ![X2: $i, X1: $i] : (f(a, b) | f(X2, y(X1, X2)) | (~f(X1, y(X1, X2))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (![X2: $i, X1: $i] : (f(a, b) | f(X2, y(X1, X2)) | (~f(X1, y(X1, X2)))) <=> ![X2: $i, X1: $i] : (f(a, b) | f(X2, y(X1, X2)) | (~f(X1, y(X1, X2))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (^[X2: $i, X1: $i] : rewrite((((~f(X1, y(X1, X2))) | f(X2, y(X1, X2))) | f(a, b)) <=> (f(a, b) | f(X2, y(X1, X2)) | (~f(X1, y(X1, X2)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (![X2: $i, X1: $i] : (((~f(X1, y(X1, X2))) | f(X2, y(X1, X2))) | f(a, b)) <=> ![X2: $i, X1: $i] : (f(a, b) | f(X2, y(X1, X2)) | (~f(X1, y(X1, X2))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.41 tff(50,axiom,(![X2: $i, X1: $i] : (((~f(X1, y(X1, X2))) | f(X2, y(X1, X2))) | f(a, b))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause2')).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (![X2: $i, X1: $i] : (f(a, b) | f(X2, y(X1, X2)) | (~f(X1, y(X1, X2))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 (![X2: $i, X1: $i] : (f(a, b) | f(X2, y(X1, X2)) | (~f(X1, y(X1, X2))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.20/0.41 tff(53,plain,(
% 0.20/0.41 ![X2: $i, X1: $i] : (f(a, b) | f(X2, y(X1, X2)) | (~f(X1, y(X1, X2))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[52])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (![X2: $i, X1: $i] : (f(a, b) | f(X2, y(X1, X2)) | (~f(X1, y(X1, X2))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 (((~![X2: $i, X1: $i] : (f(a, b) | f(X2, y(X1, X2)) | (~f(X1, y(X1, X2))))) | (f(a, b) | f(b, y(a, b)) | (~f(a, y(a, b))))) <=> ((~![X2: $i, X1: $i] : (f(a, b) | f(X2, y(X1, X2)) | (~f(X1, y(X1, X2))))) | f(a, b) | f(b, y(a, b)) | (~f(a, y(a, b))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 ((~![X2: $i, X1: $i] : (f(a, b) | f(X2, y(X1, X2)) | (~f(X1, y(X1, X2))))) | (f(a, b) | f(b, y(a, b)) | (~f(a, y(a, b))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 ((~![X2: $i, X1: $i] : (f(a, b) | f(X2, y(X1, X2)) | (~f(X1, y(X1, X2))))) | f(a, b) | f(b, y(a, b)) | (~f(a, y(a, b)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[57, 54, 33, 44, 1])).
% 0.20/0.41 tff(59,plain,(f(a, b)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(60,assumption,(~f(a, y(a, a))), introduced(assumption)).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 (^[X2: $i, X1: $i] : refl(((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2))) <=> ((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 (![X2: $i, X1: $i] : ((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2))) <=> ![X2: $i, X1: $i] : ((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[61])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 (![X2: $i, X1: $i] : ((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2))) <=> ![X2: $i, X1: $i] : ((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 (^[X2: $i, X1: $i] : rewrite(((f(X1, y(X1, X2)) | f(X2, y(X1, X2))) | (~f(a, b))) <=> ((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 (![X2: $i, X1: $i] : ((f(X1, y(X1, X2)) | f(X2, y(X1, X2))) | (~f(a, b))) <=> ![X2: $i, X1: $i] : ((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[64])).
% 0.20/0.41 tff(66,axiom,(![X2: $i, X1: $i] : ((f(X1, y(X1, X2)) | f(X2, y(X1, X2))) | (~f(a, b)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause4')).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 (![X2: $i, X1: $i] : ((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 (![X2: $i, X1: $i] : ((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.20/0.41 tff(69,plain,(
% 0.20/0.41 ![X2: $i, X1: $i] : ((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[68])).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 (![X2: $i, X1: $i] : ((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 (((~![X2: $i, X1: $i] : ((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2)))) | ((~f(a, b)) | f(a, y(a, a)))) <=> ((~![X2: $i, X1: $i] : ((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2)))) | (~f(a, b)) | f(a, y(a, a)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(72,plain,
% 0.20/0.41 (((~f(a, b)) | f(a, y(a, a)) | f(a, y(a, a))) <=> ((~f(a, b)) | f(a, y(a, a)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(73,plain,
% 0.20/0.41 (((~![X2: $i, X1: $i] : ((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2)))) | ((~f(a, b)) | f(a, y(a, a)) | f(a, y(a, a)))) <=> ((~![X2: $i, X1: $i] : ((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2)))) | ((~f(a, b)) | f(a, y(a, a))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[72])).
% 0.20/0.41 tff(74,plain,
% 0.20/0.41 (((~![X2: $i, X1: $i] : ((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2)))) | ((~f(a, b)) | f(a, y(a, a)) | f(a, y(a, a)))) <=> ((~![X2: $i, X1: $i] : ((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2)))) | (~f(a, b)) | f(a, y(a, a)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[73, 71])).
% 0.20/0.41 tff(75,plain,
% 0.20/0.41 ((~![X2: $i, X1: $i] : ((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2)))) | ((~f(a, b)) | f(a, y(a, a)) | f(a, y(a, a)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(76,plain,
% 0.20/0.41 ((~![X2: $i, X1: $i] : ((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2)))) | (~f(a, b)) | f(a, y(a, a))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.20/0.41 tff(77,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[76, 70, 60, 59])).
% 0.20/0.41 tff(78,plain,(f(a, y(a, a))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 (^[X2: $i, X1: $i] : refl(((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2)))) <=> ((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(80,plain,
% 0.20/0.41 (![X2: $i, X1: $i] : ((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2)))) <=> ![X2: $i, X1: $i] : ((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[79])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 (![X2: $i, X1: $i] : ((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2)))) <=> ![X2: $i, X1: $i] : ((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(82,plain,
% 0.20/0.41 (^[X2: $i, X1: $i] : rewrite((((~f(X1, y(X1, X2))) | (~f(X2, y(X1, X2)))) | (~f(a, b))) <=> ((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(83,plain,
% 0.20/0.41 (![X2: $i, X1: $i] : (((~f(X1, y(X1, X2))) | (~f(X2, y(X1, X2)))) | (~f(a, b))) <=> ![X2: $i, X1: $i] : ((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[82])).
% 0.20/0.41 tff(84,axiom,(![X2: $i, X1: $i] : (((~f(X1, y(X1, X2))) | (~f(X2, y(X1, X2)))) | (~f(a, b)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause3')).
% 0.20/0.41 tff(85,plain,
% 0.20/0.41 (![X2: $i, X1: $i] : ((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.20/0.41 tff(86,plain,
% 0.20/0.41 (![X2: $i, X1: $i] : ((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.20/0.41 tff(87,plain,(
% 0.20/0.41 ![X2: $i, X1: $i] : ((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[86])).
% 0.20/0.41 tff(88,plain,
% 0.20/0.41 (![X2: $i, X1: $i] : ((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.20/0.41 tff(89,plain,
% 0.20/0.41 (((~![X2: $i, X1: $i] : ((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2))))) | ((~f(a, b)) | (~f(a, y(a, a))))) <=> ((~![X2: $i, X1: $i] : ((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2))))) | (~f(a, b)) | (~f(a, y(a, a))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(90,plain,
% 0.20/0.41 (((~f(a, b)) | (~f(a, y(a, a))) | (~f(a, y(a, a)))) <=> ((~f(a, b)) | (~f(a, y(a, a))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(91,plain,
% 0.20/0.41 (((~![X2: $i, X1: $i] : ((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2))))) | ((~f(a, b)) | (~f(a, y(a, a))) | (~f(a, y(a, a))))) <=> ((~![X2: $i, X1: $i] : ((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2))))) | ((~f(a, b)) | (~f(a, y(a, a)))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[90])).
% 0.20/0.41 tff(92,plain,
% 0.20/0.41 (((~![X2: $i, X1: $i] : ((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2))))) | ((~f(a, b)) | (~f(a, y(a, a))) | (~f(a, y(a, a))))) <=> ((~![X2: $i, X1: $i] : ((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2))))) | (~f(a, b)) | (~f(a, y(a, a))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[91, 89])).
% 0.20/0.41 tff(93,plain,
% 0.20/0.41 ((~![X2: $i, X1: $i] : ((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2))))) | ((~f(a, b)) | (~f(a, y(a, a))) | (~f(a, y(a, a))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(94,plain,
% 0.20/0.41 ((~![X2: $i, X1: $i] : ((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2))))) | (~f(a, b)) | (~f(a, y(a, a)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.20/0.41 tff(95,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[94, 88, 78, 59])).
% 0.20/0.41 % SZS output end Proof
%------------------------------------------------------------------------------