TSTP Solution File: SYN345-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN345-1 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 0.12s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYN345-1 : TPTP v8.1.0. Released v1.2.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n007.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 02:29:20 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.
% 0.12/0.40 % SZS status Unsatisfiable
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(f_type, type, (
% 0.12/0.40 f: ( $i * $i * $i ) > $o)).
% 0.12/0.40 tff(z_type, type, (
% 0.12/0.40 z: ( $i * $i ) > $i)).
% 0.12/0.40 tff(b_type, type, (
% 0.12/0.40 b: $i)).
% 0.12/0.40 tff(a_type, type, (
% 0.12/0.40 a: $i)).
% 0.12/0.40 tff(1,assumption,(~f(a, a, b)), introduced(assumption)).
% 0.12/0.40 tff(2,assumption,(~f(a, b, b)), introduced(assumption)).
% 0.12/0.40 tff(3,plain,
% 0.12/0.40 (^[Y2: $i, Y1: $i] : refl((f(a, a, b) | f(a, b, b) | f(Y1, Y2, z(Y1, Y2))) <=> (f(a, a, b) | f(a, b, b) | f(Y1, Y2, z(Y1, Y2))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(4,plain,
% 0.12/0.40 (![Y2: $i, Y1: $i] : (f(a, a, b) | f(a, b, b) | f(Y1, Y2, z(Y1, Y2))) <=> ![Y2: $i, Y1: $i] : (f(a, a, b) | f(a, b, b) | f(Y1, Y2, z(Y1, Y2)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.40 tff(5,plain,
% 0.12/0.40 (![Y2: $i, Y1: $i] : (f(a, a, b) | f(a, b, b) | f(Y1, Y2, z(Y1, Y2))) <=> ![Y2: $i, Y1: $i] : (f(a, a, b) | f(a, b, b) | f(Y1, Y2, z(Y1, Y2)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(6,plain,
% 0.12/0.40 (^[Y2: $i, Y1: $i] : trans(monotonicity(rewrite((f(Y1, Y2, z(Y1, Y2)) | f(a, a, b)) <=> (f(a, a, b) | f(Y1, Y2, z(Y1, Y2)))), (((f(Y1, Y2, z(Y1, Y2)) | f(a, a, b)) | f(a, b, b)) <=> ((f(a, a, b) | f(Y1, Y2, z(Y1, Y2))) | f(a, b, b)))), rewrite(((f(a, a, b) | f(Y1, Y2, z(Y1, Y2))) | f(a, b, b)) <=> (f(a, a, b) | f(a, b, b) | f(Y1, Y2, z(Y1, Y2)))), (((f(Y1, Y2, z(Y1, Y2)) | f(a, a, b)) | f(a, b, b)) <=> (f(a, a, b) | f(a, b, b) | f(Y1, Y2, z(Y1, Y2)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(7,plain,
% 0.12/0.40 (![Y2: $i, Y1: $i] : ((f(Y1, Y2, z(Y1, Y2)) | f(a, a, b)) | f(a, b, b)) <=> ![Y2: $i, Y1: $i] : (f(a, a, b) | f(a, b, b) | f(Y1, Y2, z(Y1, Y2)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.40 tff(8,axiom,(![Y2: $i, Y1: $i] : ((f(Y1, Y2, z(Y1, Y2)) | f(a, a, b)) | f(a, b, b))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause5')).
% 0.12/0.40 tff(9,plain,
% 0.12/0.40 (![Y2: $i, Y1: $i] : (f(a, a, b) | f(a, b, b) | f(Y1, Y2, z(Y1, Y2)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.12/0.40 tff(10,plain,
% 0.12/0.40 (![Y2: $i, Y1: $i] : (f(a, a, b) | f(a, b, b) | f(Y1, Y2, z(Y1, Y2)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.12/0.40 tff(11,plain,(
% 0.12/0.40 ![Y2: $i, Y1: $i] : (f(a, a, b) | f(a, b, b) | f(Y1, Y2, z(Y1, Y2)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[10])).
% 0.12/0.40 tff(12,plain,
% 0.12/0.40 (![Y2: $i, Y1: $i] : (f(a, a, b) | f(a, b, b) | f(Y1, Y2, z(Y1, Y2)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.12/0.40 tff(13,plain,
% 0.12/0.40 (((~![Y2: $i, Y1: $i] : (f(a, a, b) | f(a, b, b) | f(Y1, Y2, z(Y1, Y2)))) | (f(a, a, b) | f(a, b, b) | f(b, b, z(b, b)))) <=> ((~![Y2: $i, Y1: $i] : (f(a, a, b) | f(a, b, b) | f(Y1, Y2, z(Y1, Y2)))) | f(a, a, b) | f(a, b, b) | f(b, b, z(b, b)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(14,plain,
% 0.12/0.40 ((~![Y2: $i, Y1: $i] : (f(a, a, b) | f(a, b, b) | f(Y1, Y2, z(Y1, Y2)))) | (f(a, a, b) | f(a, b, b) | f(b, b, z(b, b)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(15,plain,
% 0.12/0.40 ((~![Y2: $i, Y1: $i] : (f(a, a, b) | f(a, b, b) | f(Y1, Y2, z(Y1, Y2)))) | f(a, a, b) | f(a, b, b) | f(b, b, z(b, b))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.12/0.40 tff(16,plain,
% 0.12/0.40 (f(a, a, b) | f(a, b, b) | f(b, b, z(b, b))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[15, 12])).
% 0.12/0.40 tff(17,plain,
% 0.12/0.40 (f(b, b, z(b, b))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[16, 2, 1])).
% 0.12/0.40 tff(18,plain,
% 0.12/0.40 (^[Y1: $i] : refl((f(a, a, b) | f(a, b, b) | (~f(b, b, Y1))) <=> (f(a, a, b) | f(a, b, b) | (~f(b, b, Y1))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(19,plain,
% 0.12/0.40 (![Y1: $i] : (f(a, a, b) | f(a, b, b) | (~f(b, b, Y1))) <=> ![Y1: $i] : (f(a, a, b) | f(a, b, b) | (~f(b, b, Y1)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[18])).
% 0.12/0.40 tff(20,plain,
% 0.12/0.40 (![Y1: $i] : (f(a, a, b) | f(a, b, b) | (~f(b, b, Y1))) <=> ![Y1: $i] : (f(a, a, b) | f(a, b, b) | (~f(b, b, Y1)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(21,plain,
% 0.12/0.40 (^[Y1: $i] : rewrite((((~f(b, b, Y1)) | f(a, a, b)) | f(a, b, b)) <=> (f(a, a, b) | f(a, b, b) | (~f(b, b, Y1))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(22,plain,
% 0.12/0.40 (![Y1: $i] : (((~f(b, b, Y1)) | f(a, a, b)) | f(a, b, b)) <=> ![Y1: $i] : (f(a, a, b) | f(a, b, b) | (~f(b, b, Y1)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[21])).
% 0.12/0.40 tff(23,axiom,(![Y1: $i] : (((~f(b, b, Y1)) | f(a, a, b)) | f(a, b, b))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause7')).
% 0.12/0.40 tff(24,plain,
% 0.12/0.40 (![Y1: $i] : (f(a, a, b) | f(a, b, b) | (~f(b, b, Y1)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.12/0.40 tff(25,plain,
% 0.12/0.40 (![Y1: $i] : (f(a, a, b) | f(a, b, b) | (~f(b, b, Y1)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.12/0.40 tff(26,plain,(
% 0.12/0.40 ![Y1: $i] : (f(a, a, b) | f(a, b, b) | (~f(b, b, Y1)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[25])).
% 0.12/0.40 tff(27,plain,
% 0.12/0.40 (![Y1: $i] : (f(a, a, b) | f(a, b, b) | (~f(b, b, Y1)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.12/0.40 tff(28,plain,
% 0.12/0.40 (((~![Y1: $i] : (f(a, a, b) | f(a, b, b) | (~f(b, b, Y1)))) | (f(a, a, b) | f(a, b, b) | (~f(b, b, z(b, b))))) <=> ((~![Y1: $i] : (f(a, a, b) | f(a, b, b) | (~f(b, b, Y1)))) | f(a, a, b) | f(a, b, b) | (~f(b, b, z(b, b))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(29,plain,
% 0.12/0.40 ((~![Y1: $i] : (f(a, a, b) | f(a, b, b) | (~f(b, b, Y1)))) | (f(a, a, b) | f(a, b, b) | (~f(b, b, z(b, b))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(30,plain,
% 0.12/0.40 ((~![Y1: $i] : (f(a, a, b) | f(a, b, b) | (~f(b, b, Y1)))) | f(a, a, b) | f(a, b, b) | (~f(b, b, z(b, b)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.12/0.40 tff(31,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[30, 27, 1, 2, 17])).
% 0.12/0.40 tff(32,plain,(f(a, b, b) | f(a, a, b)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.40 tff(33,plain,
% 0.12/0.40 (f(a, b, b)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[32, 1])).
% 0.12/0.40 tff(34,plain,
% 0.12/0.40 (^[Y2: $i, Y1: $i] : refl((f(a, a, b) | (~f(a, b, b)) | (~f(Y1, z(Y1, Y2), z(Y1, Y2)))) <=> (f(a, a, b) | (~f(a, b, b)) | (~f(Y1, z(Y1, Y2), z(Y1, Y2)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(35,plain,
% 0.12/0.40 (![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | (~f(Y1, z(Y1, Y2), z(Y1, Y2)))) <=> ![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | (~f(Y1, z(Y1, Y2), z(Y1, Y2))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[34])).
% 0.12/0.40 tff(36,plain,
% 0.12/0.40 (![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | (~f(Y1, z(Y1, Y2), z(Y1, Y2)))) <=> ![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | (~f(Y1, z(Y1, Y2), z(Y1, Y2))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(37,plain,
% 0.12/0.40 (^[Y2: $i, Y1: $i] : rewrite((((~f(Y1, z(Y1, Y2), z(Y1, Y2))) | f(a, a, b)) | (~f(a, b, b))) <=> (f(a, a, b) | (~f(a, b, b)) | (~f(Y1, z(Y1, Y2), z(Y1, Y2)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(38,plain,
% 0.12/0.40 (![Y2: $i, Y1: $i] : (((~f(Y1, z(Y1, Y2), z(Y1, Y2))) | f(a, a, b)) | (~f(a, b, b))) <=> ![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | (~f(Y1, z(Y1, Y2), z(Y1, Y2))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[37])).
% 0.12/0.40 tff(39,axiom,(![Y2: $i, Y1: $i] : (((~f(Y1, z(Y1, Y2), z(Y1, Y2))) | f(a, a, b)) | (~f(a, b, b)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause4')).
% 0.12/0.40 tff(40,plain,
% 0.12/0.40 (![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | (~f(Y1, z(Y1, Y2), z(Y1, Y2))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.12/0.40 tff(41,plain,
% 0.12/0.40 (![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | (~f(Y1, z(Y1, Y2), z(Y1, Y2))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.12/0.40 tff(42,plain,(
% 0.12/0.40 ![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | (~f(Y1, z(Y1, Y2), z(Y1, Y2))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[41])).
% 0.12/0.40 tff(43,plain,
% 0.12/0.40 (![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | (~f(Y1, z(Y1, Y2), z(Y1, Y2))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.12/0.40 tff(44,plain,
% 0.12/0.40 (((~![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | (~f(Y1, z(Y1, Y2), z(Y1, Y2))))) | (f(a, a, b) | (~f(a, b, b)) | (~f(b, z(b, b), z(b, b))))) <=> ((~![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | (~f(Y1, z(Y1, Y2), z(Y1, Y2))))) | f(a, a, b) | (~f(a, b, b)) | (~f(b, z(b, b), z(b, b))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(45,plain,
% 0.12/0.40 ((~![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | (~f(Y1, z(Y1, Y2), z(Y1, Y2))))) | (f(a, a, b) | (~f(a, b, b)) | (~f(b, z(b, b), z(b, b))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 ((~![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | (~f(Y1, z(Y1, Y2), z(Y1, Y2))))) | f(a, a, b) | (~f(a, b, b)) | (~f(b, z(b, b), z(b, b)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 (f(a, a, b) | (~f(a, b, b)) | (~f(b, z(b, b), z(b, b)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[46, 43])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (~f(b, z(b, b), z(b, b))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[47, 33, 1])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 (^[Y2: $i, Y1: $i] : refl((f(a, a, b) | (~f(a, b, b)) | f(b, Y1, Y2)) <=> (f(a, a, b) | (~f(a, b, b)) | f(b, Y1, Y2)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 (![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | f(b, Y1, Y2)) <=> ![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | f(b, Y1, Y2))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | f(b, Y1, Y2)) <=> ![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | f(b, Y1, Y2))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (^[Y2: $i, Y1: $i] : trans(monotonicity(rewrite((f(b, Y1, Y2) | f(a, a, b)) <=> (f(a, a, b) | f(b, Y1, Y2))), (((f(b, Y1, Y2) | f(a, a, b)) | (~f(a, b, b))) <=> ((f(a, a, b) | f(b, Y1, Y2)) | (~f(a, b, b))))), rewrite(((f(a, a, b) | f(b, Y1, Y2)) | (~f(a, b, b))) <=> (f(a, a, b) | (~f(a, b, b)) | f(b, Y1, Y2))), (((f(b, Y1, Y2) | f(a, a, b)) | (~f(a, b, b))) <=> (f(a, a, b) | (~f(a, b, b)) | f(b, Y1, Y2))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 (![Y2: $i, Y1: $i] : ((f(b, Y1, Y2) | f(a, a, b)) | (~f(a, b, b))) <=> ![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | f(b, Y1, Y2))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[52])).
% 0.19/0.41 tff(54,axiom,(![Y2: $i, Y1: $i] : ((f(b, Y1, Y2) | f(a, a, b)) | (~f(a, b, b)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause3')).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 (![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | f(b, Y1, Y2))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 (![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | f(b, Y1, Y2))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.19/0.41 tff(57,plain,(
% 0.19/0.41 ![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | f(b, Y1, Y2))),
% 0.19/0.41 inference(skolemize,[status(sab)],[56])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 (![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | f(b, Y1, Y2))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (((~![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | f(b, Y1, Y2))) | (f(a, a, b) | (~f(a, b, b)) | f(b, z(b, b), z(b, b)))) <=> ((~![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | f(b, Y1, Y2))) | f(a, a, b) | (~f(a, b, b)) | f(b, z(b, b), z(b, b)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 ((~![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | f(b, Y1, Y2))) | (f(a, a, b) | (~f(a, b, b)) | f(b, z(b, b), z(b, b)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 ((~![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | f(b, Y1, Y2))) | f(a, a, b) | (~f(a, b, b)) | f(b, z(b, b), z(b, b))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[61, 58, 1, 33, 48])).
% 0.19/0.41 tff(63,plain,(f(a, a, b)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(64,assumption,(f(a, a, b)), introduced(assumption)).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (^[Y1: $i] : refl(((~f(a, a, b)) | f(a, b, b) | f(a, b, Y1)) <=> ((~f(a, a, b)) | f(a, b, b) | f(a, b, Y1)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (![Y1: $i] : ((~f(a, a, b)) | f(a, b, b) | f(a, b, Y1)) <=> ![Y1: $i] : ((~f(a, a, b)) | f(a, b, b) | f(a, b, Y1))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (![Y1: $i] : ((~f(a, a, b)) | f(a, b, b) | f(a, b, Y1)) <=> ![Y1: $i] : ((~f(a, a, b)) | f(a, b, b) | f(a, b, Y1))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 (^[Y1: $i] : trans(monotonicity(rewrite((f(a, b, Y1) | (~f(a, a, b))) <=> ((~f(a, a, b)) | f(a, b, Y1))), (((f(a, b, Y1) | (~f(a, a, b))) | f(a, b, b)) <=> (((~f(a, a, b)) | f(a, b, Y1)) | f(a, b, b)))), rewrite((((~f(a, a, b)) | f(a, b, Y1)) | f(a, b, b)) <=> ((~f(a, a, b)) | f(a, b, b) | f(a, b, Y1))), (((f(a, b, Y1) | (~f(a, a, b))) | f(a, b, b)) <=> ((~f(a, a, b)) | f(a, b, b) | f(a, b, Y1))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(69,plain,
% 0.19/0.42 (![Y1: $i] : ((f(a, b, Y1) | (~f(a, a, b))) | f(a, b, b)) <=> ![Y1: $i] : ((~f(a, a, b)) | f(a, b, b) | f(a, b, Y1))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.42 tff(70,axiom,(![Y1: $i] : ((f(a, b, Y1) | (~f(a, a, b))) | f(a, b, b))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.19/0.42 tff(71,plain,
% 0.19/0.42 (![Y1: $i] : ((~f(a, a, b)) | f(a, b, b) | f(a, b, Y1))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 (![Y1: $i] : ((~f(a, a, b)) | f(a, b, b) | f(a, b, Y1))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.19/0.42 tff(73,plain,(
% 0.19/0.42 ![Y1: $i] : ((~f(a, a, b)) | f(a, b, b) | f(a, b, Y1))),
% 0.19/0.42 inference(skolemize,[status(sab)],[72])).
% 0.19/0.42 tff(74,plain,
% 0.19/0.42 (![Y1: $i] : ((~f(a, a, b)) | f(a, b, b) | f(a, b, Y1))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.19/0.42 tff(75,plain,
% 0.19/0.42 (((~![Y1: $i] : ((~f(a, a, b)) | f(a, b, b) | f(a, b, Y1))) | ((~f(a, a, b)) | f(a, b, b))) <=> ((~![Y1: $i] : ((~f(a, a, b)) | f(a, b, b) | f(a, b, Y1))) | (~f(a, a, b)) | f(a, b, b))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(76,plain,
% 0.19/0.42 (((~f(a, a, b)) | f(a, b, b) | f(a, b, b)) <=> ((~f(a, a, b)) | f(a, b, b))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(77,plain,
% 0.19/0.42 (((~![Y1: $i] : ((~f(a, a, b)) | f(a, b, b) | f(a, b, Y1))) | ((~f(a, a, b)) | f(a, b, b) | f(a, b, b))) <=> ((~![Y1: $i] : ((~f(a, a, b)) | f(a, b, b) | f(a, b, Y1))) | ((~f(a, a, b)) | f(a, b, b)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[76])).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 (((~![Y1: $i] : ((~f(a, a, b)) | f(a, b, b) | f(a, b, Y1))) | ((~f(a, a, b)) | f(a, b, b) | f(a, b, b))) <=> ((~![Y1: $i] : ((~f(a, a, b)) | f(a, b, b) | f(a, b, Y1))) | (~f(a, a, b)) | f(a, b, b))),
% 0.19/0.42 inference(transitivity,[status(thm)],[77, 75])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 ((~![Y1: $i] : ((~f(a, a, b)) | f(a, b, b) | f(a, b, Y1))) | ((~f(a, a, b)) | f(a, b, b) | f(a, b, b))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 ((~![Y1: $i] : ((~f(a, a, b)) | f(a, b, b) | f(a, b, Y1))) | (~f(a, a, b)) | f(a, b, b)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[80, 74, 64, 2])).
% 0.19/0.42 tff(82,plain,(f(a, b, b) | (~f(a, a, b))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 (f(a, b, b)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[82, 63])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 (^[Y2: $i, Y1: $i] : refl(((~f(a, a, b)) | (~f(a, b, b)) | f(Y1, Y2, z(Y1, Y2))) <=> ((~f(a, a, b)) | (~f(a, b, b)) | f(Y1, Y2, z(Y1, Y2))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 (![Y2: $i, Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | f(Y1, Y2, z(Y1, Y2))) <=> ![Y2: $i, Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | f(Y1, Y2, z(Y1, Y2)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[84])).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 (![Y2: $i, Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | f(Y1, Y2, z(Y1, Y2))) <=> ![Y2: $i, Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | f(Y1, Y2, z(Y1, Y2)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 (^[Y2: $i, Y1: $i] : trans(monotonicity(rewrite((f(Y1, Y2, z(Y1, Y2)) | (~f(a, a, b))) <=> ((~f(a, a, b)) | f(Y1, Y2, z(Y1, Y2)))), (((f(Y1, Y2, z(Y1, Y2)) | (~f(a, a, b))) | (~f(a, b, b))) <=> (((~f(a, a, b)) | f(Y1, Y2, z(Y1, Y2))) | (~f(a, b, b))))), rewrite((((~f(a, a, b)) | f(Y1, Y2, z(Y1, Y2))) | (~f(a, b, b))) <=> ((~f(a, a, b)) | (~f(a, b, b)) | f(Y1, Y2, z(Y1, Y2)))), (((f(Y1, Y2, z(Y1, Y2)) | (~f(a, a, b))) | (~f(a, b, b))) <=> ((~f(a, a, b)) | (~f(a, b, b)) | f(Y1, Y2, z(Y1, Y2)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 (![Y2: $i, Y1: $i] : ((f(Y1, Y2, z(Y1, Y2)) | (~f(a, a, b))) | (~f(a, b, b))) <=> ![Y2: $i, Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | f(Y1, Y2, z(Y1, Y2)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[87])).
% 0.19/0.42 tff(89,axiom,(![Y2: $i, Y1: $i] : ((f(Y1, Y2, z(Y1, Y2)) | (~f(a, a, b))) | (~f(a, b, b)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause6')).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 (![Y2: $i, Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | f(Y1, Y2, z(Y1, Y2)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 (![Y2: $i, Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | f(Y1, Y2, z(Y1, Y2)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.19/0.42 tff(92,plain,(
% 0.19/0.42 ![Y2: $i, Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | f(Y1, Y2, z(Y1, Y2)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[91])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 (![Y2: $i, Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | f(Y1, Y2, z(Y1, Y2)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 (((~![Y2: $i, Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | f(Y1, Y2, z(Y1, Y2)))) | ((~f(a, a, b)) | (~f(a, b, b)) | f(b, b, z(b, b)))) <=> ((~![Y2: $i, Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | f(Y1, Y2, z(Y1, Y2)))) | (~f(a, a, b)) | (~f(a, b, b)) | f(b, b, z(b, b)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(95,plain,
% 0.19/0.42 ((~![Y2: $i, Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | f(Y1, Y2, z(Y1, Y2)))) | ((~f(a, a, b)) | (~f(a, b, b)) | f(b, b, z(b, b)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(96,plain,
% 0.19/0.42 ((~![Y2: $i, Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | f(Y1, Y2, z(Y1, Y2)))) | (~f(a, a, b)) | (~f(a, b, b)) | f(b, b, z(b, b))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.19/0.42 tff(97,plain,
% 0.19/0.42 ((~f(a, a, b)) | (~f(a, b, b)) | f(b, b, z(b, b))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[96, 93])).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 (f(b, b, z(b, b))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[97, 83, 63])).
% 0.19/0.42 tff(99,plain,
% 0.19/0.42 (^[Y1: $i] : refl(((~f(a, a, b)) | (~f(a, b, b)) | (~f(b, b, Y1))) <=> ((~f(a, a, b)) | (~f(a, b, b)) | (~f(b, b, Y1))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(100,plain,
% 0.19/0.42 (![Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | (~f(b, b, Y1))) <=> ![Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | (~f(b, b, Y1)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[99])).
% 0.19/0.42 tff(101,plain,
% 0.19/0.42 (![Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | (~f(b, b, Y1))) <=> ![Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | (~f(b, b, Y1)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(102,plain,
% 0.19/0.42 (^[Y1: $i] : trans(monotonicity(rewrite(((~f(b, b, Y1)) | (~f(a, a, b))) <=> ((~f(a, a, b)) | (~f(b, b, Y1)))), ((((~f(b, b, Y1)) | (~f(a, a, b))) | (~f(a, b, b))) <=> (((~f(a, a, b)) | (~f(b, b, Y1))) | (~f(a, b, b))))), rewrite((((~f(a, a, b)) | (~f(b, b, Y1))) | (~f(a, b, b))) <=> ((~f(a, a, b)) | (~f(a, b, b)) | (~f(b, b, Y1)))), ((((~f(b, b, Y1)) | (~f(a, a, b))) | (~f(a, b, b))) <=> ((~f(a, a, b)) | (~f(a, b, b)) | (~f(b, b, Y1)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(103,plain,
% 0.19/0.42 (![Y1: $i] : (((~f(b, b, Y1)) | (~f(a, a, b))) | (~f(a, b, b))) <=> ![Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | (~f(b, b, Y1)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[102])).
% 0.19/0.42 tff(104,axiom,(![Y1: $i] : (((~f(b, b, Y1)) | (~f(a, a, b))) | (~f(a, b, b)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause8')).
% 0.19/0.42 tff(105,plain,
% 0.19/0.42 (![Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | (~f(b, b, Y1)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.42 tff(106,plain,
% 0.19/0.42 (![Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | (~f(b, b, Y1)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.19/0.42 tff(107,plain,(
% 0.19/0.42 ![Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | (~f(b, b, Y1)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[106])).
% 0.19/0.42 tff(108,plain,
% 0.19/0.42 (![Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | (~f(b, b, Y1)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[107, 100])).
% 0.19/0.42 tff(109,plain,
% 0.19/0.42 (((~![Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | (~f(b, b, Y1)))) | ((~f(a, a, b)) | (~f(a, b, b)) | (~f(b, b, z(b, b))))) <=> ((~![Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | (~f(b, b, Y1)))) | (~f(a, a, b)) | (~f(a, b, b)) | (~f(b, b, z(b, b))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(110,plain,
% 0.19/0.42 ((~![Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | (~f(b, b, Y1)))) | ((~f(a, a, b)) | (~f(a, b, b)) | (~f(b, b, z(b, b))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(111,plain,
% 0.19/0.42 ((~![Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | (~f(b, b, Y1)))) | (~f(a, a, b)) | (~f(a, b, b)) | (~f(b, b, z(b, b)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.19/0.42 tff(112,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[111, 108, 63, 83, 98])).
% 0.19/0.42 % SZS output end Proof
%------------------------------------------------------------------------------