%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN347-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 : Sat Jun 21 05:38:51 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN347-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.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 : Fri Jun 20 12:30:40 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(f_type, type, (
% 0.12/0.38 f: ( $i * $i ) > $o)).
% 0.12/0.38 tff(y_type, type, (
% 0.12/0.38 y: ( $i * $i ) > $i)).
% 0.12/0.38 tff(elem_0_type, type, (
% 0.12/0.38 elem_0: $i)).
% 0.12/0.38 tff(b_type, type, (
% 0.12/0.38 b: $i)).
% 0.12/0.38 tff(a_type, type, (
% 0.12/0.38 a: $i)).
% 0.12/0.38 tff(1,assumption,(~f(a, b)), introduced(assumption)).
% 0.12/0.38 tff(2,assumption,(~f(b, y(b, a))), introduced(assumption)).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (^[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))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (^[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)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.38 tff(8,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')).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (![X2: $i, X1: $i] : (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (![X2: $i, X1: $i] : (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.12/0.38 tff(11,plain,(
% 0.12/0.38 ![X2: $i, X1: $i] : (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[10])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (![X2: $i, X1: $i] : (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (((~![X2: $i, X1: $i] : (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2)))) | (f(a, b) | f(b, y(b, a)) | (~f(a, y(b, a))))) <=> ((~![X2: $i, X1: $i] : (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2)))) | f(a, b) | f(b, y(b, a)) | (~f(a, y(b, a))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 ((f(a, b) | (~f(a, y(b, a))) | f(b, y(b, a))) <=> (f(a, b) | f(b, y(b, a)) | (~f(a, y(b, a))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (((~![X2: $i, X1: $i] : (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2)))) | (f(a, b) | (~f(a, y(b, a))) | f(b, y(b, a)))) <=> ((~![X2: $i, X1: $i] : (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2)))) | (f(a, b) | f(b, y(b, a)) | (~f(a, y(b, a)))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[14])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (((~![X2: $i, X1: $i] : (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2)))) | (f(a, b) | (~f(a, y(b, a))) | f(b, y(b, a)))) <=> ((~![X2: $i, X1: $i] : (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2)))) | f(a, b) | f(b, y(b, a)) | (~f(a, y(b, a))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[15, 13])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 ((~![X2: $i, X1: $i] : (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2)))) | (f(a, b) | (~f(a, y(b, a))) | f(b, y(b, a)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 ((~![X2: $i, X1: $i] : (f(a, b) | (~f(X2, y(X1, X2))) | f(X1, y(X1, X2)))) | f(a, b) | f(b, y(b, a)) | (~f(a, y(b, a)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (f(a, b) | f(b, y(b, a)) | (~f(a, y(b, a)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[18, 12])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (~f(a, y(b, a))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[19, 2, 1])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (^[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))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[21])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(24,axiom,(![X2: $i, X1: $i] : (f(a, y(X1, X2)) | f(b, y(X1, X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause5')).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (![X2: $i, X1: $i] : (f(a, y(X1, X2)) | f(b, y(X1, X2)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.12/0.38 tff(26,plain,(
% 0.12/0.38 ![X2: $i, X1: $i] : (f(a, y(X1, X2)) | f(b, y(X1, X2)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[25])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (![X2: $i, X1: $i] : (f(a, y(X1, X2)) | f(b, y(X1, X2)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (((~![X2: $i, X1: $i] : (f(a, y(X1, X2)) | f(b, y(X1, X2)))) | (f(a, y(b, a)) | f(b, y(b, a)))) <=> ((~![X2: $i, X1: $i] : (f(a, y(X1, X2)) | f(b, y(X1, X2)))) | f(a, y(b, a)) | f(b, y(b, a)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 ((~![X2: $i, X1: $i] : (f(a, y(X1, X2)) | f(b, y(X1, X2)))) | (f(a, y(b, a)) | f(b, y(b, a)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 ((~![X2: $i, X1: $i] : (f(a, y(X1, X2)) | f(b, y(X1, X2)))) | f(a, y(b, a)) | f(b, y(b, a))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[30, 27, 2, 20])).
% 0.12/0.38 tff(32,plain,(f(b, y(b, a)) | f(a, b)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (f(b, y(b, a))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[32, 1])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (^[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)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[34])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 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')).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (![X2: $i, X1: $i] : ((~f(a, y(X1, X2))) | (~f(b, y(X1, X2))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.12/0.38 tff(39,plain,(
% 0.12/0.38 ![X2: $i, X1: $i] : ((~f(a, y(X1, X2))) | (~f(b, y(X1, X2))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[38])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (![X2: $i, X1: $i] : ((~f(a, y(X1, X2))) | (~f(b, y(X1, X2))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (((~![X2: $i, X1: $i] : ((~f(a, y(X1, X2))) | (~f(b, y(X1, X2))))) | ((~f(a, y(b, a))) | (~f(b, y(b, a))))) <=> ((~![X2: $i, X1: $i] : ((~f(a, y(X1, X2))) | (~f(b, y(X1, X2))))) | (~f(a, y(b, a))) | (~f(b, y(b, a))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 ((~![X2: $i, X1: $i] : ((~f(a, y(X1, X2))) | (~f(b, y(X1, X2))))) | ((~f(a, y(b, a))) | (~f(b, y(b, a))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 ((~![X2: $i, X1: $i] : ((~f(a, y(X1, X2))) | (~f(b, y(X1, X2))))) | (~f(a, y(b, a))) | (~f(b, y(b, a)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 (~f(a, y(b, a))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[43, 40, 33])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 (^[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)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[45])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 (^[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)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[48])).
% 0.12/0.39 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')).
% 0.12/0.39 tff(51,plain,
% 0.12/0.39 (![X2: $i, X1: $i] : (f(a, b) | f(X2, y(X1, X2)) | (~f(X1, y(X1, X2))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 (![X2: $i, X1: $i] : (f(a, b) | f(X2, y(X1, X2)) | (~f(X1, y(X1, X2))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.12/0.39 tff(53,plain,(
% 0.12/0.39 ![X2: $i, X1: $i] : (f(a, b) | f(X2, y(X1, X2)) | (~f(X1, y(X1, X2))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[52])).
% 0.12/0.39 tff(54,plain,
% 0.12/0.39 (![X2: $i, X1: $i] : (f(a, b) | f(X2, y(X1, X2)) | (~f(X1, y(X1, X2))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.12/0.39 tff(55,plain,
% 0.12/0.39 (((~![X2: $i, X1: $i] : (f(a, b) | f(X2, y(X1, X2)) | (~f(X1, y(X1, X2))))) | (f(a, b) | (~f(b, y(b, a))) | f(a, y(b, a)))) <=> ((~![X2: $i, X1: $i] : (f(a, b) | f(X2, y(X1, X2)) | (~f(X1, y(X1, X2))))) | f(a, b) | (~f(b, y(b, a))) | f(a, y(b, a)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(56,plain,
% 0.12/0.39 ((f(a, b) | f(a, y(b, a)) | (~f(b, y(b, a)))) <=> (f(a, b) | (~f(b, y(b, a))) | f(a, y(b, a)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(57,plain,
% 0.12/0.39 (((~![X2: $i, X1: $i] : (f(a, b) | f(X2, y(X1, X2)) | (~f(X1, y(X1, X2))))) | (f(a, b) | f(a, y(b, a)) | (~f(b, y(b, a))))) <=> ((~![X2: $i, X1: $i] : (f(a, b) | f(X2, y(X1, X2)) | (~f(X1, y(X1, X2))))) | (f(a, b) | (~f(b, y(b, a))) | f(a, y(b, a))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[56])).
% 0.12/0.39 tff(58,plain,
% 0.12/0.39 (((~![X2: $i, X1: $i] : (f(a, b) | f(X2, y(X1, X2)) | (~f(X1, y(X1, X2))))) | (f(a, b) | f(a, y(b, a)) | (~f(b, y(b, a))))) <=> ((~![X2: $i, X1: $i] : (f(a, b) | f(X2, y(X1, X2)) | (~f(X1, y(X1, X2))))) | f(a, b) | (~f(b, y(b, a))) | f(a, y(b, a)))),
% 0.12/0.39 inference(transitivity,[status(thm)],[57, 55])).
% 0.12/0.39 tff(59,plain,
% 0.12/0.39 ((~![X2: $i, X1: $i] : (f(a, b) | f(X2, y(X1, X2)) | (~f(X1, y(X1, X2))))) | (f(a, b) | f(a, y(b, a)) | (~f(b, y(b, a))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(60,plain,
% 0.12/0.39 ((~![X2: $i, X1: $i] : (f(a, b) | f(X2, y(X1, X2)) | (~f(X1, y(X1, X2))))) | f(a, b) | (~f(b, y(b, a))) | f(a, y(b, a))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.12/0.39 tff(61,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[60, 54, 1, 33, 44])).
% 0.12/0.39 tff(62,plain,(f(a, b)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(63,plain,
% 0.12/0.39 (^[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)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[63])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 (^[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)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(67,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[66])).
% 0.12/0.39 tff(68,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')).
% 0.12/0.39 tff(69,plain,
% 0.12/0.39 (![X2: $i, X1: $i] : ((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.12/0.39 tff(70,plain,
% 0.12/0.39 (![X2: $i, X1: $i] : ((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.12/0.39 tff(71,plain,(
% 0.12/0.39 ![X2: $i, X1: $i] : ((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[70])).
% 0.12/0.39 tff(72,plain,
% 0.12/0.39 (![X2: $i, X1: $i] : ((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.12/0.39 tff(73,plain,
% 0.12/0.39 (((~![X2: $i, X1: $i] : ((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2))))) | ((~f(a, b)) | (~f(elem!0, y(elem!0, elem!0))))) <=> ((~![X2: $i, X1: $i] : ((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2))))) | (~f(a, b)) | (~f(elem!0, y(elem!0, elem!0))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(74,plain,
% 0.12/0.39 (((~f(a, b)) | (~f(elem!0, y(elem!0, elem!0))) | (~f(elem!0, y(elem!0, elem!0)))) <=> ((~f(a, b)) | (~f(elem!0, y(elem!0, elem!0))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(75,plain,
% 0.12/0.39 (((~![X2: $i, X1: $i] : ((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2))))) | ((~f(a, b)) | (~f(elem!0, y(elem!0, elem!0))) | (~f(elem!0, y(elem!0, elem!0))))) <=> ((~![X2: $i, X1: $i] : ((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2))))) | ((~f(a, b)) | (~f(elem!0, y(elem!0, elem!0)))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[74])).
% 0.12/0.39 tff(76,plain,
% 0.12/0.39 (((~![X2: $i, X1: $i] : ((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2))))) | ((~f(a, b)) | (~f(elem!0, y(elem!0, elem!0))) | (~f(elem!0, y(elem!0, elem!0))))) <=> ((~![X2: $i, X1: $i] : ((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2))))) | (~f(a, b)) | (~f(elem!0, y(elem!0, elem!0))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[75, 73])).
% 0.12/0.39 tff(77,plain,
% 0.12/0.39 ((~![X2: $i, X1: $i] : ((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2))))) | ((~f(a, b)) | (~f(elem!0, y(elem!0, elem!0))) | (~f(elem!0, y(elem!0, elem!0))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(78,plain,
% 0.12/0.39 ((~![X2: $i, X1: $i] : ((~f(a, b)) | (~f(X2, y(X1, X2))) | (~f(X1, y(X1, X2))))) | (~f(a, b)) | (~f(elem!0, y(elem!0, elem!0)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.12/0.39 tff(79,plain,
% 0.12/0.39 ((~f(a, b)) | (~f(elem!0, y(elem!0, elem!0)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[78, 72])).
% 0.12/0.39 tff(80,plain,
% 0.12/0.39 (~f(elem!0, y(elem!0, elem!0))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[79, 62])).
% 0.12/0.39 tff(81,plain,
% 0.12/0.39 (^[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))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(82,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[81])).
% 0.12/0.39 tff(83,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(84,plain,
% 0.12/0.39 (^[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))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(85,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[84])).
% 0.12/0.39 tff(86,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')).
% 0.12/0.39 tff(87,plain,
% 0.12/0.39 (![X2: $i, X1: $i] : ((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.12/0.39 tff(88,plain,
% 0.12/0.39 (![X2: $i, X1: $i] : ((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.12/0.39 tff(89,plain,(
% 0.12/0.39 ![X2: $i, X1: $i] : ((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[88])).
% 0.12/0.39 tff(90,plain,
% 0.12/0.39 (![X2: $i, X1: $i] : ((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.12/0.39 tff(91,plain,
% 0.12/0.39 (((~![X2: $i, X1: $i] : ((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2)))) | ((~f(a, b)) | f(elem!0, y(elem!0, elem!0)))) <=> ((~![X2: $i, X1: $i] : ((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2)))) | (~f(a, b)) | f(elem!0, y(elem!0, elem!0)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(92,plain,
% 0.12/0.39 (((~f(a, b)) | f(elem!0, y(elem!0, elem!0)) | f(elem!0, y(elem!0, elem!0))) <=> ((~f(a, b)) | f(elem!0, y(elem!0, elem!0)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(93,plain,
% 0.12/0.39 (((~![X2: $i, X1: $i] : ((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2)))) | ((~f(a, b)) | f(elem!0, y(elem!0, elem!0)) | f(elem!0, y(elem!0, elem!0)))) <=> ((~![X2: $i, X1: $i] : ((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2)))) | ((~f(a, b)) | f(elem!0, y(elem!0, elem!0))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[92])).
% 0.12/0.39 tff(94,plain,
% 0.12/0.39 (((~![X2: $i, X1: $i] : ((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2)))) | ((~f(a, b)) | f(elem!0, y(elem!0, elem!0)) | f(elem!0, y(elem!0, elem!0)))) <=> ((~![X2: $i, X1: $i] : ((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2)))) | (~f(a, b)) | f(elem!0, y(elem!0, elem!0)))),
% 0.12/0.39 inference(transitivity,[status(thm)],[93, 91])).
% 0.12/0.39 tff(95,plain,
% 0.12/0.39 ((~![X2: $i, X1: $i] : ((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2)))) | ((~f(a, b)) | f(elem!0, y(elem!0, elem!0)) | f(elem!0, y(elem!0, elem!0)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(96,plain,
% 0.12/0.39 ((~![X2: $i, X1: $i] : ((~f(a, b)) | f(X2, y(X1, X2)) | f(X1, y(X1, X2)))) | (~f(a, b)) | f(elem!0, y(elem!0, elem!0))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.12/0.39 tff(97,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[96, 90, 62, 80])).
% 0.12/0.39 % SZS output end Proof
% 0.12/0.40 % E exiting
%------------------------------------------------------------------------------