%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN345-1 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:38:50 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN345-1 : TPTP v9.0.0. Released v1.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n004.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:31:22 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.38 % SZS status Unsatisfiable
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(f_type, type, (
% 0.20/0.38 f: ( $i * $i * $i ) > $o)).
% 0.20/0.38 tff(z_type, type, (
% 0.20/0.38 z: ( $i * $i ) > $i)).
% 0.20/0.38 tff(b_type, type, (
% 0.20/0.38 b: $i)).
% 0.20/0.38 tff(a_type, type, (
% 0.20/0.38 a: $i)).
% 0.20/0.38 tff(1,assumption,(~f(a, b, b)), introduced(assumption)).
% 0.20/0.38 tff(2,assumption,(~f(a, a, b)), introduced(assumption)).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (^[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))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (![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)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 (![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)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 (^[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)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (![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)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.38 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')).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 (![Y2: $i, Y1: $i] : (f(a, a, b) | f(a, b, b) | f(Y1, Y2, z(Y1, Y2)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (![Y2: $i, Y1: $i] : (f(a, a, b) | f(a, b, b) | f(Y1, Y2, z(Y1, Y2)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.38 tff(11,plain,(
% 0.20/0.38 ![Y2: $i, Y1: $i] : (f(a, a, b) | f(a, b, b) | f(Y1, Y2, z(Y1, Y2)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[10])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (![Y2: $i, Y1: $i] : (f(a, a, b) | f(a, b, b) | f(Y1, Y2, z(Y1, Y2)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (((~![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)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 ((~![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)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 ((~![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))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (f(a, a, b) | f(a, b, b) | f(b, b, z(b, b))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[15, 12])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 (f(b, b, z(b, b))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[16, 1, 2])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 (^[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))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (![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)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (![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)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 (^[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))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 (![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)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.39 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')).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 (![Y1: $i] : (f(a, a, b) | f(a, b, b) | (~f(b, b, Y1)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 (![Y1: $i] : (f(a, a, b) | f(a, b, b) | (~f(b, b, Y1)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.20/0.39 tff(26,plain,(
% 0.20/0.39 ![Y1: $i] : (f(a, a, b) | f(a, b, b) | (~f(b, b, Y1)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[25])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 (![Y1: $i] : (f(a, a, b) | f(a, b, b) | (~f(b, b, Y1)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 (((~![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))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 ((~![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))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 ((~![Y1: $i] : (f(a, a, b) | f(a, b, b) | (~f(b, b, Y1)))) | f(a, a, b) | f(a, b, b) | (~f(b, b, z(b, b)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[30, 27, 2, 1, 17])).
% 0.20/0.39 tff(32,plain,(f(a, b, b) | f(a, a, b)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 (f(a, b, b)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[32, 2])).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 (^[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)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 (![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))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 (![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))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(37,plain,
% 0.20/0.39 (^[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)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 (![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))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.39 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')).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 (![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | (~f(Y1, z(Y1, Y2), z(Y1, Y2))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 (![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | (~f(Y1, z(Y1, Y2), z(Y1, Y2))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.20/0.39 tff(42,plain,(
% 0.20/0.39 ![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | (~f(Y1, z(Y1, Y2), z(Y1, Y2))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[41])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 (![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | (~f(Y1, z(Y1, Y2), z(Y1, Y2))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 (((~![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))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 ((~![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))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 ((~![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)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 (f(a, a, b) | (~f(a, b, b)) | (~f(b, z(b, b), z(b, b)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[46, 43])).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 (~f(b, z(b, b), z(b, b))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[47, 33, 2])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 (^[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)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 (![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))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 (![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))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 (^[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))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 (![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))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.39 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')).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 (![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | f(b, Y1, Y2))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 (![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | f(b, Y1, Y2))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.20/0.39 tff(57,plain,(
% 0.20/0.39 ![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | f(b, Y1, Y2))),
% 0.20/0.39 inference(skolemize,[status(sab)],[56])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 (![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | f(b, Y1, Y2))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 (((~![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)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 ((~![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)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 ((~![Y2: $i, Y1: $i] : (f(a, a, b) | (~f(a, b, b)) | f(b, Y1, Y2))) | f(a, a, b) | (~f(a, b, b)) | f(b, z(b, b), z(b, b))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[61, 58, 2, 33, 48])).
% 0.20/0.39 tff(63,plain,(f(a, a, b)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 (^[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)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 (![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))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[64])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 (![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))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(67,plain,
% 0.20/0.39 (^[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))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 (![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))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.40 tff(69,axiom,(![Y1: $i] : ((f(a, b, Y1) | (~f(a, a, b))) | f(a, b, b))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 (![Y1: $i] : ((~f(a, a, b)) | f(a, b, b) | f(a, b, Y1))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 (![Y1: $i] : ((~f(a, a, b)) | f(a, b, b) | f(a, b, Y1))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.20/0.40 tff(72,plain,(
% 0.20/0.40 ![Y1: $i] : ((~f(a, a, b)) | f(a, b, b) | f(a, b, Y1))),
% 0.20/0.40 inference(skolemize,[status(sab)],[71])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 (![Y1: $i] : ((~f(a, a, b)) | f(a, b, b) | f(a, b, Y1))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 (((~![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))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 (((~f(a, a, b)) | f(a, b, b) | f(a, b, b)) <=> ((~f(a, a, b)) | f(a, b, b))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 (((~![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)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[75])).
% 0.20/0.40 tff(77,plain,
% 0.20/0.40 (((~![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))),
% 0.20/0.40 inference(transitivity,[status(thm)],[76, 74])).
% 0.20/0.40 tff(78,plain,
% 0.20/0.40 ((~![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))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(79,plain,
% 0.20/0.40 ((~![Y1: $i] : ((~f(a, a, b)) | f(a, b, b) | f(a, b, Y1))) | (~f(a, a, b)) | f(a, b, b)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.40 tff(80,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[79, 73, 63, 1])).
% 0.20/0.40 tff(81,plain,(f(a, b, b)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(82,plain,
% 0.20/0.40 (^[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))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(83,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[82])).
% 0.20/0.40 tff(84,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(85,plain,
% 0.20/0.40 (^[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)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(86,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[85])).
% 0.20/0.40 tff(87,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')).
% 0.20/0.40 tff(88,plain,
% 0.20/0.40 (![Y2: $i, Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | f(Y1, Y2, z(Y1, Y2)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.41 tff(89,plain,
% 0.20/0.41 (![Y2: $i, Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | f(Y1, Y2, z(Y1, Y2)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.20/0.41 tff(90,plain,(
% 0.20/0.41 ![Y2: $i, Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | f(Y1, Y2, z(Y1, Y2)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[89])).
% 0.20/0.41 tff(91,plain,
% 0.20/0.41 (![Y2: $i, Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | f(Y1, Y2, z(Y1, Y2)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.20/0.41 tff(92,plain,
% 0.20/0.41 (((~![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)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(93,plain,
% 0.20/0.41 ((~![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)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(94,plain,
% 0.20/0.41 ((~![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))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.20/0.41 tff(95,plain,
% 0.20/0.41 (f(b, b, z(b, b))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[94, 91, 63, 81])).
% 0.20/0.41 tff(96,plain,
% 0.20/0.41 (^[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))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(97,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[96])).
% 0.20/0.41 tff(98,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(99,plain,
% 0.20/0.41 (^[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)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(100,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[99])).
% 0.20/0.41 tff(101,axiom,(![Y1: $i] : (((~f(b, b, Y1)) | (~f(a, a, b))) | (~f(a, b, b)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause8')).
% 0.20/0.41 tff(102,plain,
% 0.20/0.41 (![Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | (~f(b, b, Y1)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.20/0.41 tff(103,plain,
% 0.20/0.41 (![Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | (~f(b, b, Y1)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.20/0.41 tff(104,plain,(
% 0.20/0.41 ![Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | (~f(b, b, Y1)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[103])).
% 0.20/0.41 tff(105,plain,
% 0.20/0.41 (![Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | (~f(b, b, Y1)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.20/0.41 tff(106,plain,
% 0.20/0.41 (((~![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))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(107,plain,
% 0.20/0.41 ((~![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))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(108,plain,
% 0.20/0.41 ((~![Y1: $i] : ((~f(a, a, b)) | (~f(a, b, b)) | (~f(b, b, Y1)))) | (~f(a, a, b)) | (~f(a, b, b)) | (~f(b, b, z(b, b)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.20/0.41 tff(109,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[108, 105, 63, 81, 95])).
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------