%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN332-1 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:38:47 AM UTC 2025
% Result : Unsatisfiable 0.47s 0.67s
% Output : Proof 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN332-1 : TPTP v9.0.0. Released v1.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 12:32:42 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.47/0.67 % SZS status Unsatisfiable
% 0.47/0.67 % SZS output start Proof
% 0.47/0.67 tff(f_type, type, (
% 0.47/0.67 f: ( $i * $i ) > $o)).
% 0.47/0.67 tff(z_type, type, (
% 0.47/0.67 z: ( $i * $i ) > $i)).
% 0.47/0.67 tff(elem_0_type, type, (
% 0.47/0.67 elem_0: $i)).
% 0.47/0.67 tff(1,assumption,(~f(elem!0, elem!0)), introduced(assumption)).
% 0.47/0.67 tff(2,plain,
% 0.47/0.67 (^[Y: $i, X: $i] : refl((f(X, Y) | f(Y, X) | (~f(z(X, Y), Y))) <=> (f(X, Y) | f(Y, X) | (~f(z(X, Y), Y))))),
% 0.47/0.67 inference(bind,[status(th)],[])).
% 0.47/0.67 tff(3,plain,
% 0.47/0.67 (![Y: $i, X: $i] : (f(X, Y) | f(Y, X) | (~f(z(X, Y), Y))) <=> ![Y: $i, X: $i] : (f(X, Y) | f(Y, X) | (~f(z(X, Y), Y)))),
% 0.47/0.67 inference(quant_intro,[status(thm)],[2])).
% 0.47/0.67 tff(4,plain,
% 0.47/0.67 (![Y: $i, X: $i] : (f(X, Y) | f(Y, X) | (~f(z(X, Y), Y))) <=> ![Y: $i, X: $i] : (f(X, Y) | f(Y, X) | (~f(z(X, Y), Y)))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(5,plain,
% 0.47/0.67 (^[Y: $i, X: $i] : rewrite(((f(X, Y) | f(Y, X)) | (~f(z(X, Y), Y))) <=> (f(X, Y) | f(Y, X) | (~f(z(X, Y), Y))))),
% 0.47/0.67 inference(bind,[status(th)],[])).
% 0.47/0.67 tff(6,plain,
% 0.47/0.67 (![Y: $i, X: $i] : ((f(X, Y) | f(Y, X)) | (~f(z(X, Y), Y))) <=> ![Y: $i, X: $i] : (f(X, Y) | f(Y, X) | (~f(z(X, Y), Y)))),
% 0.47/0.67 inference(quant_intro,[status(thm)],[5])).
% 0.47/0.67 tff(7,axiom,(![Y: $i, X: $i] : ((f(X, Y) | f(Y, X)) | (~f(z(X, Y), Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause13')).
% 0.47/0.67 tff(8,plain,
% 0.47/0.67 (![Y: $i, X: $i] : (f(X, Y) | f(Y, X) | (~f(z(X, Y), Y)))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.47/0.67 tff(9,plain,
% 0.47/0.67 (![Y: $i, X: $i] : (f(X, Y) | f(Y, X) | (~f(z(X, Y), Y)))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.47/0.67 tff(10,plain,(
% 0.47/0.67 ![Y: $i, X: $i] : (f(X, Y) | f(Y, X) | (~f(z(X, Y), Y)))),
% 0.47/0.67 inference(skolemize,[status(sab)],[9])).
% 0.47/0.67 tff(11,plain,
% 0.47/0.67 (![Y: $i, X: $i] : (f(X, Y) | f(Y, X) | (~f(z(X, Y), Y)))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.47/0.67 tff(12,plain,
% 0.47/0.67 (((~![Y: $i, X: $i] : (f(X, Y) | f(Y, X) | (~f(z(X, Y), Y)))) | (f(elem!0, elem!0) | (~f(z(elem!0, elem!0), elem!0)))) <=> ((~![Y: $i, X: $i] : (f(X, Y) | f(Y, X) | (~f(z(X, Y), Y)))) | f(elem!0, elem!0) | (~f(z(elem!0, elem!0), elem!0)))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(13,plain,
% 0.47/0.67 ((f(elem!0, elem!0) | f(elem!0, elem!0) | (~f(z(elem!0, elem!0), elem!0))) <=> (f(elem!0, elem!0) | (~f(z(elem!0, elem!0), elem!0)))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(14,plain,
% 0.47/0.67 (((~![Y: $i, X: $i] : (f(X, Y) | f(Y, X) | (~f(z(X, Y), Y)))) | (f(elem!0, elem!0) | f(elem!0, elem!0) | (~f(z(elem!0, elem!0), elem!0)))) <=> ((~![Y: $i, X: $i] : (f(X, Y) | f(Y, X) | (~f(z(X, Y), Y)))) | (f(elem!0, elem!0) | (~f(z(elem!0, elem!0), elem!0))))),
% 0.47/0.67 inference(monotonicity,[status(thm)],[13])).
% 0.47/0.67 tff(15,plain,
% 0.47/0.67 (((~![Y: $i, X: $i] : (f(X, Y) | f(Y, X) | (~f(z(X, Y), Y)))) | (f(elem!0, elem!0) | f(elem!0, elem!0) | (~f(z(elem!0, elem!0), elem!0)))) <=> ((~![Y: $i, X: $i] : (f(X, Y) | f(Y, X) | (~f(z(X, Y), Y)))) | f(elem!0, elem!0) | (~f(z(elem!0, elem!0), elem!0)))),
% 0.47/0.67 inference(transitivity,[status(thm)],[14, 12])).
% 0.47/0.67 tff(16,plain,
% 0.47/0.67 ((~![Y: $i, X: $i] : (f(X, Y) | f(Y, X) | (~f(z(X, Y), Y)))) | (f(elem!0, elem!0) | f(elem!0, elem!0) | (~f(z(elem!0, elem!0), elem!0)))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(17,plain,
% 0.47/0.67 ((~![Y: $i, X: $i] : (f(X, Y) | f(Y, X) | (~f(z(X, Y), Y)))) | f(elem!0, elem!0) | (~f(z(elem!0, elem!0), elem!0))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.47/0.67 tff(18,plain,
% 0.47/0.67 (~f(z(elem!0, elem!0), elem!0)),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[17, 11, 1])).
% 0.47/0.67 tff(19,plain,
% 0.47/0.67 (^[Y: $i, X: $i] : refl((f(X, Y) | f(X, z(X, Y))) <=> (f(X, Y) | f(X, z(X, Y))))),
% 0.47/0.67 inference(bind,[status(th)],[])).
% 0.47/0.67 tff(20,plain,
% 0.47/0.67 (![Y: $i, X: $i] : (f(X, Y) | f(X, z(X, Y))) <=> ![Y: $i, X: $i] : (f(X, Y) | f(X, z(X, Y)))),
% 0.47/0.67 inference(quant_intro,[status(thm)],[19])).
% 0.47/0.67 tff(21,plain,
% 0.47/0.67 (![Y: $i, X: $i] : (f(X, Y) | f(X, z(X, Y))) <=> ![Y: $i, X: $i] : (f(X, Y) | f(X, z(X, Y)))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(22,axiom,(![Y: $i, X: $i] : (f(X, Y) | f(X, z(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.47/0.67 tff(23,plain,
% 0.47/0.67 (![Y: $i, X: $i] : (f(X, Y) | f(X, z(X, Y)))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.47/0.67 tff(24,plain,(
% 0.47/0.67 ![Y: $i, X: $i] : (f(X, Y) | f(X, z(X, Y)))),
% 0.47/0.67 inference(skolemize,[status(sab)],[23])).
% 0.47/0.67 tff(25,plain,
% 0.47/0.67 (![Y: $i, X: $i] : (f(X, Y) | f(X, z(X, Y)))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.47/0.67 tff(26,plain,
% 0.47/0.67 (((~![Y: $i, X: $i] : (f(X, Y) | f(X, z(X, Y)))) | (f(elem!0, elem!0) | f(elem!0, z(elem!0, elem!0)))) <=> ((~![Y: $i, X: $i] : (f(X, Y) | f(X, z(X, Y)))) | f(elem!0, elem!0) | f(elem!0, z(elem!0, elem!0)))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(27,plain,
% 0.47/0.67 ((~![Y: $i, X: $i] : (f(X, Y) | f(X, z(X, Y)))) | (f(elem!0, elem!0) | f(elem!0, z(elem!0, elem!0)))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(28,plain,
% 0.47/0.67 ((~![Y: $i, X: $i] : (f(X, Y) | f(X, z(X, Y)))) | f(elem!0, elem!0) | f(elem!0, z(elem!0, elem!0))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.47/0.67 tff(29,plain,
% 0.47/0.67 (f(elem!0, elem!0) | f(elem!0, z(elem!0, elem!0))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[28, 25])).
% 0.47/0.67 tff(30,plain,
% 0.47/0.67 (f(elem!0, z(elem!0, elem!0))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[29, 1])).
% 0.47/0.67 tff(31,plain,
% 0.47/0.67 (^[Y: $i, X: $i] : refl(((~f(X, z(X, Y))) | f(z(X, Y), X)) <=> ((~f(X, z(X, Y))) | f(z(X, Y), X)))),
% 0.47/0.67 inference(bind,[status(th)],[])).
% 0.47/0.67 tff(32,plain,
% 0.47/0.67 (![Y: $i, X: $i] : ((~f(X, z(X, Y))) | f(z(X, Y), X)) <=> ![Y: $i, X: $i] : ((~f(X, z(X, Y))) | f(z(X, Y), X))),
% 0.47/0.67 inference(quant_intro,[status(thm)],[31])).
% 0.47/0.67 tff(33,plain,
% 0.47/0.67 (![Y: $i, X: $i] : ((~f(X, z(X, Y))) | f(z(X, Y), X)) <=> ![Y: $i, X: $i] : ((~f(X, z(X, Y))) | f(z(X, Y), X))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(34,axiom,(![Y: $i, X: $i] : ((~f(X, z(X, Y))) | f(z(X, Y), X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause5')).
% 0.47/0.67 tff(35,plain,
% 0.47/0.67 (![Y: $i, X: $i] : ((~f(X, z(X, Y))) | f(z(X, Y), X))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.47/0.67 tff(36,plain,(
% 0.47/0.67 ![Y: $i, X: $i] : ((~f(X, z(X, Y))) | f(z(X, Y), X))),
% 0.47/0.67 inference(skolemize,[status(sab)],[35])).
% 0.47/0.67 tff(37,plain,
% 0.47/0.67 (![Y: $i, X: $i] : ((~f(X, z(X, Y))) | f(z(X, Y), X))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.47/0.67 tff(38,plain,
% 0.47/0.67 (((~![Y: $i, X: $i] : ((~f(X, z(X, Y))) | f(z(X, Y), X))) | ((~f(elem!0, z(elem!0, elem!0))) | f(z(elem!0, elem!0), elem!0))) <=> ((~![Y: $i, X: $i] : ((~f(X, z(X, Y))) | f(z(X, Y), X))) | (~f(elem!0, z(elem!0, elem!0))) | f(z(elem!0, elem!0), elem!0))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(39,plain,
% 0.47/0.67 ((~![Y: $i, X: $i] : ((~f(X, z(X, Y))) | f(z(X, Y), X))) | ((~f(elem!0, z(elem!0, elem!0))) | f(z(elem!0, elem!0), elem!0))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(40,plain,
% 0.47/0.67 ((~![Y: $i, X: $i] : ((~f(X, z(X, Y))) | f(z(X, Y), X))) | (~f(elem!0, z(elem!0, elem!0))) | f(z(elem!0, elem!0), elem!0)),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.47/0.67 tff(41,plain,
% 0.47/0.67 ($false),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[40, 37, 30, 18])).
% 0.47/0.67 tff(42,plain,(f(elem!0, elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.67 tff(43,plain,
% 0.47/0.67 (^[Y: $i, X: $i] : refl(((~f(X, z(X, Y))) | (~f(Y, X)) | (~f(X, Y))) <=> ((~f(X, z(X, Y))) | (~f(Y, X)) | (~f(X, Y))))),
% 0.47/0.67 inference(bind,[status(th)],[])).
% 0.47/0.67 tff(44,plain,
% 0.47/0.67 (![Y: $i, X: $i] : ((~f(X, z(X, Y))) | (~f(Y, X)) | (~f(X, Y))) <=> ![Y: $i, X: $i] : ((~f(X, z(X, Y))) | (~f(Y, X)) | (~f(X, Y)))),
% 0.47/0.67 inference(quant_intro,[status(thm)],[43])).
% 0.47/0.67 tff(45,plain,
% 0.47/0.67 (![Y: $i, X: $i] : ((~f(X, z(X, Y))) | (~f(Y, X)) | (~f(X, Y))) <=> ![Y: $i, X: $i] : ((~f(X, z(X, Y))) | (~f(Y, X)) | (~f(X, Y)))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(46,plain,
% 0.47/0.67 (^[Y: $i, X: $i] : rewrite((((~f(X, Y)) | (~f(Y, X))) | (~f(X, z(X, Y)))) <=> ((~f(X, z(X, Y))) | (~f(Y, X)) | (~f(X, Y))))),
% 0.47/0.67 inference(bind,[status(th)],[])).
% 0.47/0.67 tff(47,plain,
% 0.47/0.67 (![Y: $i, X: $i] : (((~f(X, Y)) | (~f(Y, X))) | (~f(X, z(X, Y)))) <=> ![Y: $i, X: $i] : ((~f(X, z(X, Y))) | (~f(Y, X)) | (~f(X, Y)))),
% 0.47/0.67 inference(quant_intro,[status(thm)],[46])).
% 0.47/0.67 tff(48,axiom,(![Y: $i, X: $i] : (((~f(X, Y)) | (~f(Y, X))) | (~f(X, z(X, Y))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause3')).
% 0.47/0.67 tff(49,plain,
% 0.47/0.67 (![Y: $i, X: $i] : ((~f(X, z(X, Y))) | (~f(Y, X)) | (~f(X, Y)))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.47/0.67 tff(50,plain,
% 0.47/0.67 (![Y: $i, X: $i] : ((~f(X, z(X, Y))) | (~f(Y, X)) | (~f(X, Y)))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.47/0.67 tff(51,plain,(
% 0.47/0.67 ![Y: $i, X: $i] : ((~f(X, z(X, Y))) | (~f(Y, X)) | (~f(X, Y)))),
% 0.47/0.67 inference(skolemize,[status(sab)],[50])).
% 0.47/0.67 tff(52,plain,
% 0.47/0.67 (![Y: $i, X: $i] : ((~f(X, z(X, Y))) | (~f(Y, X)) | (~f(X, Y)))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.47/0.67 tff(53,plain,
% 0.47/0.67 (((~![Y: $i, X: $i] : ((~f(X, z(X, Y))) | (~f(Y, X)) | (~f(X, Y)))) | ((~f(elem!0, elem!0)) | (~f(elem!0, z(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : ((~f(X, z(X, Y))) | (~f(Y, X)) | (~f(X, Y)))) | (~f(elem!0, elem!0)) | (~f(elem!0, z(elem!0, elem!0))))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(54,plain,
% 0.47/0.67 (((~f(elem!0, z(elem!0, elem!0))) | (~f(elem!0, elem!0)) | (~f(elem!0, elem!0))) <=> ((~f(elem!0, elem!0)) | (~f(elem!0, z(elem!0, elem!0))))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(55,plain,
% 0.47/0.67 (((~![Y: $i, X: $i] : ((~f(X, z(X, Y))) | (~f(Y, X)) | (~f(X, Y)))) | ((~f(elem!0, z(elem!0, elem!0))) | (~f(elem!0, elem!0)) | (~f(elem!0, elem!0)))) <=> ((~![Y: $i, X: $i] : ((~f(X, z(X, Y))) | (~f(Y, X)) | (~f(X, Y)))) | ((~f(elem!0, elem!0)) | (~f(elem!0, z(elem!0, elem!0)))))),
% 0.47/0.67 inference(monotonicity,[status(thm)],[54])).
% 0.47/0.67 tff(56,plain,
% 0.47/0.67 (((~![Y: $i, X: $i] : ((~f(X, z(X, Y))) | (~f(Y, X)) | (~f(X, Y)))) | ((~f(elem!0, z(elem!0, elem!0))) | (~f(elem!0, elem!0)) | (~f(elem!0, elem!0)))) <=> ((~![Y: $i, X: $i] : ((~f(X, z(X, Y))) | (~f(Y, X)) | (~f(X, Y)))) | (~f(elem!0, elem!0)) | (~f(elem!0, z(elem!0, elem!0))))),
% 0.47/0.67 inference(transitivity,[status(thm)],[55, 53])).
% 0.47/0.67 tff(57,plain,
% 0.47/0.67 ((~![Y: $i, X: $i] : ((~f(X, z(X, Y))) | (~f(Y, X)) | (~f(X, Y)))) | ((~f(elem!0, z(elem!0, elem!0))) | (~f(elem!0, elem!0)) | (~f(elem!0, elem!0)))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(58,plain,
% 0.47/0.67 ((~![Y: $i, X: $i] : ((~f(X, z(X, Y))) | (~f(Y, X)) | (~f(X, Y)))) | (~f(elem!0, elem!0)) | (~f(elem!0, z(elem!0, elem!0)))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.47/0.67 tff(59,plain,
% 0.47/0.67 (~f(elem!0, z(elem!0, elem!0))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[58, 52, 42])).
% 0.47/0.67 tff(60,plain,
% 0.47/0.67 (((~![Y: $i, X: $i] : (f(X, Y) | f(X, z(X, Y)))) | (f(elem!0, z(elem!0, elem!0)) | f(elem!0, z(elem!0, z(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : (f(X, Y) | f(X, z(X, Y)))) | f(elem!0, z(elem!0, elem!0)) | f(elem!0, z(elem!0, z(elem!0, elem!0))))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(61,plain,
% 0.47/0.67 ((~![Y: $i, X: $i] : (f(X, Y) | f(X, z(X, Y)))) | (f(elem!0, z(elem!0, elem!0)) | f(elem!0, z(elem!0, z(elem!0, elem!0))))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(62,plain,
% 0.47/0.67 ((~![Y: $i, X: $i] : (f(X, Y) | f(X, z(X, Y)))) | f(elem!0, z(elem!0, elem!0)) | f(elem!0, z(elem!0, z(elem!0, elem!0)))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.47/0.67 tff(63,plain,
% 0.47/0.67 (f(elem!0, z(elem!0, z(elem!0, elem!0)))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[62, 25, 59])).
% 0.47/0.67 tff(64,plain,
% 0.47/0.67 (^[Y: $i, X: $i] : refl(((~f(X, z(X, Y))) | f(Y, z(X, Y))) <=> ((~f(X, z(X, Y))) | f(Y, z(X, Y))))),
% 0.47/0.67 inference(bind,[status(th)],[])).
% 0.47/0.67 tff(65,plain,
% 0.47/0.67 (![Y: $i, X: $i] : ((~f(X, z(X, Y))) | f(Y, z(X, Y))) <=> ![Y: $i, X: $i] : ((~f(X, z(X, Y))) | f(Y, z(X, Y)))),
% 0.47/0.67 inference(quant_intro,[status(thm)],[64])).
% 0.47/0.67 tff(66,plain,
% 0.47/0.67 (![Y: $i, X: $i] : ((~f(X, z(X, Y))) | f(Y, z(X, Y))) <=> ![Y: $i, X: $i] : ((~f(X, z(X, Y))) | f(Y, z(X, Y)))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(67,axiom,(![Y: $i, X: $i] : ((~f(X, z(X, Y))) | f(Y, z(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause7')).
% 0.47/0.67 tff(68,plain,
% 0.47/0.67 (![Y: $i, X: $i] : ((~f(X, z(X, Y))) | f(Y, z(X, Y)))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.47/0.67 tff(69,plain,(
% 0.47/0.67 ![Y: $i, X: $i] : ((~f(X, z(X, Y))) | f(Y, z(X, Y)))),
% 0.47/0.67 inference(skolemize,[status(sab)],[68])).
% 0.47/0.67 tff(70,plain,
% 0.47/0.67 (![Y: $i, X: $i] : ((~f(X, z(X, Y))) | f(Y, z(X, Y)))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.47/0.67 tff(71,plain,
% 0.47/0.67 (((~![Y: $i, X: $i] : ((~f(X, z(X, Y))) | f(Y, z(X, Y)))) | ((~f(elem!0, z(elem!0, z(elem!0, elem!0)))) | f(z(elem!0, elem!0), z(elem!0, z(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : ((~f(X, z(X, Y))) | f(Y, z(X, Y)))) | (~f(elem!0, z(elem!0, z(elem!0, elem!0)))) | f(z(elem!0, elem!0), z(elem!0, z(elem!0, elem!0))))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(72,plain,
% 0.47/0.67 ((~![Y: $i, X: $i] : ((~f(X, z(X, Y))) | f(Y, z(X, Y)))) | ((~f(elem!0, z(elem!0, z(elem!0, elem!0)))) | f(z(elem!0, elem!0), z(elem!0, z(elem!0, elem!0))))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(73,plain,
% 0.47/0.67 ((~![Y: $i, X: $i] : ((~f(X, z(X, Y))) | f(Y, z(X, Y)))) | (~f(elem!0, z(elem!0, z(elem!0, elem!0)))) | f(z(elem!0, elem!0), z(elem!0, z(elem!0, elem!0)))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.47/0.67 tff(74,plain,
% 0.47/0.67 (f(z(elem!0, elem!0), z(elem!0, z(elem!0, elem!0)))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[73, 70, 63])).
% 0.47/0.67 tff(75,plain,
% 0.47/0.67 (^[Y: $i, X: $i] : refl(((~f(Y, X)) | (~f(X, Y)) | (~f(z(X, Y), Y))) <=> ((~f(Y, X)) | (~f(X, Y)) | (~f(z(X, Y), Y))))),
% 0.47/0.67 inference(bind,[status(th)],[])).
% 0.47/0.67 tff(76,plain,
% 0.47/0.67 (![Y: $i, X: $i] : ((~f(Y, X)) | (~f(X, Y)) | (~f(z(X, Y), Y))) <=> ![Y: $i, X: $i] : ((~f(Y, X)) | (~f(X, Y)) | (~f(z(X, Y), Y)))),
% 0.47/0.67 inference(quant_intro,[status(thm)],[75])).
% 0.47/0.67 tff(77,plain,
% 0.47/0.67 (![Y: $i, X: $i] : ((~f(Y, X)) | (~f(X, Y)) | (~f(z(X, Y), Y))) <=> ![Y: $i, X: $i] : ((~f(Y, X)) | (~f(X, Y)) | (~f(z(X, Y), Y)))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(78,plain,
% 0.47/0.67 (^[Y: $i, X: $i] : rewrite((((~f(X, Y)) | (~f(Y, X))) | (~f(z(X, Y), Y))) <=> ((~f(Y, X)) | (~f(X, Y)) | (~f(z(X, Y), Y))))),
% 0.47/0.67 inference(bind,[status(th)],[])).
% 0.47/0.67 tff(79,plain,
% 0.47/0.67 (![Y: $i, X: $i] : (((~f(X, Y)) | (~f(Y, X))) | (~f(z(X, Y), Y))) <=> ![Y: $i, X: $i] : ((~f(Y, X)) | (~f(X, Y)) | (~f(z(X, Y), Y)))),
% 0.47/0.67 inference(quant_intro,[status(thm)],[78])).
% 0.47/0.67 tff(80,axiom,(![Y: $i, X: $i] : (((~f(X, Y)) | (~f(Y, X))) | (~f(z(X, Y), Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause14')).
% 0.47/0.67 tff(81,plain,
% 0.47/0.67 (![Y: $i, X: $i] : ((~f(Y, X)) | (~f(X, Y)) | (~f(z(X, Y), Y)))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.47/0.67 tff(82,plain,
% 0.47/0.67 (![Y: $i, X: $i] : ((~f(Y, X)) | (~f(X, Y)) | (~f(z(X, Y), Y)))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.47/0.67 tff(83,plain,(
% 0.47/0.67 ![Y: $i, X: $i] : ((~f(Y, X)) | (~f(X, Y)) | (~f(z(X, Y), Y)))),
% 0.47/0.67 inference(skolemize,[status(sab)],[82])).
% 0.47/0.67 tff(84,plain,
% 0.47/0.67 (![Y: $i, X: $i] : ((~f(Y, X)) | (~f(X, Y)) | (~f(z(X, Y), Y)))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.47/0.67 tff(85,plain,
% 0.47/0.67 (((~![Y: $i, X: $i] : ((~f(Y, X)) | (~f(X, Y)) | (~f(z(X, Y), Y)))) | ((~f(elem!0, elem!0)) | (~f(z(elem!0, elem!0), elem!0)))) <=> ((~![Y: $i, X: $i] : ((~f(Y, X)) | (~f(X, Y)) | (~f(z(X, Y), Y)))) | (~f(elem!0, elem!0)) | (~f(z(elem!0, elem!0), elem!0)))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(86,plain,
% 0.47/0.67 (((~f(elem!0, elem!0)) | (~f(elem!0, elem!0)) | (~f(z(elem!0, elem!0), elem!0))) <=> ((~f(elem!0, elem!0)) | (~f(z(elem!0, elem!0), elem!0)))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(87,plain,
% 0.47/0.67 (((~![Y: $i, X: $i] : ((~f(Y, X)) | (~f(X, Y)) | (~f(z(X, Y), Y)))) | ((~f(elem!0, elem!0)) | (~f(elem!0, elem!0)) | (~f(z(elem!0, elem!0), elem!0)))) <=> ((~![Y: $i, X: $i] : ((~f(Y, X)) | (~f(X, Y)) | (~f(z(X, Y), Y)))) | ((~f(elem!0, elem!0)) | (~f(z(elem!0, elem!0), elem!0))))),
% 0.47/0.67 inference(monotonicity,[status(thm)],[86])).
% 0.47/0.67 tff(88,plain,
% 0.47/0.67 (((~![Y: $i, X: $i] : ((~f(Y, X)) | (~f(X, Y)) | (~f(z(X, Y), Y)))) | ((~f(elem!0, elem!0)) | (~f(elem!0, elem!0)) | (~f(z(elem!0, elem!0), elem!0)))) <=> ((~![Y: $i, X: $i] : ((~f(Y, X)) | (~f(X, Y)) | (~f(z(X, Y), Y)))) | (~f(elem!0, elem!0)) | (~f(z(elem!0, elem!0), elem!0)))),
% 0.47/0.67 inference(transitivity,[status(thm)],[87, 85])).
% 0.47/0.67 tff(89,plain,
% 0.47/0.67 ((~![Y: $i, X: $i] : ((~f(Y, X)) | (~f(X, Y)) | (~f(z(X, Y), Y)))) | ((~f(elem!0, elem!0)) | (~f(elem!0, elem!0)) | (~f(z(elem!0, elem!0), elem!0)))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(90,plain,
% 0.47/0.68 ((~![Y: $i, X: $i] : ((~f(Y, X)) | (~f(X, Y)) | (~f(z(X, Y), Y)))) | (~f(elem!0, elem!0)) | (~f(z(elem!0, elem!0), elem!0))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.47/0.68 tff(91,plain,
% 0.47/0.68 (~f(z(elem!0, elem!0), elem!0)),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[90, 84, 42])).
% 0.47/0.68 tff(92,plain,
% 0.47/0.68 (((~![Y: $i, X: $i] : (f(X, Y) | f(Y, X) | (~f(z(X, Y), Y)))) | (f(elem!0, z(elem!0, elem!0)) | f(z(elem!0, elem!0), elem!0) | (~f(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : (f(X, Y) | f(Y, X) | (~f(z(X, Y), Y)))) | f(elem!0, z(elem!0, elem!0)) | f(z(elem!0, elem!0), elem!0) | (~f(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(93,plain,
% 0.47/0.68 ((~![Y: $i, X: $i] : (f(X, Y) | f(Y, X) | (~f(z(X, Y), Y)))) | (f(elem!0, z(elem!0, elem!0)) | f(z(elem!0, elem!0), elem!0) | (~f(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))))),
% 0.47/0.68 inference(quant_inst,[status(thm)],[])).
% 0.47/0.68 tff(94,plain,
% 0.47/0.68 ((~![Y: $i, X: $i] : (f(X, Y) | f(Y, X) | (~f(z(X, Y), Y)))) | f(elem!0, z(elem!0, elem!0)) | f(z(elem!0, elem!0), elem!0) | (~f(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.47/0.68 tff(95,plain,
% 0.47/0.68 (~f(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[94, 11, 59, 91])).
% 0.47/0.68 tff(96,plain,
% 0.47/0.68 (^[Y: $i, X: $i] : refl((f(X, Y) | (~f(Y, X)) | (~f(z(X, Y), z(X, Y)))) <=> (f(X, Y) | (~f(Y, X)) | (~f(z(X, Y), z(X, Y)))))),
% 0.47/0.68 inference(bind,[status(th)],[])).
% 0.47/0.68 tff(97,plain,
% 0.47/0.68 (![Y: $i, X: $i] : (f(X, Y) | (~f(Y, X)) | (~f(z(X, Y), z(X, Y)))) <=> ![Y: $i, X: $i] : (f(X, Y) | (~f(Y, X)) | (~f(z(X, Y), z(X, Y))))),
% 0.47/0.68 inference(quant_intro,[status(thm)],[96])).
% 0.47/0.68 tff(98,plain,
% 0.47/0.68 (![Y: $i, X: $i] : (f(X, Y) | (~f(Y, X)) | (~f(z(X, Y), z(X, Y)))) <=> ![Y: $i, X: $i] : (f(X, Y) | (~f(Y, X)) | (~f(z(X, Y), z(X, Y))))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(99,plain,
% 0.47/0.68 (^[Y: $i, X: $i] : rewrite((((~f(Y, X)) | f(X, Y)) | (~f(z(X, Y), z(X, Y)))) <=> (f(X, Y) | (~f(Y, X)) | (~f(z(X, Y), z(X, Y)))))),
% 0.47/0.68 inference(bind,[status(th)],[])).
% 0.47/0.68 tff(100,plain,
% 0.47/0.68 (![Y: $i, X: $i] : (((~f(Y, X)) | f(X, Y)) | (~f(z(X, Y), z(X, Y)))) <=> ![Y: $i, X: $i] : (f(X, Y) | (~f(Y, X)) | (~f(z(X, Y), z(X, Y))))),
% 0.47/0.68 inference(quant_intro,[status(thm)],[99])).
% 0.47/0.68 tff(101,axiom,(![Y: $i, X: $i] : (((~f(Y, X)) | f(X, Y)) | (~f(z(X, Y), z(X, Y))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause8')).
% 0.47/0.68 tff(102,plain,
% 0.47/0.68 (![Y: $i, X: $i] : (f(X, Y) | (~f(Y, X)) | (~f(z(X, Y), z(X, Y))))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.47/0.68 tff(103,plain,
% 0.47/0.68 (![Y: $i, X: $i] : (f(X, Y) | (~f(Y, X)) | (~f(z(X, Y), z(X, Y))))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.47/0.68 tff(104,plain,(
% 0.47/0.68 ![Y: $i, X: $i] : (f(X, Y) | (~f(Y, X)) | (~f(z(X, Y), z(X, Y))))),
% 0.47/0.68 inference(skolemize,[status(sab)],[103])).
% 0.47/0.68 tff(105,plain,
% 0.47/0.68 (![Y: $i, X: $i] : (f(X, Y) | (~f(Y, X)) | (~f(z(X, Y), z(X, Y))))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.47/0.68 tff(106,plain,
% 0.47/0.68 (((~![Y: $i, X: $i] : (f(X, Y) | (~f(Y, X)) | (~f(z(X, Y), z(X, Y))))) | (f(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)) | (~f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)))) | (~f(z(elem!0, elem!0), z(elem!0, z(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : (f(X, Y) | (~f(Y, X)) | (~f(z(X, Y), z(X, Y))))) | f(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)) | (~f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)))) | (~f(z(elem!0, elem!0), z(elem!0, z(elem!0, elem!0)))))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(107,plain,
% 0.47/0.68 ((f(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)) | (~f(z(elem!0, elem!0), z(elem!0, z(elem!0, elem!0)))) | (~f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))))) <=> (f(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)) | (~f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)))) | (~f(z(elem!0, elem!0), z(elem!0, z(elem!0, elem!0)))))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(108,plain,
% 0.47/0.68 (((~![Y: $i, X: $i] : (f(X, Y) | (~f(Y, X)) | (~f(z(X, Y), z(X, Y))))) | (f(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)) | (~f(z(elem!0, elem!0), z(elem!0, z(elem!0, elem!0)))) | (~f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : (f(X, Y) | (~f(Y, X)) | (~f(z(X, Y), z(X, Y))))) | (f(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)) | (~f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)))) | (~f(z(elem!0, elem!0), z(elem!0, z(elem!0, elem!0))))))),
% 0.47/0.68 inference(monotonicity,[status(thm)],[107])).
% 0.47/0.68 tff(109,plain,
% 0.47/0.68 (((~![Y: $i, X: $i] : (f(X, Y) | (~f(Y, X)) | (~f(z(X, Y), z(X, Y))))) | (f(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)) | (~f(z(elem!0, elem!0), z(elem!0, z(elem!0, elem!0)))) | (~f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : (f(X, Y) | (~f(Y, X)) | (~f(z(X, Y), z(X, Y))))) | f(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)) | (~f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)))) | (~f(z(elem!0, elem!0), z(elem!0, z(elem!0, elem!0)))))),
% 0.47/0.68 inference(transitivity,[status(thm)],[108, 106])).
% 0.47/0.68 tff(110,plain,
% 0.47/0.68 ((~![Y: $i, X: $i] : (f(X, Y) | (~f(Y, X)) | (~f(z(X, Y), z(X, Y))))) | (f(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)) | (~f(z(elem!0, elem!0), z(elem!0, z(elem!0, elem!0)))) | (~f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)))))),
% 0.47/0.68 inference(quant_inst,[status(thm)],[])).
% 0.47/0.68 tff(111,plain,
% 0.47/0.68 ((~![Y: $i, X: $i] : (f(X, Y) | (~f(Y, X)) | (~f(z(X, Y), z(X, Y))))) | f(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)) | (~f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)))) | (~f(z(elem!0, elem!0), z(elem!0, z(elem!0, elem!0))))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.47/0.68 tff(112,plain,
% 0.47/0.68 (~f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)))),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[111, 105, 95, 74])).
% 0.47/0.68 tff(113,plain,
% 0.47/0.68 (((~![Y: $i, X: $i] : (f(X, Y) | f(Y, X) | (~f(z(X, Y), Y)))) | (f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))) | (~f(z(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : (f(X, Y) | f(Y, X) | (~f(z(X, Y), Y)))) | f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))) | (~f(z(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)))))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(114,plain,
% 0.47/0.68 ((f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))) | f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))) | (~f(z(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))))) <=> (f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))) | (~f(z(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)))))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(115,plain,
% 0.47/0.68 (((~![Y: $i, X: $i] : (f(X, Y) | f(Y, X) | (~f(z(X, Y), Y)))) | (f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))) | f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))) | (~f(z(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : (f(X, Y) | f(Y, X) | (~f(z(X, Y), Y)))) | (f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))) | (~f(z(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))))))),
% 0.47/0.68 inference(monotonicity,[status(thm)],[114])).
% 0.47/0.68 tff(116,plain,
% 0.47/0.68 (((~![Y: $i, X: $i] : (f(X, Y) | f(Y, X) | (~f(z(X, Y), Y)))) | (f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))) | f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))) | (~f(z(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : (f(X, Y) | f(Y, X) | (~f(z(X, Y), Y)))) | f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))) | (~f(z(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)))))),
% 0.47/0.68 inference(transitivity,[status(thm)],[115, 113])).
% 0.47/0.68 tff(117,plain,
% 0.47/0.68 ((~![Y: $i, X: $i] : (f(X, Y) | f(Y, X) | (~f(z(X, Y), Y)))) | (f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))) | f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))) | (~f(z(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)))))),
% 0.47/0.68 inference(quant_inst,[status(thm)],[])).
% 0.47/0.68 tff(118,plain,
% 0.47/0.68 ((~![Y: $i, X: $i] : (f(X, Y) | f(Y, X) | (~f(z(X, Y), Y)))) | f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))) | (~f(z(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.47/0.68 tff(119,plain,
% 0.47/0.68 (~f(z(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)))),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[118, 11, 112])).
% 0.47/0.68 tff(120,plain,
% 0.47/0.68 (((~![Y: $i, X: $i] : ((~f(X, z(X, Y))) | f(z(X, Y), X))) | ((~f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))))) | f(z(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : ((~f(X, z(X, Y))) | f(z(X, Y), X))) | (~f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))))) | f(z(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(121,plain,
% 0.47/0.68 ((~![Y: $i, X: $i] : ((~f(X, z(X, Y))) | f(z(X, Y), X))) | ((~f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))))) | f(z(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))))),
% 0.47/0.68 inference(quant_inst,[status(thm)],[])).
% 0.47/0.68 tff(122,plain,
% 0.47/0.68 ((~![Y: $i, X: $i] : ((~f(X, z(X, Y))) | f(z(X, Y), X))) | (~f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))))) | f(z(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.47/0.68 tff(123,plain,
% 0.47/0.68 (~f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))))),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[122, 37, 119])).
% 0.47/0.68 tff(124,plain,
% 0.47/0.68 (((~![Y: $i, X: $i] : (f(X, Y) | f(X, z(X, Y)))) | (f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))) | f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : (f(X, Y) | f(X, z(X, Y)))) | f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))) | f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)))))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(125,plain,
% 0.47/0.68 ((~![Y: $i, X: $i] : (f(X, Y) | f(X, z(X, Y)))) | (f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))) | f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)))))),
% 0.47/0.68 inference(quant_inst,[status(thm)],[])).
% 0.47/0.68 tff(126,plain,
% 0.47/0.68 ((~![Y: $i, X: $i] : (f(X, Y) | f(X, z(X, Y)))) | f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))) | f(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0)), z(z(elem!0, z(elem!0, elem!0)), z(elem!0, elem!0))))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.47/0.68 tff(127,plain,
% 0.47/0.68 ($false),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[126, 25, 112, 123])).
% 0.47/0.68 % SZS output end Proof
% 0.53/0.69 % E exiting
%------------------------------------------------------------------------------