%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN333-1 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN333-1 : TPTP v9.0.0. Released v1.2.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.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 12:32:32 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.37 % SZS status Unsatisfiable
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 tff(f_type, type, (
% 0.19/0.37 f: ( $i * $i ) > $o)).
% 0.19/0.37 tff(z_type, type, (
% 0.19/0.37 z: ( $i * $i ) > $i)).
% 0.19/0.37 tff(elem_0_type, type, (
% 0.19/0.37 elem_0: $i)).
% 0.19/0.37 tff(g_type, type, (
% 0.19/0.37 g: ( $i * $i ) > $o)).
% 0.19/0.37 tff(1,assumption,(~f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))), introduced(assumption)).
% 0.19/0.37 tff(2,plain,
% 0.19/0.37 (^[Y: $i, X: $i] : refl(f(X, Y) <=> f(X, Y))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(3,plain,
% 0.19/0.37 (![Y: $i, X: $i] : f(X, Y) <=> ![Y: $i, X: $i] : f(X, Y)),
% 0.19/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.37 tff(4,plain,
% 0.19/0.37 (![Y: $i, X: $i] : f(X, Y) <=> ![Y: $i, X: $i] : f(X, Y)),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(5,axiom,(![Y: $i, X: $i] : f(X, Y)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 0.19/0.37 tff(6,plain,
% 0.19/0.37 (![Y: $i, X: $i] : f(X, Y)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.37 tff(7,plain,(
% 0.19/0.37 ![Y: $i, X: $i] : f(X, Y)),
% 0.19/0.37 inference(skolemize,[status(sab)],[6])).
% 0.19/0.37 tff(8,plain,
% 0.19/0.37 (![Y: $i, X: $i] : f(X, Y)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.37 tff(9,plain,
% 0.19/0.37 ((~![Y: $i, X: $i] : f(X, Y)) | f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(10,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.19/0.37 tff(11,plain,(f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(12,assumption,(~f(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))), introduced(assumption)).
% 0.19/0.37 tff(13,plain,
% 0.19/0.37 ((~![Y: $i, X: $i] : f(X, Y)) | f(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(14,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[13, 8, 12])).
% 0.19/0.37 tff(15,plain,(f(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(16,assumption,(~f(z(elem!0, elem!0), z(elem!0, z(elem!0, elem!0)))), introduced(assumption)).
% 0.19/0.37 tff(17,plain,
% 0.19/0.37 ((~![Y: $i, X: $i] : f(X, Y)) | f(z(elem!0, elem!0), z(elem!0, z(elem!0, elem!0)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(18,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[17, 8, 16])).
% 0.19/0.37 tff(19,plain,(f(z(elem!0, elem!0), z(elem!0, z(elem!0, elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(20,plain,
% 0.19/0.37 (^[Y: $i, X: $i] : refl((g(X, Y) | (~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y)))) <=> (g(X, Y) | (~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(21,plain,
% 0.19/0.37 (![Y: $i, X: $i] : (g(X, Y) | (~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y)))) <=> ![Y: $i, X: $i] : (g(X, Y) | (~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[20])).
% 0.19/0.37 tff(22,plain,
% 0.19/0.37 (![Y: $i, X: $i] : (g(X, Y) | (~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y)))) <=> ![Y: $i, X: $i] : (g(X, Y) | (~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(23,plain,
% 0.19/0.37 (^[Y: $i, X: $i] : trans(monotonicity(rewrite(((~f(Y, z(X, Y))) | (~f(z(X, Y), z(X, Y)))) <=> ((~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))))), ((((~f(Y, z(X, Y))) | (~f(z(X, Y), z(X, Y)))) | g(X, Y)) <=> (((~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y)))) | g(X, Y)))), rewrite((((~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y)))) | g(X, Y)) <=> (g(X, Y) | (~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))))), ((((~f(Y, z(X, Y))) | (~f(z(X, Y), z(X, Y)))) | g(X, Y)) <=> (g(X, Y) | (~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(24,plain,
% 0.19/0.37 (![Y: $i, X: $i] : (((~f(Y, z(X, Y))) | (~f(z(X, Y), z(X, Y)))) | g(X, Y)) <=> ![Y: $i, X: $i] : (g(X, Y) | (~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.37 tff(25,axiom,(![Y: $i, X: $i] : (((~f(Y, z(X, Y))) | (~f(z(X, Y), z(X, Y)))) | g(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause2')).
% 0.19/0.37 tff(26,plain,
% 0.19/0.37 (![Y: $i, X: $i] : (g(X, Y) | (~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.19/0.37 tff(27,plain,
% 0.19/0.37 (![Y: $i, X: $i] : (g(X, Y) | (~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.19/0.37 tff(28,plain,(
% 0.19/0.37 ![Y: $i, X: $i] : (g(X, Y) | (~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))))),
% 0.19/0.37 inference(skolemize,[status(sab)],[27])).
% 0.19/0.37 tff(29,plain,
% 0.19/0.37 (![Y: $i, X: $i] : (g(X, Y) | (~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.19/0.37 tff(30,plain,
% 0.19/0.37 (((~![Y: $i, X: $i] : (g(X, Y) | (~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))))) | (g(elem!0, z(elem!0, elem!0)) | (~f(z(elem!0, z(elem!0, 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] : (g(X, Y) | (~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))))) | g(elem!0, z(elem!0, elem!0)) | (~f(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))) | (~f(z(elem!0, elem!0), z(elem!0, z(elem!0, elem!0)))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(31,plain,
% 0.19/0.37 ((~![Y: $i, X: $i] : (g(X, Y) | (~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))))) | (g(elem!0, z(elem!0, elem!0)) | (~f(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))) | (~f(z(elem!0, elem!0), z(elem!0, z(elem!0, elem!0)))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(32,plain,
% 0.19/0.37 ((~![Y: $i, X: $i] : (g(X, Y) | (~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))))) | g(elem!0, z(elem!0, elem!0)) | (~f(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0)))) | (~f(z(elem!0, elem!0), z(elem!0, z(elem!0, elem!0))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.37 tff(33,plain,
% 0.19/0.37 (g(elem!0, z(elem!0, elem!0)) | (~f(z(elem!0, z(elem!0, elem!0)), z(elem!0, z(elem!0, elem!0))))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[32, 29, 19])).
% 0.19/0.37 tff(34,plain,
% 0.19/0.37 (g(elem!0, z(elem!0, elem!0))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[33, 15])).
% 0.19/0.37 tff(35,assumption,(~f(z(elem!0, elem!0), z(elem!0, elem!0))), introduced(assumption)).
% 0.19/0.37 tff(36,plain,
% 0.19/0.37 ((~![Y: $i, X: $i] : f(X, Y)) | f(z(elem!0, elem!0), z(elem!0, elem!0))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(37,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[36, 8, 35])).
% 0.19/0.37 tff(38,plain,(f(z(elem!0, elem!0), z(elem!0, elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(39,assumption,(~f(elem!0, z(elem!0, elem!0))), introduced(assumption)).
% 0.19/0.37 tff(40,plain,
% 0.19/0.37 ((~![Y: $i, X: $i] : f(X, Y)) | f(elem!0, z(elem!0, elem!0))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(41,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[40, 8, 39])).
% 0.19/0.37 tff(42,plain,(f(elem!0, z(elem!0, elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(43,plain,
% 0.19/0.37 (^[Y: $i, X: $i] : refl(((~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))) | (~g(z(X, Y), z(X, Y))) | (~g(X, z(X, Y)))) <=> ((~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))) | (~g(z(X, Y), z(X, Y))) | (~g(X, z(X, Y)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(44,plain,
% 0.19/0.37 (![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))) | (~g(z(X, Y), z(X, Y))) | (~g(X, z(X, Y)))) <=> ![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))) | (~g(z(X, Y), z(X, Y))) | (~g(X, z(X, Y))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[43])).
% 0.19/0.37 tff(45,plain,
% 0.19/0.37 (![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))) | (~g(z(X, Y), z(X, Y))) | (~g(X, z(X, Y)))) <=> ![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))) | (~g(z(X, Y), z(X, Y))) | (~g(X, z(X, Y))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(46,plain,
% 0.19/0.37 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~f(Y, z(X, Y))) | (~f(z(X, Y), z(X, Y)))) <=> ((~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))))), ((((~f(Y, z(X, Y))) | (~f(z(X, Y), z(X, Y)))) | (~g(X, z(X, Y)))) <=> (((~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y)))) | (~g(X, z(X, Y)))))), rewrite((((~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y)))) | (~g(X, z(X, Y)))) <=> ((~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))) | (~g(X, z(X, Y))))), ((((~f(Y, z(X, Y))) | (~f(z(X, Y), z(X, Y)))) | (~g(X, z(X, Y)))) <=> ((~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))) | (~g(X, z(X, Y)))))), (((((~f(Y, z(X, Y))) | (~f(z(X, Y), z(X, Y)))) | (~g(X, z(X, Y)))) | (~g(z(X, Y), z(X, Y)))) <=> (((~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))) | (~g(X, z(X, Y)))) | (~g(z(X, Y), z(X, Y)))))), rewrite((((~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))) | (~g(X, z(X, Y)))) | (~g(z(X, Y), z(X, Y)))) <=> ((~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))) | (~g(z(X, Y), z(X, Y))) | (~g(X, z(X, Y))))), (((((~f(Y, z(X, Y))) | (~f(z(X, Y), z(X, Y)))) | (~g(X, z(X, Y)))) | (~g(z(X, Y), z(X, Y)))) <=> ((~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))) | (~g(z(X, Y), z(X, Y))) | (~g(X, z(X, Y))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(47,plain,
% 0.19/0.37 (![Y: $i, X: $i] : ((((~f(Y, z(X, Y))) | (~f(z(X, Y), z(X, Y)))) | (~g(X, z(X, Y)))) | (~g(z(X, Y), z(X, Y)))) <=> ![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))) | (~g(z(X, Y), z(X, Y))) | (~g(X, z(X, Y))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[46])).
% 0.19/0.37 tff(48,axiom,(![Y: $i, X: $i] : ((((~f(Y, z(X, Y))) | (~f(z(X, Y), z(X, Y)))) | (~g(X, z(X, Y)))) | (~g(z(X, Y), z(X, Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause3')).
% 0.19/0.37 tff(49,plain,
% 0.19/0.37 (![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))) | (~g(z(X, Y), z(X, Y))) | (~g(X, z(X, Y))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.19/0.37 tff(50,plain,
% 0.19/0.37 (![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))) | (~g(z(X, Y), z(X, Y))) | (~g(X, z(X, Y))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.19/0.37 tff(51,plain,(
% 0.19/0.37 ![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))) | (~g(z(X, Y), z(X, Y))) | (~g(X, z(X, Y))))),
% 0.19/0.37 inference(skolemize,[status(sab)],[50])).
% 0.19/0.37 tff(52,plain,
% 0.19/0.37 (![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))) | (~g(z(X, Y), z(X, Y))) | (~g(X, z(X, Y))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.19/0.37 tff(53,plain,
% 0.19/0.37 (((~![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))) | (~g(z(X, Y), z(X, Y))) | (~g(X, z(X, Y))))) | ((~f(elem!0, z(elem!0, elem!0))) | (~f(z(elem!0, elem!0), z(elem!0, elem!0))) | (~g(z(elem!0, elem!0), z(elem!0, elem!0))) | (~g(elem!0, z(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))) | (~g(z(X, Y), z(X, Y))) | (~g(X, z(X, Y))))) | (~f(elem!0, z(elem!0, elem!0))) | (~f(z(elem!0, elem!0), z(elem!0, elem!0))) | (~g(z(elem!0, elem!0), z(elem!0, elem!0))) | (~g(elem!0, z(elem!0, elem!0))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(54,plain,
% 0.19/0.37 (((~f(z(elem!0, elem!0), z(elem!0, elem!0))) | (~f(elem!0, z(elem!0, elem!0))) | (~g(z(elem!0, elem!0), z(elem!0, elem!0))) | (~g(elem!0, z(elem!0, elem!0)))) <=> ((~f(elem!0, z(elem!0, elem!0))) | (~f(z(elem!0, elem!0), z(elem!0, elem!0))) | (~g(z(elem!0, elem!0), z(elem!0, elem!0))) | (~g(elem!0, z(elem!0, elem!0))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(55,plain,
% 0.19/0.37 (((~![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))) | (~g(z(X, Y), z(X, Y))) | (~g(X, z(X, Y))))) | ((~f(z(elem!0, elem!0), z(elem!0, elem!0))) | (~f(elem!0, z(elem!0, elem!0))) | (~g(z(elem!0, elem!0), z(elem!0, elem!0))) | (~g(elem!0, z(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))) | (~g(z(X, Y), z(X, Y))) | (~g(X, z(X, Y))))) | ((~f(elem!0, z(elem!0, elem!0))) | (~f(z(elem!0, elem!0), z(elem!0, elem!0))) | (~g(z(elem!0, elem!0), z(elem!0, elem!0))) | (~g(elem!0, z(elem!0, elem!0)))))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[54])).
% 0.19/0.37 tff(56,plain,
% 0.19/0.37 (((~![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))) | (~g(z(X, Y), z(X, Y))) | (~g(X, z(X, Y))))) | ((~f(z(elem!0, elem!0), z(elem!0, elem!0))) | (~f(elem!0, z(elem!0, elem!0))) | (~g(z(elem!0, elem!0), z(elem!0, elem!0))) | (~g(elem!0, z(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))) | (~g(z(X, Y), z(X, Y))) | (~g(X, z(X, Y))))) | (~f(elem!0, z(elem!0, elem!0))) | (~f(z(elem!0, elem!0), z(elem!0, elem!0))) | (~g(z(elem!0, elem!0), z(elem!0, elem!0))) | (~g(elem!0, z(elem!0, elem!0))))),
% 0.19/0.37 inference(transitivity,[status(thm)],[55, 53])).
% 0.19/0.37 tff(57,plain,
% 0.19/0.37 ((~![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))) | (~g(z(X, Y), z(X, Y))) | (~g(X, z(X, Y))))) | ((~f(z(elem!0, elem!0), z(elem!0, elem!0))) | (~f(elem!0, z(elem!0, elem!0))) | (~g(z(elem!0, elem!0), z(elem!0, elem!0))) | (~g(elem!0, z(elem!0, elem!0))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(58,plain,
% 0.19/0.38 ((~![Y: $i, X: $i] : ((~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))) | (~g(z(X, Y), z(X, Y))) | (~g(X, z(X, Y))))) | (~f(elem!0, z(elem!0, elem!0))) | (~f(z(elem!0, elem!0), z(elem!0, elem!0))) | (~g(z(elem!0, elem!0), z(elem!0, elem!0))) | (~g(elem!0, z(elem!0, elem!0)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.19/0.38 tff(59,plain,
% 0.19/0.38 ((~f(z(elem!0, elem!0), z(elem!0, elem!0))) | (~g(z(elem!0, elem!0), z(elem!0, elem!0))) | (~g(elem!0, z(elem!0, elem!0)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[58, 52, 42])).
% 0.19/0.38 tff(60,plain,
% 0.19/0.38 ((~g(z(elem!0, elem!0), z(elem!0, elem!0))) | (~g(elem!0, z(elem!0, elem!0)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[59, 38])).
% 0.19/0.38 tff(61,plain,
% 0.19/0.38 (~g(z(elem!0, elem!0), z(elem!0, elem!0))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[60, 34])).
% 0.19/0.38 tff(62,plain,
% 0.19/0.38 (((~![Y: $i, X: $i] : (g(X, Y) | (~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))))) | (g(z(elem!0, elem!0), z(elem!0, elem!0)) | (~f(z(z(elem!0, elem!0), z(elem!0, elem!0)), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | (~f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : (g(X, Y) | (~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))))) | g(z(elem!0, elem!0), z(elem!0, elem!0)) | (~f(z(z(elem!0, elem!0), z(elem!0, elem!0)), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | (~f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(63,plain,
% 0.19/0.38 ((~![Y: $i, X: $i] : (g(X, Y) | (~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))))) | (g(z(elem!0, elem!0), z(elem!0, elem!0)) | (~f(z(z(elem!0, elem!0), z(elem!0, elem!0)), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | (~f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0)))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(64,plain,
% 0.19/0.38 ((~![Y: $i, X: $i] : (g(X, Y) | (~f(z(X, Y), z(X, Y))) | (~f(Y, z(X, Y))))) | g(z(elem!0, elem!0), z(elem!0, elem!0)) | (~f(z(z(elem!0, elem!0), z(elem!0, elem!0)), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | (~f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.19/0.38 tff(65,plain,
% 0.19/0.38 ((~f(z(z(elem!0, elem!0), z(elem!0, elem!0)), z(z(elem!0, elem!0), z(elem!0, elem!0)))) | (~f(z(elem!0, elem!0), z(z(elem!0, elem!0), z(elem!0, elem!0))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[64, 29, 61])).
% 0.19/0.38 tff(66,plain,
% 0.19/0.38 (~f(z(z(elem!0, elem!0), z(elem!0, elem!0)), z(z(elem!0, elem!0), z(elem!0, elem!0)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[65, 11])).
% 0.19/0.38 tff(67,plain,
% 0.19/0.38 ((~![Y: $i, X: $i] : f(X, Y)) | f(z(z(elem!0, elem!0), z(elem!0, elem!0)), z(z(elem!0, elem!0), z(elem!0, elem!0)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(68,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[67, 8, 66])).
% 0.19/0.38 % SZS output end Proof
% 0.19/0.38 % E exiting
%------------------------------------------------------------------------------