%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : CAT003-2 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:00:18 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT003-2 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.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 : Thu Jun 19 11:54:18 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(domain_type, type, (
% 0.12/0.38 domain: $i > $i)).
% 0.12/0.38 tff(g_type, type, (
% 0.12/0.38 g: $i)).
% 0.12/0.38 tff(codomain_type, type, (
% 0.12/0.38 codomain: $i > $i)).
% 0.12/0.38 tff(compose_type, type, (
% 0.12/0.38 compose: ( $i * $i ) > $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(h_type, type, (
% 0.12/0.38 h: $i)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 ((codomain(b) = domain(h)) <=> (codomain(b) = domain(h))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(2,axiom,(codomain(b) = domain(h)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','codomain_of_b_equals_domain_of_h')).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (codomain(b) = domain(h)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 ((codomain(b) = domain(g)) <=> (codomain(b) = domain(g))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(5,axiom,(codomain(b) = domain(g)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','codomain_of_b_equals_domain_of_g')).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (codomain(b) = domain(g)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (domain(g) = codomain(b)),
% 0.12/0.38 inference(symmetry,[status(thm)],[6])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (domain(g) = domain(h)),
% 0.12/0.38 inference(transitivity,[status(thm)],[7, 3])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 ((codomain(compose(a, b)) = domain(g)) <=> (codomain(compose(a, b)) = domain(h))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[8])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 ((codomain(compose(a, b)) = domain(h)) <=> (codomain(compose(a, b)) = domain(g))),
% 0.12/0.38 inference(symmetry,[status(thm)],[9])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 ((codomain(a) = domain(b)) <=> (codomain(a) = domain(b))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(12,axiom,(codomain(a) = domain(b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','codomain_of_a_equals_domain_of_b')).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (codomain(a) = domain(b)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (^[Y: $i, X: $i] : refl(((~(codomain(X) = domain(Y))) | (codomain(compose(X, Y)) = codomain(Y))) <=> ((~(codomain(X) = domain(Y))) | (codomain(compose(X, Y)) = codomain(Y))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 (![Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (codomain(compose(X, Y)) = codomain(Y))) <=> ![Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (codomain(compose(X, Y)) = codomain(Y)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (![Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (codomain(compose(X, Y)) = codomain(Y))) <=> ![Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (codomain(compose(X, Y)) = codomain(Y)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(17,axiom,(![Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (codomain(compose(X, Y)) = codomain(Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/CAT002-0.ax','codomain_domain2')).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (![Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (codomain(compose(X, Y)) = codomain(Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.38 tff(19,plain,(
% 0.19/0.38 ![Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (codomain(compose(X, Y)) = codomain(Y)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[18])).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 (![Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (codomain(compose(X, Y)) = codomain(Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 (((~![Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (codomain(compose(X, Y)) = codomain(Y)))) | ((~(codomain(a) = domain(b))) | (codomain(compose(a, b)) = codomain(b)))) <=> ((~![Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (codomain(compose(X, Y)) = codomain(Y)))) | (~(codomain(a) = domain(b))) | (codomain(compose(a, b)) = codomain(b)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(22,plain,
% 0.19/0.38 ((~![Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (codomain(compose(X, Y)) = codomain(Y)))) | ((~(codomain(a) = domain(b))) | (codomain(compose(a, b)) = codomain(b)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(23,plain,
% 0.19/0.38 ((~![Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (codomain(compose(X, Y)) = codomain(Y)))) | (~(codomain(a) = domain(b))) | (codomain(compose(a, b)) = codomain(b))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.38 tff(24,plain,
% 0.19/0.38 (codomain(compose(a, b)) = codomain(b)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[23, 20, 13])).
% 0.19/0.38 tff(25,plain,
% 0.19/0.38 (codomain(compose(a, b)) = domain(h)),
% 0.19/0.38 inference(transitivity,[status(thm)],[24, 3])).
% 0.19/0.38 tff(26,plain,
% 0.19/0.38 (codomain(compose(a, b)) = domain(g)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[25, 10])).
% 0.19/0.38 tff(27,plain,
% 0.19/0.38 (^[Z: $i, Y: $i, X: $i] : refl(((~(codomain(X) = domain(Y))) | (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)) | (~(codomain(Y) = domain(Z)))) <=> ((~(codomain(X) = domain(Y))) | (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)) | (~(codomain(Y) = domain(Z)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(28,plain,
% 0.19/0.38 (![Z: $i, Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)) | (~(codomain(Y) = domain(Z)))) <=> ![Z: $i, Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)) | (~(codomain(Y) = domain(Z))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.38 tff(29,plain,
% 0.19/0.38 (![Z: $i, Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)) | (~(codomain(Y) = domain(Z)))) <=> ![Z: $i, Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)) | (~(codomain(Y) = domain(Z))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(30,plain,
% 0.19/0.38 (^[Z: $i, Y: $i, X: $i] : rewrite((((~(codomain(X) = domain(Y))) | (~(codomain(Y) = domain(Z)))) | (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z))) <=> ((~(codomain(X) = domain(Y))) | (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)) | (~(codomain(Y) = domain(Z)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(31,plain,
% 0.19/0.38 (![Z: $i, Y: $i, X: $i] : (((~(codomain(X) = domain(Y))) | (~(codomain(Y) = domain(Z)))) | (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)) | (~(codomain(Y) = domain(Z))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[30])).
% 0.19/0.38 tff(32,axiom,(![Z: $i, Y: $i, X: $i] : (((~(codomain(X) = domain(Y))) | (~(codomain(Y) = domain(Z)))) | (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/CAT002-0.ax','star_property')).
% 0.19/0.38 tff(33,plain,
% 0.19/0.38 (![Z: $i, Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)) | (~(codomain(Y) = domain(Z))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 (![Z: $i, Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)) | (~(codomain(Y) = domain(Z))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.19/0.38 tff(35,plain,(
% 0.19/0.38 ![Z: $i, Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)) | (~(codomain(Y) = domain(Z))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[34])).
% 0.19/0.38 tff(36,plain,
% 0.19/0.38 (![Z: $i, Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)) | (~(codomain(Y) = domain(Z))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.19/0.38 tff(37,plain,
% 0.19/0.38 (((~![Z: $i, Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)) | (~(codomain(Y) = domain(Z))))) | ((~(codomain(b) = domain(g))) | (~(codomain(a) = domain(b))) | (compose(a, compose(b, g)) = compose(compose(a, b), g)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)) | (~(codomain(Y) = domain(Z))))) | (~(codomain(b) = domain(g))) | (~(codomain(a) = domain(b))) | (compose(a, compose(b, g)) = compose(compose(a, b), g)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(38,plain,
% 0.19/0.38 (((~(codomain(a) = domain(b))) | (compose(a, compose(b, g)) = compose(compose(a, b), g)) | (~(codomain(b) = domain(g)))) <=> ((~(codomain(b) = domain(g))) | (~(codomain(a) = domain(b))) | (compose(a, compose(b, g)) = compose(compose(a, b), g)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (((~![Z: $i, Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)) | (~(codomain(Y) = domain(Z))))) | ((~(codomain(a) = domain(b))) | (compose(a, compose(b, g)) = compose(compose(a, b), g)) | (~(codomain(b) = domain(g))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)) | (~(codomain(Y) = domain(Z))))) | ((~(codomain(b) = domain(g))) | (~(codomain(a) = domain(b))) | (compose(a, compose(b, g)) = compose(compose(a, b), g))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[38])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (((~![Z: $i, Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)) | (~(codomain(Y) = domain(Z))))) | ((~(codomain(a) = domain(b))) | (compose(a, compose(b, g)) = compose(compose(a, b), g)) | (~(codomain(b) = domain(g))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)) | (~(codomain(Y) = domain(Z))))) | (~(codomain(b) = domain(g))) | (~(codomain(a) = domain(b))) | (compose(a, compose(b, g)) = compose(compose(a, b), g)))),
% 0.19/0.39 inference(transitivity,[status(thm)],[39, 37])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 ((~![Z: $i, Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)) | (~(codomain(Y) = domain(Z))))) | ((~(codomain(a) = domain(b))) | (compose(a, compose(b, g)) = compose(compose(a, b), g)) | (~(codomain(b) = domain(g))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 ((~![Z: $i, Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)) | (~(codomain(Y) = domain(Z))))) | (~(codomain(b) = domain(g))) | (~(codomain(a) = domain(b))) | (compose(a, compose(b, g)) = compose(compose(a, b), g))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 (compose(a, compose(b, g)) = compose(compose(a, b), g)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[42, 36, 13, 6])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 ((compose(b, h) = compose(b, g)) <=> (compose(b, h) = compose(b, g))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(45,axiom,(compose(b, h) = compose(b, g)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bh_equals_bg')).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 (compose(b, h) = compose(b, g)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 (compose(a, compose(b, h)) = compose(a, compose(b, g))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[46])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 (((~![Z: $i, Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)) | (~(codomain(Y) = domain(Z))))) | ((~(codomain(b) = domain(h))) | (~(codomain(a) = domain(b))) | (compose(a, compose(b, h)) = compose(compose(a, b), h)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)) | (~(codomain(Y) = domain(Z))))) | (~(codomain(b) = domain(h))) | (~(codomain(a) = domain(b))) | (compose(a, compose(b, h)) = compose(compose(a, b), h)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 (((~(codomain(a) = domain(b))) | (compose(a, compose(b, h)) = compose(compose(a, b), h)) | (~(codomain(b) = domain(h)))) <=> ((~(codomain(b) = domain(h))) | (~(codomain(a) = domain(b))) | (compose(a, compose(b, h)) = compose(compose(a, b), h)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 (((~![Z: $i, Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)) | (~(codomain(Y) = domain(Z))))) | ((~(codomain(a) = domain(b))) | (compose(a, compose(b, h)) = compose(compose(a, b), h)) | (~(codomain(b) = domain(h))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)) | (~(codomain(Y) = domain(Z))))) | ((~(codomain(b) = domain(h))) | (~(codomain(a) = domain(b))) | (compose(a, compose(b, h)) = compose(compose(a, b), h))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[49])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 (((~![Z: $i, Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)) | (~(codomain(Y) = domain(Z))))) | ((~(codomain(a) = domain(b))) | (compose(a, compose(b, h)) = compose(compose(a, b), h)) | (~(codomain(b) = domain(h))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)) | (~(codomain(Y) = domain(Z))))) | (~(codomain(b) = domain(h))) | (~(codomain(a) = domain(b))) | (compose(a, compose(b, h)) = compose(compose(a, b), h)))),
% 0.19/0.39 inference(transitivity,[status(thm)],[50, 48])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 ((~![Z: $i, Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)) | (~(codomain(Y) = domain(Z))))) | ((~(codomain(a) = domain(b))) | (compose(a, compose(b, h)) = compose(compose(a, b), h)) | (~(codomain(b) = domain(h))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 ((~![Z: $i, Y: $i, X: $i] : ((~(codomain(X) = domain(Y))) | (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)) | (~(codomain(Y) = domain(Z))))) | (~(codomain(b) = domain(h))) | (~(codomain(a) = domain(b))) | (compose(a, compose(b, h)) = compose(compose(a, b), h))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 (compose(a, compose(b, h)) = compose(compose(a, b), h)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[53, 36, 13, 3])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 (compose(compose(a, b), h) = compose(a, compose(b, h))),
% 0.19/0.39 inference(symmetry,[status(thm)],[54])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (compose(compose(a, b), h) = compose(compose(a, b), g)),
% 0.19/0.39 inference(transitivity,[status(thm)],[55, 47, 43])).
% 0.19/0.39 tff(57,assumption,(~(compose(compose(a, b), h) = compose(compose(a, b), g))), introduced(assumption)).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.19/0.39 tff(59,plain,(compose(compose(a, b), h) = compose(compose(a, b), g)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 ((h = g) <=> (g = h)),
% 0.19/0.39 inference(commutativity,[status(thm)],[])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 ((g = h) <=> (h = g)),
% 0.19/0.39 inference(symmetry,[status(thm)],[60])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 ((~(g = h)) <=> (~(h = g))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[61])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 ((~(g = h)) <=> (~(g = h))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(64,axiom,(~(g = h)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_g_equals_h')).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 (~(g = h)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.39 tff(66,plain,
% 0.19/0.39 (~(h = g)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[65, 62])).
% 0.19/0.39 tff(67,plain,
% 0.19/0.39 (^[Z: $i, X: $i] : refl(((~(codomain(compose(a, b)) = domain(X))) | (X = Z) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = compose(compose(a, b), Z)))) <=> ((~(codomain(compose(a, b)) = domain(X))) | (X = Z) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = compose(compose(a, b), Z)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(68,plain,
% 0.19/0.39 (![Z: $i, X: $i] : ((~(codomain(compose(a, b)) = domain(X))) | (X = Z) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = compose(compose(a, b), Z)))) <=> ![Z: $i, X: $i] : ((~(codomain(compose(a, b)) = domain(X))) | (X = Z) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = compose(compose(a, b), Z))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[67])).
% 0.19/0.39 tff(69,plain,
% 0.19/0.39 (![Z: $i, X: $i] : ((~(codomain(compose(a, b)) = domain(X))) | (X = Z) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = compose(compose(a, b), Z)))) <=> ![Z: $i, X: $i] : ((~(codomain(compose(a, b)) = domain(X))) | (X = Z) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = compose(compose(a, b), Z))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(70,plain,
% 0.19/0.39 (![Z: $i, Y: $i, X: $i] : ((~(codomain(compose(a, b)) = domain(X))) | (X = Z) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = compose(compose(a, b), Z)))) <=> ![Z: $i, X: $i] : ((~(codomain(compose(a, b)) = domain(X))) | (X = Z) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = compose(compose(a, b), Z))))),
% 0.19/0.39 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.39 tff(71,plain,
% 0.19/0.39 (![Z: $i, Y: $i, X: $i] : ((X = Z) | (~(compose(compose(a, b), Z) = Y)) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = Y)) | (~(codomain(compose(a, b)) = domain(X)))) <=> ![Z: $i, Y: $i, X: $i] : ((~(codomain(compose(a, b)) = domain(X))) | (X = Z) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = compose(compose(a, b), Z))))),
% 0.19/0.39 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.19/0.39 tff(72,plain,
% 0.19/0.39 (![Z: $i, Y: $i, X: $i] : ((X = Z) | (~(compose(compose(a, b), Z) = Y)) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = Y)) | (~(codomain(compose(a, b)) = domain(X)))) <=> ![Z: $i, X: $i] : ((~(codomain(compose(a, b)) = domain(X))) | (X = Z) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = compose(compose(a, b), Z))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[71, 70])).
% 0.19/0.39 tff(73,plain,
% 0.19/0.39 (^[Z: $i, Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~(codomain(compose(a, b)) = domain(X))) | (~(compose(compose(a, b), X) = Y))) | (~(codomain(compose(a, b)) = domain(Z)))) <=> ((~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = Y)) | (~(codomain(compose(a, b)) = domain(X))))), (((((~(codomain(compose(a, b)) = domain(X))) | (~(compose(compose(a, b), X) = Y))) | (~(codomain(compose(a, b)) = domain(Z)))) | (~(compose(compose(a, b), Z) = Y))) <=> (((~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = Y)) | (~(codomain(compose(a, b)) = domain(X)))) | (~(compose(compose(a, b), Z) = Y))))), rewrite((((~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = Y)) | (~(codomain(compose(a, b)) = domain(X)))) | (~(compose(compose(a, b), Z) = Y))) <=> ((~(compose(compose(a, b), Z) = Y)) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = Y)) | (~(codomain(compose(a, b)) = domain(X))))), (((((~(codomain(compose(a, b)) = domain(X))) | (~(compose(compose(a, b), X) = Y))) | (~(codomain(compose(a, b)) = domain(Z)))) | (~(compose(compose(a, b), Z) = Y))) <=> ((~(compose(compose(a, b), Z) = Y)) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = Y)) | (~(codomain(compose(a, b)) = domain(X)))))), ((((((~(codomain(compose(a, b)) = domain(X))) | (~(compose(compose(a, b), X) = Y))) | (~(codomain(compose(a, b)) = domain(Z)))) | (~(compose(compose(a, b), Z) = Y))) | (X = Z)) <=> (((~(compose(compose(a, b), Z) = Y)) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = Y)) | (~(codomain(compose(a, b)) = domain(X)))) | (X = Z)))), rewrite((((~(compose(compose(a, b), Z) = Y)) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = Y)) | (~(codomain(compose(a, b)) = domain(X)))) | (X = Z)) <=> ((X = Z) | (~(compose(compose(a, b), Z) = Y)) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = Y)) | (~(codomain(compose(a, b)) = domain(X))))), ((((((~(codomain(compose(a, b)) = domain(X))) | (~(compose(compose(a, b), X) = Y))) | (~(codomain(compose(a, b)) = domain(Z)))) | (~(compose(compose(a, b), Z) = Y))) | (X = Z)) <=> ((X = Z) | (~(compose(compose(a, b), Z) = Y)) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = Y)) | (~(codomain(compose(a, b)) = domain(X))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(74,plain,
% 0.19/0.39 (![Z: $i, Y: $i, X: $i] : (((((~(codomain(compose(a, b)) = domain(X))) | (~(compose(compose(a, b), X) = Y))) | (~(codomain(compose(a, b)) = domain(Z)))) | (~(compose(compose(a, b), Z) = Y))) | (X = Z)) <=> ![Z: $i, Y: $i, X: $i] : ((X = Z) | (~(compose(compose(a, b), Z) = Y)) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = Y)) | (~(codomain(compose(a, b)) = domain(X))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[73])).
% 0.19/0.39 tff(75,plain,
% 0.19/0.40 (![Z: $i, Y: $i, X: $i] : (((((~(codomain(compose(a, b)) = domain(X))) | (~(compose(compose(a, b), X) = Y))) | (~(codomain(compose(a, b)) = domain(Z)))) | (~(compose(compose(a, b), Z) = Y))) | (X = Z)) <=> ![Z: $i, X: $i] : ((~(codomain(compose(a, b)) = domain(X))) | (X = Z) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = compose(compose(a, b), Z))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[74, 72])).
% 0.19/0.40 tff(76,axiom,(![Z: $i, Y: $i, X: $i] : (((((~(codomain(compose(a, b)) = domain(X))) | (~(compose(compose(a, b), X) = Y))) | (~(codomain(compose(a, b)) = domain(Z)))) | (~(compose(compose(a, b), Z) = Y))) | (X = Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','endomorphism')).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 (![Z: $i, X: $i] : ((~(codomain(compose(a, b)) = domain(X))) | (X = Z) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = compose(compose(a, b), Z))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 (![Z: $i, X: $i] : ((~(codomain(compose(a, b)) = domain(X))) | (X = Z) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = compose(compose(a, b), Z))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[77, 69])).
% 0.19/0.40 tff(79,plain,(
% 0.19/0.40 ![Z: $i, X: $i] : ((~(codomain(compose(a, b)) = domain(X))) | (X = Z) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = compose(compose(a, b), Z))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[78])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 (![Z: $i, X: $i] : ((~(codomain(compose(a, b)) = domain(X))) | (X = Z) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = compose(compose(a, b), Z))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[79, 68])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 (((~![Z: $i, X: $i] : ((~(codomain(compose(a, b)) = domain(X))) | (X = Z) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = compose(compose(a, b), Z))))) | ((~(codomain(compose(a, b)) = domain(h))) | (~(codomain(compose(a, b)) = domain(g))) | (h = g) | (~(compose(compose(a, b), h) = compose(compose(a, b), g))))) <=> ((~![Z: $i, X: $i] : ((~(codomain(compose(a, b)) = domain(X))) | (X = Z) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = compose(compose(a, b), Z))))) | (~(codomain(compose(a, b)) = domain(h))) | (~(codomain(compose(a, b)) = domain(g))) | (h = g) | (~(compose(compose(a, b), h) = compose(compose(a, b), g))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 (((~(codomain(compose(a, b)) = domain(h))) | (h = g) | (~(codomain(compose(a, b)) = domain(g))) | (~(compose(compose(a, b), h) = compose(compose(a, b), g)))) <=> ((~(codomain(compose(a, b)) = domain(h))) | (~(codomain(compose(a, b)) = domain(g))) | (h = g) | (~(compose(compose(a, b), h) = compose(compose(a, b), g))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 (((~![Z: $i, X: $i] : ((~(codomain(compose(a, b)) = domain(X))) | (X = Z) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = compose(compose(a, b), Z))))) | ((~(codomain(compose(a, b)) = domain(h))) | (h = g) | (~(codomain(compose(a, b)) = domain(g))) | (~(compose(compose(a, b), h) = compose(compose(a, b), g))))) <=> ((~![Z: $i, X: $i] : ((~(codomain(compose(a, b)) = domain(X))) | (X = Z) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = compose(compose(a, b), Z))))) | ((~(codomain(compose(a, b)) = domain(h))) | (~(codomain(compose(a, b)) = domain(g))) | (h = g) | (~(compose(compose(a, b), h) = compose(compose(a, b), g)))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[82])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 (((~![Z: $i, X: $i] : ((~(codomain(compose(a, b)) = domain(X))) | (X = Z) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = compose(compose(a, b), Z))))) | ((~(codomain(compose(a, b)) = domain(h))) | (h = g) | (~(codomain(compose(a, b)) = domain(g))) | (~(compose(compose(a, b), h) = compose(compose(a, b), g))))) <=> ((~![Z: $i, X: $i] : ((~(codomain(compose(a, b)) = domain(X))) | (X = Z) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = compose(compose(a, b), Z))))) | (~(codomain(compose(a, b)) = domain(h))) | (~(codomain(compose(a, b)) = domain(g))) | (h = g) | (~(compose(compose(a, b), h) = compose(compose(a, b), g))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[83, 81])).
% 0.19/0.40 tff(85,plain,
% 0.19/0.40 ((~![Z: $i, X: $i] : ((~(codomain(compose(a, b)) = domain(X))) | (X = Z) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = compose(compose(a, b), Z))))) | ((~(codomain(compose(a, b)) = domain(h))) | (h = g) | (~(codomain(compose(a, b)) = domain(g))) | (~(compose(compose(a, b), h) = compose(compose(a, b), g))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 ((~![Z: $i, X: $i] : ((~(codomain(compose(a, b)) = domain(X))) | (X = Z) | (~(codomain(compose(a, b)) = domain(Z))) | (~(compose(compose(a, b), X) = compose(compose(a, b), Z))))) | (~(codomain(compose(a, b)) = domain(h))) | (~(codomain(compose(a, b)) = domain(g))) | (h = g) | (~(compose(compose(a, b), h) = compose(compose(a, b), g)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 ((~(codomain(compose(a, b)) = domain(h))) | (~(codomain(compose(a, b)) = domain(g))) | (h = g) | (~(compose(compose(a, b), h) = compose(compose(a, b), g)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[86, 80])).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 ((~(codomain(compose(a, b)) = domain(h))) | (~(codomain(compose(a, b)) = domain(g))) | (~(compose(compose(a, b), h) = compose(compose(a, b), g)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[87, 66])).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 (~(codomain(compose(a, b)) = domain(g))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[88, 25, 59])).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[89, 26])).
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------