%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : CAT002-4 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : CAT002-4 : TPTP v9.0.0. Released v1.0.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n015.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 : Thu Jun 19 11:51:10 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.18/0.37 % SZS status Unsatisfiable
% 0.18/0.37 % SZS output start Proof
% 0.18/0.37 tff(h_type, type, (
% 0.18/0.37 h: $i)).
% 0.18/0.37 tff(g_type, type, (
% 0.18/0.37 g: $i)).
% 0.18/0.37 tff(inj_1_type, type, (
% 0.18/0.37 inj_1: $i > $i)).
% 0.18/0.37 tff(compose_type, type, (
% 0.18/0.37 compose: ( $i * $i ) > $i)).
% 0.18/0.37 tff(b_type, type, (
% 0.18/0.37 b: $i)).
% 0.18/0.37 tff(inj_0_type, type, (
% 0.18/0.37 inj_0: $i > $i)).
% 0.18/0.37 tff(a_type, type, (
% 0.18/0.37 a: $i)).
% 0.18/0.37 tff(1,plain,
% 0.18/0.37 (![Z: $i, X: $i] : ((X = Z) | (~(compose(b, Z) = compose(b, X)))) <=> ![Xk!1: $i] : (inj_1(compose(b, Xk!1)) = Xk!1)),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(2,plain,
% 0.18/0.37 (![Z: $i, X: $i] : ((X = Z) | (~(compose(b, Z) = compose(b, X)))) <=> ![Z: $i, X: $i] : ((X = Z) | (~(compose(b, Z) = compose(b, X))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(3,plain,
% 0.18/0.37 (![Z: $i, Y: $i, X: $i] : ((X = Z) | (~(compose(b, Z) = compose(b, X)))) <=> ![Z: $i, X: $i] : ((X = Z) | (~(compose(b, Z) = compose(b, X))))),
% 0.18/0.37 inference(elim_unused_vars,[status(thm)],[])).
% 0.18/0.37 tff(4,plain,
% 0.18/0.37 (![Z: $i, Y: $i, X: $i] : ((X = Z) | (~(compose(b, Z) = Y)) | (~(compose(b, X) = Y))) <=> ![Z: $i, Y: $i, X: $i] : ((X = Z) | (~(compose(b, Z) = compose(b, X))))),
% 0.18/0.37 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.18/0.37 tff(5,plain,
% 0.18/0.37 (![Z: $i, Y: $i, X: $i] : ((X = Z) | (~(compose(b, Z) = Y)) | (~(compose(b, X) = Y))) <=> ![Z: $i, X: $i] : ((X = Z) | (~(compose(b, Z) = compose(b, X))))),
% 0.18/0.37 inference(transitivity,[status(thm)],[4, 3])).
% 0.18/0.37 tff(6,plain,
% 0.18/0.37 (^[Z: $i, Y: $i, X: $i] : rewrite((((~(compose(b, X) = Y)) | (~(compose(b, Z) = Y))) | (X = Z)) <=> ((X = Z) | (~(compose(b, Z) = Y)) | (~(compose(b, X) = Y))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(7,plain,
% 0.18/0.37 (![Z: $i, Y: $i, X: $i] : (((~(compose(b, X) = Y)) | (~(compose(b, Z) = Y))) | (X = Z)) <=> ![Z: $i, Y: $i, X: $i] : ((X = Z) | (~(compose(b, Z) = Y)) | (~(compose(b, X) = Y)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[6])).
% 0.18/0.37 tff(8,plain,
% 0.18/0.37 (![Z: $i, Y: $i, X: $i] : (((~(compose(b, X) = Y)) | (~(compose(b, Z) = Y))) | (X = Z)) <=> ![Z: $i, X: $i] : ((X = Z) | (~(compose(b, Z) = compose(b, X))))),
% 0.18/0.37 inference(transitivity,[status(thm)],[7, 5])).
% 0.18/0.37 tff(9,axiom,(![Z: $i, Y: $i, X: $i] : (((~(compose(b, X) = Y)) | (~(compose(b, Z) = Y))) | (X = Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cancellation_for_compose2')).
% 0.18/0.37 tff(10,plain,
% 0.18/0.37 (![Z: $i, X: $i] : ((X = Z) | (~(compose(b, Z) = compose(b, X))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.18/0.37 tff(11,plain,
% 0.18/0.37 (![Z: $i, X: $i] : ((X = Z) | (~(compose(b, Z) = compose(b, X))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.18/0.37 tff(12,plain,(
% 0.18/0.37 ![Z: $i, X: $i] : ((X = Z) | (~(compose(b, Z) = compose(b, X))))),
% 0.18/0.37 inference(skolemize,[status(sab)],[11])).
% 0.18/0.37 tff(13,plain,
% 0.18/0.37 (![Xk!1: $i] : (inj_1(compose(b, Xk!1)) = Xk!1)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[12, 1])).
% 0.18/0.37 tff(14,plain,
% 0.18/0.37 ((~![Xk!1: $i] : (inj_1(compose(b, Xk!1)) = Xk!1)) | (inj_1(compose(b, h)) = h)),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(15,plain,
% 0.18/0.37 (inj_1(compose(b, h)) = h),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.18/0.37 tff(16,plain,
% 0.18/0.37 (![Z: $i, X: $i] : ((X = Z) | (~(compose(a, Z) = compose(a, X)))) <=> ![Xk!1: $i] : (inj_0(compose(a, Xk!1)) = Xk!1)),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(17,plain,
% 0.18/0.37 (![Z: $i, X: $i] : ((X = Z) | (~(compose(a, Z) = compose(a, X)))) <=> ![Z: $i, X: $i] : ((X = Z) | (~(compose(a, Z) = compose(a, X))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(18,plain,
% 0.18/0.37 (![Z: $i, Y: $i, X: $i] : ((X = Z) | (~(compose(a, Z) = compose(a, X)))) <=> ![Z: $i, X: $i] : ((X = Z) | (~(compose(a, Z) = compose(a, X))))),
% 0.18/0.37 inference(elim_unused_vars,[status(thm)],[])).
% 0.18/0.37 tff(19,plain,
% 0.18/0.37 (![Z: $i, Y: $i, X: $i] : ((X = Z) | (~(compose(a, Z) = Y)) | (~(compose(a, X) = Y))) <=> ![Z: $i, Y: $i, X: $i] : ((X = Z) | (~(compose(a, Z) = compose(a, X))))),
% 0.18/0.37 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.18/0.37 tff(20,plain,
% 0.18/0.37 (![Z: $i, Y: $i, X: $i] : ((X = Z) | (~(compose(a, Z) = Y)) | (~(compose(a, X) = Y))) <=> ![Z: $i, X: $i] : ((X = Z) | (~(compose(a, Z) = compose(a, X))))),
% 0.18/0.37 inference(transitivity,[status(thm)],[19, 18])).
% 0.18/0.37 tff(21,plain,
% 0.18/0.37 (^[Z: $i, Y: $i, X: $i] : rewrite((((~(compose(a, X) = Y)) | (~(compose(a, Z) = Y))) | (X = Z)) <=> ((X = Z) | (~(compose(a, Z) = Y)) | (~(compose(a, X) = Y))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(22,plain,
% 0.18/0.37 (![Z: $i, Y: $i, X: $i] : (((~(compose(a, X) = Y)) | (~(compose(a, Z) = Y))) | (X = Z)) <=> ![Z: $i, Y: $i, X: $i] : ((X = Z) | (~(compose(a, Z) = Y)) | (~(compose(a, X) = Y)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[21])).
% 0.18/0.37 tff(23,plain,
% 0.18/0.37 (![Z: $i, Y: $i, X: $i] : (((~(compose(a, X) = Y)) | (~(compose(a, Z) = Y))) | (X = Z)) <=> ![Z: $i, X: $i] : ((X = Z) | (~(compose(a, Z) = compose(a, X))))),
% 0.18/0.37 inference(transitivity,[status(thm)],[22, 20])).
% 0.18/0.37 tff(24,axiom,(![Z: $i, Y: $i, X: $i] : (((~(compose(a, X) = Y)) | (~(compose(a, Z) = Y))) | (X = Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cancellation_for_compose1')).
% 0.18/0.37 tff(25,plain,
% 0.18/0.37 (![Z: $i, X: $i] : ((X = Z) | (~(compose(a, Z) = compose(a, X))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.18/0.37 tff(26,plain,
% 0.18/0.37 (![Z: $i, X: $i] : ((X = Z) | (~(compose(a, Z) = compose(a, X))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[25, 17])).
% 0.18/0.37 tff(27,plain,(
% 0.18/0.37 ![Z: $i, X: $i] : ((X = Z) | (~(compose(a, Z) = compose(a, X))))),
% 0.18/0.37 inference(skolemize,[status(sab)],[26])).
% 0.18/0.37 tff(28,plain,
% 0.18/0.37 (![Xk!1: $i] : (inj_0(compose(a, Xk!1)) = Xk!1)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[27, 16])).
% 0.18/0.37 tff(29,plain,
% 0.18/0.37 ((~![Xk!1: $i] : (inj_0(compose(a, Xk!1)) = Xk!1)) | (inj_0(compose(a, compose(b, h))) = compose(b, h))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(30,plain,
% 0.18/0.37 (inj_0(compose(a, compose(b, h))) = compose(b, h)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.18/0.37 tff(31,plain,
% 0.18/0.37 (^[Z: $i, Y: $i, X: $i] : refl((compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)) <=> (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(32,plain,
% 0.18/0.37 (![Z: $i, Y: $i, X: $i] : (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)) <=> ![Z: $i, Y: $i, X: $i] : (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[31])).
% 0.18/0.37 tff(33,plain,
% 0.18/0.37 (![Z: $i, Y: $i, X: $i] : (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)) <=> ![Z: $i, Y: $i, X: $i] : (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(34,axiom,(![Z: $i, Y: $i, X: $i] : (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z))), file('/export/starexec/sandbox/benchmark/Axioms/CAT004-0.ax','associativity_of_compose')).
% 0.18/0.37 tff(35,plain,
% 0.18/0.37 (![Z: $i, Y: $i, X: $i] : (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.18/0.37 tff(36,plain,(
% 0.18/0.37 ![Z: $i, Y: $i, X: $i] : (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z))),
% 0.18/0.37 inference(skolemize,[status(sab)],[35])).
% 0.18/0.37 tff(37,plain,
% 0.18/0.37 (![Z: $i, Y: $i, X: $i] : (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.18/0.37 tff(38,plain,
% 0.18/0.37 ((~![Z: $i, Y: $i, X: $i] : (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z))) | (compose(a, compose(b, h)) = compose(compose(a, b), h))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(39,plain,
% 0.18/0.37 (compose(a, compose(b, h)) = compose(compose(a, b), h)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.18/0.37 tff(40,plain,
% 0.18/0.37 (compose(compose(a, b), h) = compose(a, compose(b, h))),
% 0.18/0.37 inference(symmetry,[status(thm)],[39])).
% 0.18/0.37 tff(41,plain,
% 0.18/0.37 ((compose(compose(a, b), h) = compose(compose(a, b), g)) <=> (compose(compose(a, b), h) = compose(compose(a, b), g))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(42,axiom,(compose(compose(a, b), h) = compose(compose(a, b), g)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ab_h_equals_ab_g')).
% 0.18/0.37 tff(43,plain,
% 0.18/0.37 (compose(compose(a, b), h) = compose(compose(a, b), g)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.18/0.37 tff(44,plain,
% 0.18/0.37 (compose(compose(a, b), g) = compose(compose(a, b), h)),
% 0.18/0.37 inference(symmetry,[status(thm)],[43])).
% 0.18/0.37 tff(45,plain,
% 0.18/0.37 ((~![Z: $i, Y: $i, X: $i] : (compose(X, compose(Y, Z)) = compose(compose(X, Y), Z))) | (compose(a, compose(b, g)) = compose(compose(a, b), g))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(46,plain,
% 0.18/0.37 (compose(a, compose(b, g)) = compose(compose(a, b), g)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[45, 37])).
% 0.18/0.37 tff(47,plain,
% 0.18/0.37 (compose(a, compose(b, g)) = compose(a, compose(b, h))),
% 0.18/0.37 inference(transitivity,[status(thm)],[46, 44, 40])).
% 0.18/0.37 tff(48,plain,
% 0.18/0.37 (inj_0(compose(a, compose(b, g))) = inj_0(compose(a, compose(b, h)))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[47])).
% 0.18/0.37 tff(49,plain,
% 0.18/0.37 ((~![Xk!1: $i] : (inj_0(compose(a, Xk!1)) = Xk!1)) | (inj_0(compose(a, compose(b, g))) = compose(b, g))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(50,plain,
% 0.18/0.37 (inj_0(compose(a, compose(b, g))) = compose(b, g)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[49, 28])).
% 0.18/0.37 tff(51,plain,
% 0.18/0.37 (compose(b, g) = inj_0(compose(a, compose(b, g)))),
% 0.18/0.37 inference(symmetry,[status(thm)],[50])).
% 0.18/0.37 tff(52,plain,
% 0.18/0.37 (compose(b, g) = compose(b, h)),
% 0.18/0.37 inference(transitivity,[status(thm)],[51, 48, 30])).
% 0.18/0.37 tff(53,plain,
% 0.18/0.37 (inj_1(compose(b, g)) = inj_1(compose(b, h))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[52])).
% 0.18/0.37 tff(54,plain,
% 0.18/0.37 ((~![Xk!1: $i] : (inj_1(compose(b, Xk!1)) = Xk!1)) | (inj_1(compose(b, g)) = g)),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(55,plain,
% 0.18/0.37 (inj_1(compose(b, g)) = g),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[54, 13])).
% 0.18/0.37 tff(56,plain,
% 0.18/0.37 (g = inj_1(compose(b, g))),
% 0.18/0.37 inference(symmetry,[status(thm)],[55])).
% 0.18/0.37 tff(57,plain,
% 0.18/0.37 (g = h),
% 0.18/0.37 inference(transitivity,[status(thm)],[56, 53, 15])).
% 0.18/0.37 tff(58,plain,
% 0.18/0.37 ((~(g = h)) <=> (~(g = h))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(59,axiom,(~(g = h)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_g_equals_h')).
% 0.18/0.37 tff(60,plain,
% 0.18/0.37 (~(g = h)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.18/0.37 tff(61,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[60, 57])).
% 0.18/0.37 % SZS output end Proof
% 0.18/0.37 % E exiting
%------------------------------------------------------------------------------