%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP008-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:06:49 AM UTC 2025
% Result : Unsatisfiable 0.48s 0.65s
% Output : Proof 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP008-1 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n008.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 15:27:48 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.48/0.65 % SZS status Unsatisfiable
% 0.48/0.65 % SZS output start Proof
% 0.48/0.65 tff(product_type, type, (
% 0.48/0.65 product: ( $i * $i * $i ) > $o)).
% 0.48/0.65 tff(identity_type, type, (
% 0.48/0.65 identity: $i)).
% 0.48/0.65 tff(inverse_type, type, (
% 0.48/0.65 inverse: $i > $i)).
% 0.48/0.65 tff(j_type, type, (
% 0.48/0.65 j: $i > $i)).
% 0.48/0.65 tff(h_type, type, (
% 0.48/0.65 h: $i > $i)).
% 0.48/0.65 tff(q_type, type, (
% 0.48/0.65 q: $i > $o)).
% 0.48/0.65 tff(1,plain,
% 0.48/0.65 (^[X: $i] : refl(product(X, identity, X) <=> product(X, identity, X))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(2,plain,
% 0.48/0.65 (![X: $i] : product(X, identity, X) <=> ![X: $i] : product(X, identity, X)),
% 0.48/0.65 inference(quant_intro,[status(thm)],[1])).
% 0.48/0.65 tff(3,plain,
% 0.48/0.65 (![X: $i] : product(X, identity, X) <=> ![X: $i] : product(X, identity, X)),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(4,axiom,(![X: $i] : product(X, identity, X)), file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax','right_identity')).
% 0.48/0.65 tff(5,plain,
% 0.48/0.65 (![X: $i] : product(X, identity, X)),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.48/0.65 tff(6,plain,(
% 0.48/0.65 ![X: $i] : product(X, identity, X)),
% 0.48/0.65 inference(skolemize,[status(sab)],[5])).
% 0.48/0.65 tff(7,plain,
% 0.48/0.65 (![X: $i] : product(X, identity, X)),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.48/0.65 tff(8,plain,
% 0.48/0.65 ((~![X: $i] : product(X, identity, X)) | product(inverse(identity), identity, inverse(identity))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(9,plain,
% 0.48/0.65 (product(inverse(identity), identity, inverse(identity))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.48/0.65 tff(10,plain,
% 0.48/0.65 (^[X: $i] : refl(product(inverse(X), X, identity) <=> product(inverse(X), X, identity))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(11,plain,
% 0.48/0.65 (![X: $i] : product(inverse(X), X, identity) <=> ![X: $i] : product(inverse(X), X, identity)),
% 0.48/0.65 inference(quant_intro,[status(thm)],[10])).
% 0.48/0.65 tff(12,plain,
% 0.48/0.65 (![X: $i] : product(inverse(X), X, identity) <=> ![X: $i] : product(inverse(X), X, identity)),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(13,axiom,(![X: $i] : product(inverse(X), X, identity)), file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax','left_inverse')).
% 0.48/0.65 tff(14,plain,
% 0.48/0.65 (![X: $i] : product(inverse(X), X, identity)),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.48/0.65 tff(15,plain,(
% 0.48/0.65 ![X: $i] : product(inverse(X), X, identity)),
% 0.48/0.65 inference(skolemize,[status(sab)],[14])).
% 0.48/0.65 tff(16,plain,
% 0.48/0.65 (![X: $i] : product(inverse(X), X, identity)),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.48/0.65 tff(17,plain,
% 0.48/0.65 ((~![X: $i] : product(inverse(X), X, identity)) | product(inverse(identity), identity, identity)),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(18,plain,
% 0.48/0.65 (product(inverse(identity), identity, identity)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.48/0.65 tff(19,plain,
% 0.48/0.65 (^[W: $i, Z: $i, Y: $i, X: $i] : refl(((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z))) <=> ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(20,plain,
% 0.48/0.65 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[19])).
% 0.48/0.65 tff(21,plain,
% 0.48/0.65 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(22,plain,
% 0.48/0.65 (^[W: $i, Z: $i, Y: $i, X: $i] : rewrite((((~product(X, Y, Z)) | (~product(X, Y, W))) | (Z = W)) <=> ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(23,plain,
% 0.48/0.65 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, Y, Z)) | (~product(X, Y, W))) | (Z = W)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[22])).
% 0.48/0.65 tff(24,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, Y, Z)) | (~product(X, Y, W))) | (Z = W))), file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax','total_function2')).
% 0.48/0.65 tff(25,plain,
% 0.48/0.65 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.48/0.65 tff(26,plain,
% 0.48/0.65 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.48/0.65 tff(27,plain,(
% 0.48/0.65 ![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.48/0.65 inference(skolemize,[status(sab)],[26])).
% 0.48/0.65 tff(28,plain,
% 0.48/0.65 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.48/0.65 tff(29,plain,
% 0.48/0.65 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((inverse(identity) = identity) | (~product(inverse(identity), identity, inverse(identity))) | (~product(inverse(identity), identity, identity)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (inverse(identity) = identity) | (~product(inverse(identity), identity, inverse(identity))) | (~product(inverse(identity), identity, identity)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(30,plain,
% 0.48/0.65 (((inverse(identity) = identity) | (~product(inverse(identity), identity, identity)) | (~product(inverse(identity), identity, inverse(identity)))) <=> ((inverse(identity) = identity) | (~product(inverse(identity), identity, inverse(identity))) | (~product(inverse(identity), identity, identity)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(31,plain,
% 0.48/0.65 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((inverse(identity) = identity) | (~product(inverse(identity), identity, identity)) | (~product(inverse(identity), identity, inverse(identity))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((inverse(identity) = identity) | (~product(inverse(identity), identity, inverse(identity))) | (~product(inverse(identity), identity, identity))))),
% 0.48/0.65 inference(monotonicity,[status(thm)],[30])).
% 0.48/0.65 tff(32,plain,
% 0.48/0.65 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((inverse(identity) = identity) | (~product(inverse(identity), identity, identity)) | (~product(inverse(identity), identity, inverse(identity))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (inverse(identity) = identity) | (~product(inverse(identity), identity, inverse(identity))) | (~product(inverse(identity), identity, identity)))),
% 0.48/0.65 inference(transitivity,[status(thm)],[31, 29])).
% 0.48/0.65 tff(33,plain,
% 0.48/0.65 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((inverse(identity) = identity) | (~product(inverse(identity), identity, identity)) | (~product(inverse(identity), identity, inverse(identity))))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(34,plain,
% 0.48/0.65 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (inverse(identity) = identity) | (~product(inverse(identity), identity, inverse(identity))) | (~product(inverse(identity), identity, identity))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.48/0.65 tff(35,plain,
% 0.48/0.65 (inverse(identity) = identity),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[34, 28, 18, 9])).
% 0.48/0.65 tff(36,plain,
% 0.48/0.65 (j(inverse(identity)) = j(identity)),
% 0.48/0.65 inference(monotonicity,[status(thm)],[35])).
% 0.48/0.65 tff(37,plain,
% 0.48/0.65 (j(identity) = j(inverse(identity))),
% 0.48/0.65 inference(symmetry,[status(thm)],[36])).
% 0.48/0.65 tff(38,plain,
% 0.48/0.65 (product(j(identity), inverse(j(inverse(identity))), identity) <=> product(j(inverse(identity)), inverse(j(inverse(identity))), identity)),
% 0.48/0.65 inference(monotonicity,[status(thm)],[37])).
% 0.48/0.65 tff(39,plain,
% 0.48/0.65 (product(j(inverse(identity)), inverse(j(inverse(identity))), identity) <=> product(j(identity), inverse(j(inverse(identity))), identity)),
% 0.48/0.65 inference(symmetry,[status(thm)],[38])).
% 0.48/0.65 tff(40,plain,
% 0.48/0.65 (^[X: $i] : refl(product(X, inverse(X), identity) <=> product(X, inverse(X), identity))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(41,plain,
% 0.48/0.65 (![X: $i] : product(X, inverse(X), identity) <=> ![X: $i] : product(X, inverse(X), identity)),
% 0.48/0.65 inference(quant_intro,[status(thm)],[40])).
% 0.48/0.65 tff(42,plain,
% 0.48/0.65 (![X: $i] : product(X, inverse(X), identity) <=> ![X: $i] : product(X, inverse(X), identity)),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(43,axiom,(![X: $i] : product(X, inverse(X), identity)), file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax','right_inverse')).
% 0.48/0.65 tff(44,plain,
% 0.48/0.65 (![X: $i] : product(X, inverse(X), identity)),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.48/0.65 tff(45,plain,(
% 0.48/0.65 ![X: $i] : product(X, inverse(X), identity)),
% 0.48/0.65 inference(skolemize,[status(sab)],[44])).
% 0.48/0.65 tff(46,plain,
% 0.48/0.65 (![X: $i] : product(X, inverse(X), identity)),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.48/0.65 tff(47,plain,
% 0.48/0.65 ((~![X: $i] : product(X, inverse(X), identity)) | product(j(inverse(identity)), inverse(j(inverse(identity))), identity)),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(48,plain,
% 0.48/0.65 (product(j(inverse(identity)), inverse(j(inverse(identity))), identity)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.48/0.65 tff(49,plain,
% 0.48/0.65 (product(j(identity), inverse(j(inverse(identity))), identity)),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[48, 39])).
% 0.48/0.65 tff(50,plain,
% 0.48/0.65 (product(inverse(j(inverse(identity))), j(identity), identity) <=> product(inverse(j(inverse(identity))), j(inverse(identity)), identity)),
% 0.48/0.65 inference(monotonicity,[status(thm)],[37])).
% 0.48/0.65 tff(51,plain,
% 0.48/0.65 (product(inverse(j(inverse(identity))), j(inverse(identity)), identity) <=> product(inverse(j(inverse(identity))), j(identity), identity)),
% 0.48/0.65 inference(symmetry,[status(thm)],[50])).
% 0.48/0.65 tff(52,assumption,(~product(inverse(j(inverse(identity))), j(inverse(identity)), identity)), introduced(assumption)).
% 0.48/0.65 tff(53,plain,
% 0.48/0.65 ((~![X: $i] : product(inverse(X), X, identity)) | product(inverse(j(inverse(identity))), j(inverse(identity)), identity)),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(54,plain,
% 0.48/0.65 ($false),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[53, 16, 52])).
% 0.48/0.65 tff(55,plain,(product(inverse(j(inverse(identity))), j(inverse(identity)), identity)), inference(lemma,lemma(discharge,[]))).
% 0.48/0.65 tff(56,plain,
% 0.48/0.65 (product(inverse(j(inverse(identity))), j(identity), identity)),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.48/0.65 tff(57,assumption,(product(inverse(j(inverse(identity))), j(inverse(identity)), identity)), introduced(assumption)).
% 0.48/0.65 tff(58,plain,
% 0.48/0.65 (product(inverse(j(inverse(identity))), j(identity), identity)),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[57, 51])).
% 0.48/0.65 tff(59,assumption,(~product(identity, j(identity), h(identity))), introduced(assumption)).
% 0.48/0.65 tff(60,plain,
% 0.48/0.65 ((~q(identity)) <=> (~q(identity))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(61,axiom,(~q(identity)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_identity_is_q')).
% 0.48/0.65 tff(62,plain,
% 0.48/0.65 (~q(identity)),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.48/0.65 tff(63,plain,
% 0.48/0.65 (^[A: $i] : refl((q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A))) <=> (q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(64,plain,
% 0.48/0.65 (![A: $i] : (q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A))) <=> ![A: $i] : (q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A)))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[63])).
% 0.48/0.65 tff(65,plain,
% 0.48/0.65 (![A: $i] : (q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A))) <=> ![A: $i] : (q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(66,plain,
% 0.48/0.65 (^[A: $i] : rewrite(((product(j(A), A, h(A)) | product(A, j(A), h(A))) | q(A)) <=> (q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(67,plain,
% 0.48/0.65 (![A: $i] : ((product(j(A), A, h(A)) | product(A, j(A), h(A))) | q(A)) <=> ![A: $i] : (q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A)))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[66])).
% 0.48/0.65 tff(68,axiom,(![A: $i] : ((product(j(A), A, h(A)) | product(A, j(A), h(A))) | q(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','unknown_meaning3')).
% 0.48/0.65 tff(69,plain,
% 0.48/0.65 (![A: $i] : (q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.48/0.65 tff(70,plain,
% 0.48/0.65 (![A: $i] : (q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.48/0.65 tff(71,plain,(
% 0.48/0.65 ![A: $i] : (q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A)))),
% 0.48/0.65 inference(skolemize,[status(sab)],[70])).
% 0.48/0.65 tff(72,plain,
% 0.48/0.65 (![A: $i] : (q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.48/0.65 tff(73,plain,
% 0.48/0.65 (((~![A: $i] : (q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A)))) | (q(identity) | product(identity, j(identity), h(identity)) | product(j(identity), identity, h(identity)))) <=> ((~![A: $i] : (q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A)))) | q(identity) | product(identity, j(identity), h(identity)) | product(j(identity), identity, h(identity)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(74,plain,
% 0.48/0.65 ((~![A: $i] : (q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A)))) | (q(identity) | product(identity, j(identity), h(identity)) | product(j(identity), identity, h(identity)))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(75,plain,
% 0.48/0.65 ((~![A: $i] : (q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A)))) | q(identity) | product(identity, j(identity), h(identity)) | product(j(identity), identity, h(identity))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.48/0.65 tff(76,plain,
% 0.48/0.65 (product(identity, j(identity), h(identity)) | product(j(identity), identity, h(identity))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[75, 72, 62])).
% 0.48/0.65 tff(77,plain,
% 0.48/0.65 (product(j(identity), identity, h(identity))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[76, 59])).
% 0.48/0.65 tff(78,plain,
% 0.48/0.65 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : refl((product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W))) <=> (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(79,plain,
% 0.48/0.65 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[78])).
% 0.48/0.65 tff(80,plain,
% 0.48/0.65 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(81,plain,
% 0.48/0.65 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(rewrite((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(X, V, W))) <=> ((~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))), (((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(X, V, W))) | product(U, Z, W)) <=> (((~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W))) | product(U, Z, W)))), rewrite((((~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W))) | product(U, Z, W)) <=> (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))), (((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(X, V, W))) | product(U, Z, W)) <=> (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(82,plain,
% 0.48/0.65 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(X, V, W))) | product(U, Z, W)) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[81])).
% 0.48/0.65 tff(83,axiom,(![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(X, V, W))) | product(U, Z, W))), file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax','associativity2')).
% 0.48/0.65 tff(84,plain,
% 0.48/0.65 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.48/0.65 tff(85,plain,
% 0.48/0.65 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.48/0.65 tff(86,plain,(
% 0.48/0.65 ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))),
% 0.48/0.65 inference(skolemize,[status(sab)],[85])).
% 0.48/0.65 tff(87,plain,
% 0.48/0.65 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.48/0.65 tff(88,plain,
% 0.48/0.65 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(identity, j(identity), h(identity)) | (~product(j(identity), identity, h(identity))) | (~product(j(identity), inverse(j(inverse(identity))), identity)) | (~product(inverse(j(inverse(identity))), j(identity), identity)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | product(identity, j(identity), h(identity)) | (~product(j(identity), identity, h(identity))) | (~product(j(identity), inverse(j(inverse(identity))), identity)) | (~product(inverse(j(inverse(identity))), j(identity), identity)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(89,plain,
% 0.48/0.65 ((product(identity, j(identity), h(identity)) | (~product(inverse(j(inverse(identity))), j(identity), identity)) | (~product(j(identity), inverse(j(inverse(identity))), identity)) | (~product(j(identity), identity, h(identity)))) <=> (product(identity, j(identity), h(identity)) | (~product(j(identity), identity, h(identity))) | (~product(j(identity), inverse(j(inverse(identity))), identity)) | (~product(inverse(j(inverse(identity))), j(identity), identity)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(90,plain,
% 0.48/0.65 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(identity, j(identity), h(identity)) | (~product(inverse(j(inverse(identity))), j(identity), identity)) | (~product(j(identity), inverse(j(inverse(identity))), identity)) | (~product(j(identity), identity, h(identity))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(identity, j(identity), h(identity)) | (~product(j(identity), identity, h(identity))) | (~product(j(identity), inverse(j(inverse(identity))), identity)) | (~product(inverse(j(inverse(identity))), j(identity), identity))))),
% 0.48/0.65 inference(monotonicity,[status(thm)],[89])).
% 0.48/0.65 tff(91,plain,
% 0.48/0.65 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(identity, j(identity), h(identity)) | (~product(inverse(j(inverse(identity))), j(identity), identity)) | (~product(j(identity), inverse(j(inverse(identity))), identity)) | (~product(j(identity), identity, h(identity))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | product(identity, j(identity), h(identity)) | (~product(j(identity), identity, h(identity))) | (~product(j(identity), inverse(j(inverse(identity))), identity)) | (~product(inverse(j(inverse(identity))), j(identity), identity)))),
% 0.48/0.65 inference(transitivity,[status(thm)],[90, 88])).
% 0.48/0.65 tff(92,plain,
% 0.48/0.65 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(identity, j(identity), h(identity)) | (~product(inverse(j(inverse(identity))), j(identity), identity)) | (~product(j(identity), inverse(j(inverse(identity))), identity)) | (~product(j(identity), identity, h(identity))))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(93,plain,
% 0.48/0.65 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | product(identity, j(identity), h(identity)) | (~product(j(identity), identity, h(identity))) | (~product(j(identity), inverse(j(inverse(identity))), identity)) | (~product(inverse(j(inverse(identity))), j(identity), identity))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.48/0.65 tff(94,plain,
% 0.48/0.65 ((~product(j(identity), inverse(j(inverse(identity))), identity)) | (~product(inverse(j(inverse(identity))), j(identity), identity))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[93, 87, 59, 77])).
% 0.48/0.65 tff(95,plain,
% 0.48/0.65 ($false),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[94, 58, 49])).
% 0.48/0.65 tff(96,plain,((~product(inverse(j(inverse(identity))), j(inverse(identity)), identity)) | product(identity, j(identity), h(identity))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.65 tff(97,plain,
% 0.48/0.65 (product(identity, j(identity), h(identity))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[96, 55])).
% 0.48/0.65 tff(98,plain,
% 0.48/0.65 (^[A: $i] : refl((q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A)))) <=> (q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A)))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(99,plain,
% 0.48/0.65 (![A: $i] : (q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A)))) <=> ![A: $i] : (q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A))))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[98])).
% 0.48/0.65 tff(100,plain,
% 0.48/0.65 (![A: $i] : (q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A)))) <=> ![A: $i] : (q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A))))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(101,plain,
% 0.48/0.65 (^[A: $i] : rewrite((((~product(j(A), A, h(A))) | (~product(A, j(A), h(A)))) | q(A)) <=> (q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A)))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(102,plain,
% 0.48/0.65 (![A: $i] : (((~product(j(A), A, h(A))) | (~product(A, j(A), h(A)))) | q(A)) <=> ![A: $i] : (q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A))))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[101])).
% 0.48/0.65 tff(103,axiom,(![A: $i] : (((~product(j(A), A, h(A))) | (~product(A, j(A), h(A)))) | q(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','unknown_meaning4')).
% 0.48/0.65 tff(104,plain,
% 0.48/0.65 (![A: $i] : (q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A))))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.48/0.65 tff(105,plain,
% 0.48/0.65 (![A: $i] : (q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A))))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.48/0.65 tff(106,plain,(
% 0.48/0.65 ![A: $i] : (q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A))))),
% 0.48/0.65 inference(skolemize,[status(sab)],[105])).
% 0.48/0.65 tff(107,plain,
% 0.48/0.65 (![A: $i] : (q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A))))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.48/0.65 tff(108,plain,
% 0.48/0.65 (((~![A: $i] : (q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A))))) | (q(identity) | (~product(identity, j(identity), h(identity))) | (~product(j(identity), identity, h(identity))))) <=> ((~![A: $i] : (q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A))))) | q(identity) | (~product(identity, j(identity), h(identity))) | (~product(j(identity), identity, h(identity))))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(109,plain,
% 0.48/0.65 ((~![A: $i] : (q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A))))) | (q(identity) | (~product(identity, j(identity), h(identity))) | (~product(j(identity), identity, h(identity))))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(110,plain,
% 0.48/0.65 ((~![A: $i] : (q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A))))) | q(identity) | (~product(identity, j(identity), h(identity))) | (~product(j(identity), identity, h(identity)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.48/0.65 tff(111,plain,
% 0.48/0.65 ((~product(identity, j(identity), h(identity))) | (~product(j(identity), identity, h(identity)))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[110, 107, 62])).
% 0.48/0.65 tff(112,plain,
% 0.48/0.65 (~product(j(identity), identity, h(identity))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[111, 97])).
% 0.48/0.65 tff(113,plain,
% 0.48/0.65 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : refl((product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U))) <=> (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(114,plain,
% 0.48/0.65 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[113])).
% 0.48/0.65 tff(115,plain,
% 0.48/0.65 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(116,plain,
% 0.48/0.65 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(rewrite((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(U, Z, W))) <=> ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))), (((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(U, Z, W))) | product(X, V, W)) <=> (((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U))) | product(X, V, W)))), rewrite((((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U))) | product(X, V, W)) <=> (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))), (((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(U, Z, W))) | product(X, V, W)) <=> (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(117,plain,
% 0.48/0.65 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(U, Z, W))) | product(X, V, W)) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[116])).
% 0.48/0.65 tff(118,axiom,(![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(U, Z, W))) | product(X, V, W))), file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax','associativity1')).
% 0.48/0.65 tff(119,plain,
% 0.48/0.65 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.48/0.65 tff(120,plain,
% 0.48/0.65 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.48/0.65 tff(121,plain,(
% 0.48/0.65 ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 0.48/0.65 inference(skolemize,[status(sab)],[120])).
% 0.48/0.65 tff(122,plain,
% 0.48/0.65 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.48/0.65 tff(123,plain,
% 0.48/0.65 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(j(identity), identity, h(identity)) | (~product(identity, j(identity), h(identity))) | (~product(j(identity), inverse(j(inverse(identity))), identity)) | (~product(inverse(j(inverse(identity))), j(identity), identity)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | product(j(identity), identity, h(identity)) | (~product(identity, j(identity), h(identity))) | (~product(j(identity), inverse(j(inverse(identity))), identity)) | (~product(inverse(j(inverse(identity))), j(identity), identity)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(124,plain,
% 0.48/0.66 ((product(j(identity), identity, h(identity)) | (~product(identity, j(identity), h(identity))) | (~product(inverse(j(inverse(identity))), j(identity), identity)) | (~product(j(identity), inverse(j(inverse(identity))), identity))) <=> (product(j(identity), identity, h(identity)) | (~product(identity, j(identity), h(identity))) | (~product(j(identity), inverse(j(inverse(identity))), identity)) | (~product(inverse(j(inverse(identity))), j(identity), identity)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(125,plain,
% 0.48/0.66 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(j(identity), identity, h(identity)) | (~product(identity, j(identity), h(identity))) | (~product(inverse(j(inverse(identity))), j(identity), identity)) | (~product(j(identity), inverse(j(inverse(identity))), identity)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(j(identity), identity, h(identity)) | (~product(identity, j(identity), h(identity))) | (~product(j(identity), inverse(j(inverse(identity))), identity)) | (~product(inverse(j(inverse(identity))), j(identity), identity))))),
% 0.48/0.66 inference(monotonicity,[status(thm)],[124])).
% 0.48/0.66 tff(126,plain,
% 0.48/0.66 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(j(identity), identity, h(identity)) | (~product(identity, j(identity), h(identity))) | (~product(inverse(j(inverse(identity))), j(identity), identity)) | (~product(j(identity), inverse(j(inverse(identity))), identity)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | product(j(identity), identity, h(identity)) | (~product(identity, j(identity), h(identity))) | (~product(j(identity), inverse(j(inverse(identity))), identity)) | (~product(inverse(j(inverse(identity))), j(identity), identity)))),
% 0.48/0.66 inference(transitivity,[status(thm)],[125, 123])).
% 0.48/0.66 tff(127,plain,
% 0.48/0.66 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(j(identity), identity, h(identity)) | (~product(identity, j(identity), h(identity))) | (~product(inverse(j(inverse(identity))), j(identity), identity)) | (~product(j(identity), inverse(j(inverse(identity))), identity)))),
% 0.48/0.66 inference(quant_inst,[status(thm)],[])).
% 0.48/0.66 tff(128,plain,
% 0.48/0.66 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | product(j(identity), identity, h(identity)) | (~product(identity, j(identity), h(identity))) | (~product(j(identity), inverse(j(inverse(identity))), identity)) | (~product(inverse(j(inverse(identity))), j(identity), identity))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.48/0.66 tff(129,plain,
% 0.48/0.66 ((~product(j(identity), inverse(j(inverse(identity))), identity)) | (~product(inverse(j(inverse(identity))), j(identity), identity))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[128, 122, 97, 112])).
% 0.48/0.66 tff(130,plain,
% 0.48/0.66 ($false),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[129, 56, 49])).
% 0.48/0.66 % SZS output end Proof
% 0.48/0.66 % E exiting
%------------------------------------------------------------------------------