%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP012-2 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:06:50 AM UTC 2025
% Result : Unsatisfiable 3.85s 4.12s
% Output : Proof 3.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP012-2 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n010.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 15:29:26 EDT 2025
% 0.11/0.33 % CPUTime :
% 3.85/4.12 % SZS status Unsatisfiable
% 3.85/4.12 % SZS output start Proof
% 3.85/4.12 tff(product_type, type, (
% 3.85/4.12 product: ( $i * $i * $i ) > $o)).
% 3.85/4.12 tff(d_type, type, (
% 3.85/4.12 d: $i)).
% 3.85/4.12 tff(identity_type, type, (
% 3.85/4.12 identity: $i)).
% 3.85/4.12 tff(inverse_type, type, (
% 3.85/4.12 inverse: $i > $i)).
% 3.85/4.12 tff(c_type, type, (
% 3.85/4.12 c: $i)).
% 3.85/4.12 tff(a_type, type, (
% 3.85/4.12 a: $i)).
% 3.85/4.12 tff(b_type, type, (
% 3.85/4.12 b: $i)).
% 3.85/4.12 tff(1,assumption,(~product(identity, inverse(a), inverse(a))), introduced(assumption)).
% 3.85/4.12 tff(2,plain,
% 3.85/4.12 (^[X: $i] : refl(product(identity, X, X) <=> product(identity, X, X))),
% 3.85/4.12 inference(bind,[status(th)],[])).
% 3.85/4.12 tff(3,plain,
% 3.85/4.12 (![X: $i] : product(identity, X, X) <=> ![X: $i] : product(identity, X, X)),
% 3.85/4.12 inference(quant_intro,[status(thm)],[2])).
% 3.85/4.12 tff(4,plain,
% 3.85/4.12 (![X: $i] : product(identity, X, X) <=> ![X: $i] : product(identity, X, X)),
% 3.85/4.12 inference(rewrite,[status(thm)],[])).
% 3.85/4.12 tff(5,axiom,(![X: $i] : product(identity, X, X)), file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax','left_identity')).
% 3.85/4.12 tff(6,plain,
% 3.85/4.12 (![X: $i] : product(identity, X, X)),
% 3.85/4.12 inference(modus_ponens,[status(thm)],[5, 4])).
% 3.85/4.12 tff(7,plain,(
% 3.85/4.12 ![X: $i] : product(identity, X, X)),
% 3.85/4.12 inference(skolemize,[status(sab)],[6])).
% 3.85/4.12 tff(8,plain,
% 3.85/4.12 (![X: $i] : product(identity, X, X)),
% 3.85/4.12 inference(modus_ponens,[status(thm)],[7, 3])).
% 3.85/4.12 tff(9,plain,
% 3.85/4.12 ((~![X: $i] : product(identity, X, X)) | product(identity, inverse(a), inverse(a))),
% 3.85/4.12 inference(quant_inst,[status(thm)],[])).
% 3.85/4.12 tff(10,plain,
% 3.85/4.12 ($false),
% 3.85/4.12 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 3.85/4.12 tff(11,plain,(product(identity, inverse(a), inverse(a))), inference(lemma,lemma(discharge,[]))).
% 3.85/4.12 tff(12,plain,
% 3.85/4.12 (^[X: $i] : refl(product(X, inverse(X), identity) <=> product(X, inverse(X), identity))),
% 3.85/4.12 inference(bind,[status(th)],[])).
% 3.85/4.12 tff(13,plain,
% 3.85/4.12 (![X: $i] : product(X, inverse(X), identity) <=> ![X: $i] : product(X, inverse(X), identity)),
% 3.85/4.12 inference(quant_intro,[status(thm)],[12])).
% 3.85/4.12 tff(14,plain,
% 3.85/4.12 (![X: $i] : product(X, inverse(X), identity) <=> ![X: $i] : product(X, inverse(X), identity)),
% 3.85/4.12 inference(rewrite,[status(thm)],[])).
% 3.85/4.12 tff(15,axiom,(![X: $i] : product(X, inverse(X), identity)), file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax','right_inverse')).
% 3.85/4.12 tff(16,plain,
% 3.85/4.12 (![X: $i] : product(X, inverse(X), identity)),
% 3.85/4.12 inference(modus_ponens,[status(thm)],[15, 14])).
% 3.85/4.12 tff(17,plain,(
% 3.85/4.12 ![X: $i] : product(X, inverse(X), identity)),
% 3.85/4.12 inference(skolemize,[status(sab)],[16])).
% 3.85/4.12 tff(18,plain,
% 3.85/4.12 (![X: $i] : product(X, inverse(X), identity)),
% 3.85/4.12 inference(modus_ponens,[status(thm)],[17, 13])).
% 3.85/4.12 tff(19,plain,
% 3.85/4.12 ((~![X: $i] : product(X, inverse(X), identity)) | product(b, inverse(b), identity)),
% 3.85/4.12 inference(quant_inst,[status(thm)],[])).
% 3.85/4.12 tff(20,plain,
% 3.85/4.12 (product(b, inverse(b), identity)),
% 3.85/4.12 inference(unit_resolution,[status(thm)],[19, 18])).
% 3.85/4.12 tff(21,plain,
% 3.85/4.12 (product(inverse(b), inverse(a), d) <=> product(inverse(b), inverse(a), d)),
% 3.85/4.12 inference(rewrite,[status(thm)],[])).
% 3.85/4.12 tff(22,axiom,(product(inverse(b), inverse(a), d)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','inverse_b_multiply_inverse_a_is_d')).
% 3.85/4.12 tff(23,plain,
% 3.85/4.12 (product(inverse(b), inverse(a), d)),
% 3.85/4.12 inference(modus_ponens,[status(thm)],[22, 21])).
% 3.85/4.12 tff(24,plain,
% 3.85/4.12 (^[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))))),
% 3.85/4.12 inference(bind,[status(th)],[])).
% 3.85/4.12 tff(25,plain,
% 3.85/4.12 (![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)))),
% 3.85/4.12 inference(quant_intro,[status(thm)],[24])).
% 3.85/4.12 tff(26,plain,
% 3.85/4.12 (![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)))),
% 3.85/4.12 inference(rewrite,[status(thm)],[])).
% 3.85/4.12 tff(27,plain,
% 3.85/4.12 (^[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)))))),
% 3.85/4.12 inference(bind,[status(th)],[])).
% 3.85/4.12 tff(28,plain,
% 3.85/4.12 (![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)))),
% 3.85/4.12 inference(quant_intro,[status(thm)],[27])).
% 3.85/4.12 tff(29,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')).
% 3.85/4.12 tff(30,plain,
% 3.85/4.12 (![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)))),
% 3.85/4.12 inference(modus_ponens,[status(thm)],[29, 28])).
% 3.85/4.12 tff(31,plain,
% 3.85/4.12 (![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)))),
% 3.85/4.12 inference(modus_ponens,[status(thm)],[30, 26])).
% 3.85/4.12 tff(32,plain,(
% 3.85/4.12 ![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)))),
% 3.85/4.12 inference(skolemize,[status(sab)],[31])).
% 3.85/4.12 tff(33,plain,
% 3.85/4.12 (![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)))),
% 3.85/4.12 inference(modus_ponens,[status(thm)],[32, 25])).
% 3.85/4.12 tff(34,plain,
% 3.85/4.12 (((~![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(b, d, inverse(a)) | (~product(inverse(b), inverse(a), d)) | (~product(b, inverse(b), identity)) | (~product(identity, inverse(a), inverse(a))))) <=> ((~![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(b, d, inverse(a)) | (~product(inverse(b), inverse(a), d)) | (~product(b, inverse(b), identity)) | (~product(identity, inverse(a), inverse(a))))),
% 3.85/4.12 inference(rewrite,[status(thm)],[])).
% 3.85/4.12 tff(35,plain,
% 3.85/4.12 ((product(b, d, inverse(a)) | (~product(identity, inverse(a), inverse(a))) | (~product(inverse(b), inverse(a), d)) | (~product(b, inverse(b), identity))) <=> (product(b, d, inverse(a)) | (~product(inverse(b), inverse(a), d)) | (~product(b, inverse(b), identity)) | (~product(identity, inverse(a), inverse(a))))),
% 3.85/4.12 inference(rewrite,[status(thm)],[])).
% 3.85/4.12 tff(36,plain,
% 3.85/4.12 (((~![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(b, d, inverse(a)) | (~product(identity, inverse(a), inverse(a))) | (~product(inverse(b), inverse(a), d)) | (~product(b, inverse(b), 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(b, d, inverse(a)) | (~product(inverse(b), inverse(a), d)) | (~product(b, inverse(b), identity)) | (~product(identity, inverse(a), inverse(a)))))),
% 3.85/4.12 inference(monotonicity,[status(thm)],[35])).
% 3.85/4.12 tff(37,plain,
% 3.85/4.12 (((~![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(b, d, inverse(a)) | (~product(identity, inverse(a), inverse(a))) | (~product(inverse(b), inverse(a), d)) | (~product(b, inverse(b), 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(b, d, inverse(a)) | (~product(inverse(b), inverse(a), d)) | (~product(b, inverse(b), identity)) | (~product(identity, inverse(a), inverse(a))))),
% 3.94/4.12 inference(transitivity,[status(thm)],[36, 34])).
% 3.94/4.12 tff(38,plain,
% 3.94/4.12 ((~![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(b, d, inverse(a)) | (~product(identity, inverse(a), inverse(a))) | (~product(inverse(b), inverse(a), d)) | (~product(b, inverse(b), identity)))),
% 3.94/4.12 inference(quant_inst,[status(thm)],[])).
% 3.94/4.12 tff(39,plain,
% 3.94/4.12 ((~![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(b, d, inverse(a)) | (~product(inverse(b), inverse(a), d)) | (~product(b, inverse(b), identity)) | (~product(identity, inverse(a), inverse(a)))),
% 3.94/4.12 inference(modus_ponens,[status(thm)],[38, 37])).
% 3.94/4.12 tff(40,plain,
% 3.94/4.12 (product(b, d, inverse(a))),
% 3.94/4.12 inference(unit_resolution,[status(thm)],[39, 33, 23, 20, 11])).
% 3.94/4.12 tff(41,plain,
% 3.94/4.12 ((~![X: $i] : product(X, inverse(X), identity)) | product(a, inverse(a), identity)),
% 3.94/4.12 inference(quant_inst,[status(thm)],[])).
% 3.94/4.12 tff(42,plain,
% 3.94/4.12 (product(a, inverse(a), identity)),
% 3.94/4.12 inference(unit_resolution,[status(thm)],[41, 18])).
% 3.94/4.12 tff(43,plain,
% 3.94/4.12 (product(a, b, c) <=> product(a, b, c)),
% 3.94/4.12 inference(rewrite,[status(thm)],[])).
% 3.94/4.12 tff(44,axiom,(product(a, b, c)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a_multiply_b_is_c')).
% 3.94/4.12 tff(45,plain,
% 3.94/4.12 (product(a, b, c)),
% 3.94/4.12 inference(modus_ponens,[status(thm)],[44, 43])).
% 3.94/4.12 tff(46,plain,
% 3.94/4.12 (^[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))))),
% 3.94/4.12 inference(bind,[status(th)],[])).
% 3.94/4.12 tff(47,plain,
% 3.94/4.12 (![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)))),
% 3.94/4.12 inference(quant_intro,[status(thm)],[46])).
% 3.94/4.12 tff(48,plain,
% 3.94/4.12 (![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)))),
% 3.94/4.12 inference(rewrite,[status(thm)],[])).
% 3.94/4.12 tff(49,plain,
% 3.94/4.12 (^[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)))))),
% 3.94/4.12 inference(bind,[status(th)],[])).
% 3.94/4.12 tff(50,plain,
% 3.94/4.12 (![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)))),
% 3.94/4.12 inference(quant_intro,[status(thm)],[49])).
% 3.94/4.12 tff(51,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')).
% 3.94/4.12 tff(52,plain,
% 3.94/4.12 (![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)))),
% 3.94/4.12 inference(modus_ponens,[status(thm)],[51, 50])).
% 3.94/4.12 tff(53,plain,
% 3.94/4.12 (![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)))),
% 3.94/4.12 inference(modus_ponens,[status(thm)],[52, 48])).
% 3.94/4.12 tff(54,plain,(
% 3.94/4.12 ![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)))),
% 3.94/4.12 inference(skolemize,[status(sab)],[53])).
% 3.94/4.12 tff(55,plain,
% 3.94/4.12 (![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)))),
% 3.94/4.12 inference(modus_ponens,[status(thm)],[54, 47])).
% 3.94/4.12 tff(56,plain,
% 3.94/4.12 (((~![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(b, d, inverse(a))) | (~product(a, inverse(a), identity)) | (~product(a, b, c)) | product(c, d, 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(b, d, inverse(a))) | (~product(a, inverse(a), identity)) | (~product(a, b, c)) | product(c, d, identity))),
% 3.94/4.12 inference(rewrite,[status(thm)],[])).
% 3.94/4.12 tff(57,plain,
% 3.94/4.12 ((product(c, d, identity) | (~product(b, d, inverse(a))) | (~product(a, b, c)) | (~product(a, inverse(a), identity))) <=> ((~product(b, d, inverse(a))) | (~product(a, inverse(a), identity)) | (~product(a, b, c)) | product(c, d, identity))),
% 3.94/4.12 inference(rewrite,[status(thm)],[])).
% 3.94/4.12 tff(58,plain,
% 3.94/4.12 (((~![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(c, d, identity) | (~product(b, d, inverse(a))) | (~product(a, b, c)) | (~product(a, inverse(a), 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(b, d, inverse(a))) | (~product(a, inverse(a), identity)) | (~product(a, b, c)) | product(c, d, identity)))),
% 3.94/4.12 inference(monotonicity,[status(thm)],[57])).
% 3.94/4.12 tff(59,plain,
% 3.94/4.12 (((~![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(c, d, identity) | (~product(b, d, inverse(a))) | (~product(a, b, c)) | (~product(a, inverse(a), 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(b, d, inverse(a))) | (~product(a, inverse(a), identity)) | (~product(a, b, c)) | product(c, d, identity))),
% 3.94/4.12 inference(transitivity,[status(thm)],[58, 56])).
% 3.94/4.12 tff(60,plain,
% 3.94/4.12 ((~![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(c, d, identity) | (~product(b, d, inverse(a))) | (~product(a, b, c)) | (~product(a, inverse(a), identity)))),
% 3.94/4.12 inference(quant_inst,[status(thm)],[])).
% 3.94/4.12 tff(61,plain,
% 3.94/4.12 ((~![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(b, d, inverse(a))) | (~product(a, inverse(a), identity)) | (~product(a, b, c)) | product(c, d, identity)),
% 3.94/4.12 inference(modus_ponens,[status(thm)],[60, 59])).
% 3.94/4.12 tff(62,plain,
% 3.94/4.12 (product(c, d, identity)),
% 3.94/4.12 inference(unit_resolution,[status(thm)],[61, 55, 45, 42, 40])).
% 3.94/4.12 tff(63,plain,
% 3.94/4.12 ((~![X: $i] : product(identity, X, X)) | product(identity, d, d)),
% 3.94/4.12 inference(quant_inst,[status(thm)],[])).
% 3.94/4.12 tff(64,plain,
% 3.94/4.12 (product(identity, d, d)),
% 3.94/4.12 inference(unit_resolution,[status(thm)],[63, 8])).
% 3.94/4.12 tff(65,plain,
% 3.94/4.12 (^[X: $i] : refl(product(inverse(X), X, identity) <=> product(inverse(X), X, identity))),
% 3.94/4.12 inference(bind,[status(th)],[])).
% 3.94/4.12 tff(66,plain,
% 3.94/4.12 (![X: $i] : product(inverse(X), X, identity) <=> ![X: $i] : product(inverse(X), X, identity)),
% 3.94/4.12 inference(quant_intro,[status(thm)],[65])).
% 3.94/4.12 tff(67,plain,
% 3.94/4.12 (![X: $i] : product(inverse(X), X, identity) <=> ![X: $i] : product(inverse(X), X, identity)),
% 3.94/4.12 inference(rewrite,[status(thm)],[])).
% 3.94/4.12 tff(68,axiom,(![X: $i] : product(inverse(X), X, identity)), file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax','left_inverse')).
% 3.94/4.12 tff(69,plain,
% 3.94/4.12 (![X: $i] : product(inverse(X), X, identity)),
% 3.94/4.12 inference(modus_ponens,[status(thm)],[68, 67])).
% 3.94/4.12 tff(70,plain,(
% 3.94/4.12 ![X: $i] : product(inverse(X), X, identity)),
% 3.94/4.12 inference(skolemize,[status(sab)],[69])).
% 3.94/4.12 tff(71,plain,
% 3.94/4.12 (![X: $i] : product(inverse(X), X, identity)),
% 3.94/4.12 inference(modus_ponens,[status(thm)],[70, 66])).
% 3.94/4.12 tff(72,plain,
% 3.94/4.12 ((~![X: $i] : product(inverse(X), X, identity)) | product(inverse(c), c, identity)),
% 3.94/4.12 inference(quant_inst,[status(thm)],[])).
% 3.94/4.12 tff(73,plain,
% 3.94/4.12 (product(inverse(c), c, identity)),
% 3.94/4.12 inference(unit_resolution,[status(thm)],[72, 71])).
% 3.94/4.12 tff(74,plain,
% 3.94/4.12 (((~![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(inverse(c), c, identity)) | (~product(identity, d, d)) | (~product(c, d, identity)) | product(inverse(c), identity, d))) <=> ((~![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(inverse(c), c, identity)) | (~product(identity, d, d)) | (~product(c, d, identity)) | product(inverse(c), identity, d))),
% 3.94/4.12 inference(rewrite,[status(thm)],[])).
% 3.94/4.12 tff(75,plain,
% 3.94/4.12 ((product(inverse(c), identity, d) | (~product(identity, d, d)) | (~product(c, d, identity)) | (~product(inverse(c), c, identity))) <=> ((~product(inverse(c), c, identity)) | (~product(identity, d, d)) | (~product(c, d, identity)) | product(inverse(c), identity, d))),
% 3.94/4.12 inference(rewrite,[status(thm)],[])).
% 3.94/4.12 tff(76,plain,
% 3.94/4.12 (((~![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(inverse(c), identity, d) | (~product(identity, d, d)) | (~product(c, d, identity)) | (~product(inverse(c), c, 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(inverse(c), c, identity)) | (~product(identity, d, d)) | (~product(c, d, identity)) | product(inverse(c), identity, d)))),
% 3.94/4.12 inference(monotonicity,[status(thm)],[75])).
% 3.94/4.12 tff(77,plain,
% 3.94/4.12 (((~![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(inverse(c), identity, d) | (~product(identity, d, d)) | (~product(c, d, identity)) | (~product(inverse(c), c, 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(inverse(c), c, identity)) | (~product(identity, d, d)) | (~product(c, d, identity)) | product(inverse(c), identity, d))),
% 3.94/4.12 inference(transitivity,[status(thm)],[76, 74])).
% 3.94/4.12 tff(78,plain,
% 3.94/4.12 ((~![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(inverse(c), identity, d) | (~product(identity, d, d)) | (~product(c, d, identity)) | (~product(inverse(c), c, identity)))),
% 3.94/4.12 inference(quant_inst,[status(thm)],[])).
% 3.94/4.12 tff(79,plain,
% 3.94/4.12 ((~![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(inverse(c), c, identity)) | (~product(identity, d, d)) | (~product(c, d, identity)) | product(inverse(c), identity, d)),
% 3.94/4.12 inference(modus_ponens,[status(thm)],[78, 77])).
% 3.94/4.12 tff(80,plain,
% 3.94/4.12 (product(inverse(c), identity, d)),
% 3.94/4.12 inference(unit_resolution,[status(thm)],[79, 33, 73, 64, 62])).
% 3.94/4.12 tff(81,plain,
% 3.94/4.12 (^[X: $i] : refl(product(X, identity, X) <=> product(X, identity, X))),
% 3.94/4.12 inference(bind,[status(th)],[])).
% 3.94/4.12 tff(82,plain,
% 3.94/4.12 (![X: $i] : product(X, identity, X) <=> ![X: $i] : product(X, identity, X)),
% 3.94/4.12 inference(quant_intro,[status(thm)],[81])).
% 3.94/4.12 tff(83,plain,
% 3.94/4.12 (![X: $i] : product(X, identity, X) <=> ![X: $i] : product(X, identity, X)),
% 3.94/4.12 inference(rewrite,[status(thm)],[])).
% 3.94/4.12 tff(84,axiom,(![X: $i] : product(X, identity, X)), file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax','right_identity')).
% 3.94/4.12 tff(85,plain,
% 3.94/4.12 (![X: $i] : product(X, identity, X)),
% 3.94/4.12 inference(modus_ponens,[status(thm)],[84, 83])).
% 3.94/4.12 tff(86,plain,(
% 3.94/4.12 ![X: $i] : product(X, identity, X)),
% 3.94/4.12 inference(skolemize,[status(sab)],[85])).
% 3.94/4.12 tff(87,plain,
% 3.94/4.12 (![X: $i] : product(X, identity, X)),
% 3.94/4.12 inference(modus_ponens,[status(thm)],[86, 82])).
% 3.94/4.12 tff(88,plain,
% 3.94/4.12 ((~![X: $i] : product(X, identity, X)) | product(inverse(c), identity, inverse(c))),
% 3.94/4.12 inference(quant_inst,[status(thm)],[])).
% 3.94/4.12 tff(89,plain,
% 3.94/4.12 (product(inverse(c), identity, inverse(c))),
% 3.94/4.12 inference(unit_resolution,[status(thm)],[88, 87])).
% 3.94/4.12 tff(90,plain,
% 3.94/4.12 ((~(inverse(c) = d)) <=> (~(inverse(c) = d))),
% 3.94/4.12 inference(rewrite,[status(thm)],[])).
% 3.94/4.12 tff(91,axiom,(~(inverse(c) = d)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_c_inverse_equals_d')).
% 3.94/4.12 tff(92,plain,
% 3.94/4.12 (~(inverse(c) = d)),
% 3.94/4.12 inference(modus_ponens,[status(thm)],[91, 90])).
% 3.94/4.12 tff(93,plain,
% 3.94/4.12 (^[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))))),
% 3.94/4.12 inference(bind,[status(th)],[])).
% 3.94/4.12 tff(94,plain,
% 3.94/4.12 (![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)))),
% 3.94/4.12 inference(quant_intro,[status(thm)],[93])).
% 3.94/4.12 tff(95,plain,
% 3.94/4.12 (![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)))),
% 3.94/4.12 inference(rewrite,[status(thm)],[])).
% 3.94/4.12 tff(96,plain,
% 3.94/4.12 (^[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))))),
% 3.94/4.12 inference(bind,[status(th)],[])).
% 3.94/4.12 tff(97,plain,
% 3.94/4.12 (![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)))),
% 3.94/4.12 inference(quant_intro,[status(thm)],[96])).
% 3.94/4.12 tff(98,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')).
% 3.94/4.12 tff(99,plain,
% 3.94/4.12 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 3.94/4.12 inference(modus_ponens,[status(thm)],[98, 97])).
% 3.94/4.12 tff(100,plain,
% 3.94/4.12 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 3.94/4.12 inference(modus_ponens,[status(thm)],[99, 95])).
% 3.94/4.12 tff(101,plain,(
% 3.94/4.12 ![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 3.94/4.12 inference(skolemize,[status(sab)],[100])).
% 3.94/4.12 tff(102,plain,
% 3.94/4.12 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 3.94/4.12 inference(modus_ponens,[status(thm)],[101, 94])).
% 3.94/4.12 tff(103,plain,
% 3.94/4.12 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((inverse(c) = d) | (~product(inverse(c), identity, inverse(c))) | (~product(inverse(c), identity, d)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (inverse(c) = d) | (~product(inverse(c), identity, inverse(c))) | (~product(inverse(c), identity, d)))),
% 3.94/4.12 inference(rewrite,[status(thm)],[])).
% 3.94/4.12 tff(104,plain,
% 3.94/4.12 (((inverse(c) = d) | (~product(inverse(c), identity, d)) | (~product(inverse(c), identity, inverse(c)))) <=> ((inverse(c) = d) | (~product(inverse(c), identity, inverse(c))) | (~product(inverse(c), identity, d)))),
% 3.94/4.12 inference(rewrite,[status(thm)],[])).
% 3.94/4.13 tff(105,plain,
% 3.94/4.13 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((inverse(c) = d) | (~product(inverse(c), identity, d)) | (~product(inverse(c), identity, inverse(c))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((inverse(c) = d) | (~product(inverse(c), identity, inverse(c))) | (~product(inverse(c), identity, d))))),
% 3.94/4.13 inference(monotonicity,[status(thm)],[104])).
% 3.94/4.13 tff(106,plain,
% 3.94/4.13 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((inverse(c) = d) | (~product(inverse(c), identity, d)) | (~product(inverse(c), identity, inverse(c))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (inverse(c) = d) | (~product(inverse(c), identity, inverse(c))) | (~product(inverse(c), identity, d)))),
% 3.94/4.13 inference(transitivity,[status(thm)],[105, 103])).
% 3.94/4.13 tff(107,plain,
% 3.94/4.13 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((inverse(c) = d) | (~product(inverse(c), identity, d)) | (~product(inverse(c), identity, inverse(c))))),
% 3.94/4.13 inference(quant_inst,[status(thm)],[])).
% 3.94/4.13 tff(108,plain,
% 3.94/4.13 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (inverse(c) = d) | (~product(inverse(c), identity, inverse(c))) | (~product(inverse(c), identity, d))),
% 3.94/4.13 inference(modus_ponens,[status(thm)],[107, 106])).
% 3.94/4.13 tff(109,plain,
% 3.94/4.13 ($false),
% 3.94/4.13 inference(unit_resolution,[status(thm)],[108, 102, 92, 89, 80])).
% 3.94/4.13 % SZS output end Proof
% 3.94/4.13 % E exiting
%------------------------------------------------------------------------------