%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP042-2 : 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 05:06:56 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP042-2 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 15:32:11 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.19/0.41 % SZS status Unsatisfiable
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(product_type, type, (
% 0.19/0.41 product: ( $i * $i * $i ) > $o)).
% 0.19/0.41 tff(a_type, type, (
% 0.19/0.41 a: $i)).
% 0.19/0.41 tff(multiply_type, type, (
% 0.19/0.41 multiply: ( $i * $i ) > $i)).
% 0.19/0.41 tff(b_type, type, (
% 0.19/0.41 b: $i)).
% 0.19/0.41 tff(inverse_type, type, (
% 0.19/0.41 inverse: $i > $i)).
% 0.19/0.41 tff(identity_type, type, (
% 0.19/0.41 identity: $i)).
% 0.19/0.41 tff(equalish_type, type, (
% 0.19/0.41 equalish: ( $i * $i ) > $o)).
% 0.19/0.41 tff(1,plain,
% 0.19/0.41 (^[Y: $i, X: $i] : refl(product(X, Y, multiply(X, Y)) <=> product(X, Y, multiply(X, Y)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 (![Y: $i, X: $i] : product(X, Y, multiply(X, Y)) <=> ![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 (![Y: $i, X: $i] : product(X, Y, multiply(X, Y)) <=> ![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(4,axiom,(![Y: $i, X: $i] : product(X, Y, multiply(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax','total_function1')).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 (![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.41 tff(6,plain,(
% 0.19/0.41 ![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 0.19/0.41 inference(skolemize,[status(sab)],[5])).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 ((~![Y: $i, X: $i] : product(X, Y, multiply(X, Y))) | product(b, a, multiply(b, a))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(9,plain,
% 0.19/0.41 (product(b, a, multiply(b, a))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (^[X: $i] : refl(product(inverse(X), X, identity) <=> product(inverse(X), X, identity))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(11,plain,
% 0.19/0.41 (![X: $i] : product(inverse(X), X, identity) <=> ![X: $i] : product(inverse(X), X, identity)),
% 0.19/0.41 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 (![X: $i] : product(inverse(X), X, identity) <=> ![X: $i] : product(inverse(X), X, identity)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(13,axiom,(![X: $i] : product(inverse(X), X, identity)), file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax','left_inverse')).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 (![X: $i] : product(inverse(X), X, identity)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.41 tff(15,plain,(
% 0.19/0.41 ![X: $i] : product(inverse(X), X, identity)),
% 0.19/0.41 inference(skolemize,[status(sab)],[14])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (![X: $i] : product(inverse(X), X, identity)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 ((~![X: $i] : product(inverse(X), X, identity)) | product(inverse(b), b, identity)),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 (product(inverse(b), b, identity)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (^[X: $i] : refl(product(identity, X, X) <=> product(identity, X, X))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 (![X: $i] : product(identity, X, X) <=> ![X: $i] : product(identity, X, X)),
% 0.19/0.41 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (![X: $i] : product(identity, X, X) <=> ![X: $i] : product(identity, X, X)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(22,axiom,(![X: $i] : product(identity, X, X)), file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax','left_identity')).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 (![X: $i] : product(identity, X, X)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.41 tff(24,plain,(
% 0.19/0.41 ![X: $i] : product(identity, X, X)),
% 0.19/0.41 inference(skolemize,[status(sab)],[23])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 (![X: $i] : product(identity, X, X)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 ((~![X: $i] : product(identity, X, X)) | product(identity, a, a)),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 (product(identity, a, a)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[28])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (^[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)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.41 tff(33,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/sandbox2/benchmark/Axioms/GRP005-0.ax','associativity1')).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.19/0.41 tff(36,plain,(
% 0.19/0.41 ![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)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[35])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (((~![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(identity, a, a)) | (~product(inverse(b), b, identity)) | (~product(b, a, multiply(b, a))) | product(inverse(b), multiply(b, a), 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(identity, a, a)) | (~product(inverse(b), b, identity)) | (~product(b, a, multiply(b, a))) | product(inverse(b), multiply(b, a), a))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 ((product(inverse(b), multiply(b, a), a) | (~product(identity, a, a)) | (~product(b, a, multiply(b, a))) | (~product(inverse(b), b, identity))) <=> ((~product(identity, a, a)) | (~product(inverse(b), b, identity)) | (~product(b, a, multiply(b, a))) | product(inverse(b), multiply(b, a), a))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 (((~![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(b), multiply(b, a), a) | (~product(identity, a, a)) | (~product(b, a, multiply(b, a))) | (~product(inverse(b), 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(identity, a, a)) | (~product(inverse(b), b, identity)) | (~product(b, a, multiply(b, a))) | product(inverse(b), multiply(b, a), a)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[39])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (((~![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(b), multiply(b, a), a) | (~product(identity, a, a)) | (~product(b, a, multiply(b, a))) | (~product(inverse(b), 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(identity, a, a)) | (~product(inverse(b), b, identity)) | (~product(b, a, multiply(b, a))) | product(inverse(b), multiply(b, a), a))),
% 0.19/0.41 inference(transitivity,[status(thm)],[40, 38])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 ((~![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(b), multiply(b, a), a) | (~product(identity, a, a)) | (~product(b, a, multiply(b, a))) | (~product(inverse(b), b, identity)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 ((~![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(identity, a, a)) | (~product(inverse(b), b, identity)) | (~product(b, a, multiply(b, a))) | product(inverse(b), multiply(b, a), a)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 (product(inverse(b), multiply(b, a), a)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[43, 37, 27, 18, 9])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 ((~![X: $i] : product(identity, X, X)) | product(identity, inverse(b), inverse(b))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 (product(identity, inverse(b), inverse(b))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[45, 25])).
% 0.19/0.41 tff(47,assumption,(~product(inverse(b), multiply(b, a), b)), introduced(assumption)).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (equalish(a, b) <=> equalish(a, b)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(49,axiom,(equalish(a, b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_equals_b')).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 (equalish(a, b)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (^[W: $i, Z: $i, Y: $i, X: $i] : refl(((~product(W, Z, X)) | product(W, Z, Y) | (~equalish(X, Y))) <=> ((~product(W, Z, X)) | product(W, Z, Y) | (~equalish(X, Y))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Z, X)) | product(W, Z, Y) | (~equalish(X, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Z, X)) | product(W, Z, Y) | (~equalish(X, Y)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[51])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Z, X)) | product(W, Z, Y) | (~equalish(X, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Z, X)) | product(W, Z, Y) | (~equalish(X, Y)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (^[W: $i, Z: $i, Y: $i, X: $i] : rewrite((((~equalish(X, Y)) | (~product(W, Z, X))) | product(W, Z, Y)) <=> ((~product(W, Z, X)) | product(W, Z, Y) | (~equalish(X, Y))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (((~equalish(X, Y)) | (~product(W, Z, X))) | product(W, Z, Y)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Z, X)) | product(W, Z, Y) | (~equalish(X, Y)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.41 tff(56,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~equalish(X, Y)) | (~product(W, Z, X))) | product(W, Z, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax','product_substitution3')).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Z, X)) | product(W, Z, Y) | (~equalish(X, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.42 tff(58,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Z, X)) | product(W, Z, Y) | (~equalish(X, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.19/0.42 tff(59,plain,(
% 0.19/0.42 ![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Z, X)) | product(W, Z, Y) | (~equalish(X, Y)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[58])).
% 0.19/0.42 tff(60,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Z, X)) | product(W, Z, Y) | (~equalish(X, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.19/0.42 tff(61,plain,
% 0.19/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Z, X)) | product(W, Z, Y) | (~equalish(X, Y)))) | ((~equalish(a, b)) | product(inverse(b), multiply(b, a), b) | (~product(inverse(b), multiply(b, a), a)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Z, X)) | product(W, Z, Y) | (~equalish(X, Y)))) | (~equalish(a, b)) | product(inverse(b), multiply(b, a), b) | (~product(inverse(b), multiply(b, a), a)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(62,plain,
% 0.19/0.42 (((~product(inverse(b), multiply(b, a), a)) | product(inverse(b), multiply(b, a), b) | (~equalish(a, b))) <=> ((~equalish(a, b)) | product(inverse(b), multiply(b, a), b) | (~product(inverse(b), multiply(b, a), a)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(63,plain,
% 0.19/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Z, X)) | product(W, Z, Y) | (~equalish(X, Y)))) | ((~product(inverse(b), multiply(b, a), a)) | product(inverse(b), multiply(b, a), b) | (~equalish(a, b)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Z, X)) | product(W, Z, Y) | (~equalish(X, Y)))) | ((~equalish(a, b)) | product(inverse(b), multiply(b, a), b) | (~product(inverse(b), multiply(b, a), a))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[62])).
% 0.19/0.42 tff(64,plain,
% 0.19/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Z, X)) | product(W, Z, Y) | (~equalish(X, Y)))) | ((~product(inverse(b), multiply(b, a), a)) | product(inverse(b), multiply(b, a), b) | (~equalish(a, b)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Z, X)) | product(W, Z, Y) | (~equalish(X, Y)))) | (~equalish(a, b)) | product(inverse(b), multiply(b, a), b) | (~product(inverse(b), multiply(b, a), a)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[63, 61])).
% 0.19/0.42 tff(65,plain,
% 0.19/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Z, X)) | product(W, Z, Y) | (~equalish(X, Y)))) | ((~product(inverse(b), multiply(b, a), a)) | product(inverse(b), multiply(b, a), b) | (~equalish(a, b)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(66,plain,
% 0.19/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Z, X)) | product(W, Z, Y) | (~equalish(X, Y)))) | (~equalish(a, b)) | product(inverse(b), multiply(b, a), b) | (~product(inverse(b), multiply(b, a), a))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.19/0.42 tff(67,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[66, 60, 50, 47, 44])).
% 0.19/0.42 tff(68,plain,(product(inverse(b), multiply(b, a), b)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(69,assumption,(~product(identity, b, b)), introduced(assumption)).
% 0.19/0.42 tff(70,plain,
% 0.19/0.42 ((~![X: $i] : product(identity, X, X)) | product(identity, b, b)),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(71,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[70, 25, 69])).
% 0.19/0.42 tff(72,plain,(product(identity, b, b)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(73,plain,
% 0.19/0.42 ((~equalish(b, a)) <=> (~equalish(b, a))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(74,axiom,(~equalish(b, a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_symmetry')).
% 0.19/0.42 tff(75,plain,
% 0.19/0.42 (~equalish(b, a)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.19/0.42 tff(76,plain,
% 0.19/0.42 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(Z, W) | (~product(X, Y, W)) | (~product(X, Y, Z))) <=> (equalish(Z, W) | (~product(X, Y, W)) | (~product(X, Y, Z))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(77,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(Z, W) | (~product(X, Y, W)) | (~product(X, Y, Z))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(Z, W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[76])).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(Z, W) | (~product(X, Y, W)) | (~product(X, Y, Z))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(Z, W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 (^[W: $i, Z: $i, Y: $i, X: $i] : rewrite((((~product(X, Y, Z)) | (~product(X, Y, W))) | equalish(Z, W)) <=> (equalish(Z, W) | (~product(X, Y, W)) | (~product(X, Y, Z))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, Y, Z)) | (~product(X, Y, W))) | equalish(Z, W)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(Z, W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[79])).
% 0.19/0.42 tff(81,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, Y, Z)) | (~product(X, Y, W))) | equalish(Z, W))), file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax','total_function2')).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(Z, W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(Z, W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.19/0.42 tff(84,plain,(
% 0.19/0.42 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(Z, W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[83])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(Z, W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(Z, W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (equalish(b, a) | (~product(identity, b, a)) | (~product(identity, b, b)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(Z, W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | equalish(b, a) | (~product(identity, b, a)) | (~product(identity, b, b)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(Z, W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (equalish(b, a) | (~product(identity, b, a)) | (~product(identity, b, b)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(Z, W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | equalish(b, a) | (~product(identity, b, a)) | (~product(identity, b, b))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 ((~product(identity, b, a)) | (~product(identity, b, b))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[88, 85, 75])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 (~product(identity, b, a)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[89, 72])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 (((~![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(identity, b, a) | (~product(inverse(b), multiply(b, a), b)) | (~product(identity, inverse(b), inverse(b))) | (~product(inverse(b), multiply(b, a), 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(identity, b, a) | (~product(inverse(b), multiply(b, a), b)) | (~product(identity, inverse(b), inverse(b))) | (~product(inverse(b), multiply(b, a), a)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 ((product(identity, b, a) | (~product(inverse(b), multiply(b, a), a)) | (~product(inverse(b), multiply(b, a), b)) | (~product(identity, inverse(b), inverse(b)))) <=> (product(identity, b, a) | (~product(inverse(b), multiply(b, a), b)) | (~product(identity, inverse(b), inverse(b))) | (~product(inverse(b), multiply(b, a), a)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 (((~![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(identity, b, a) | (~product(inverse(b), multiply(b, a), a)) | (~product(inverse(b), multiply(b, a), b)) | (~product(identity, inverse(b), inverse(b))))) <=> ((~![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(identity, b, a) | (~product(inverse(b), multiply(b, a), b)) | (~product(identity, inverse(b), inverse(b))) | (~product(inverse(b), multiply(b, a), a))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[92])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 (((~![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(identity, b, a) | (~product(inverse(b), multiply(b, a), a)) | (~product(inverse(b), multiply(b, a), b)) | (~product(identity, inverse(b), inverse(b))))) <=> ((~![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(identity, b, a) | (~product(inverse(b), multiply(b, a), b)) | (~product(identity, inverse(b), inverse(b))) | (~product(inverse(b), multiply(b, a), a)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[93, 91])).
% 0.19/0.43 tff(95,plain,
% 0.19/0.43 ((~![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(identity, b, a) | (~product(inverse(b), multiply(b, a), a)) | (~product(inverse(b), multiply(b, a), b)) | (~product(identity, inverse(b), inverse(b))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(96,plain,
% 0.19/0.43 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | product(identity, b, a) | (~product(inverse(b), multiply(b, a), b)) | (~product(identity, inverse(b), inverse(b))) | (~product(inverse(b), multiply(b, a), a))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.19/0.43 tff(97,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[96, 37, 90, 68, 46, 44])).
% 0.19/0.43 % SZS output end Proof
% 0.19/0.43 % E exiting
%------------------------------------------------------------------------------