%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP029-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:06:53 AM UTC 2025
% Result : Unsatisfiable 12.28s 12.51s
% Output : Proof 12.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP029-1 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 15:30:01 EDT 2025
% 0.12/0.33 % CPUTime :
% 12.28/12.51 % SZS status Unsatisfiable
% 12.28/12.51 % SZS output start Proof
% 12.28/12.51 tff(product_type, type, (
% 12.28/12.51 product: ( $i * $i * $i ) > $o)).
% 12.28/12.51 tff(multiply_type, type, (
% 12.28/12.51 multiply: ( $i * $i ) > $i)).
% 12.28/12.51 tff(not_right_identity_type, type, (
% 12.28/12.51 not_right_identity: $i > $i)).
% 12.28/12.51 tff(identity_type, type, (
% 12.28/12.51 identity: $i)).
% 12.28/12.51 tff(elem_0_type, type, (
% 12.28/12.51 elem_0: $i)).
% 12.28/12.51 tff(inverse_type, type, (
% 12.28/12.51 inverse: $i > $i)).
% 12.28/12.51 tff(1,plain,
% 12.28/12.51 (^[Y: $i, X: $i] : refl(product(X, Y, multiply(X, Y)) <=> product(X, Y, multiply(X, Y)))),
% 12.28/12.51 inference(bind,[status(th)],[])).
% 12.28/12.51 tff(2,plain,
% 12.28/12.51 (![Y: $i, X: $i] : product(X, Y, multiply(X, Y)) <=> ![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 12.28/12.51 inference(quant_intro,[status(thm)],[1])).
% 12.28/12.51 tff(3,plain,
% 12.28/12.51 (![Y: $i, X: $i] : product(X, Y, multiply(X, Y)) <=> ![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 12.28/12.51 inference(rewrite,[status(thm)],[])).
% 12.28/12.51 tff(4,axiom,(![Y: $i, X: $i] : product(X, Y, multiply(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GRP002-0.ax','total_function1')).
% 12.28/12.51 tff(5,plain,
% 12.28/12.51 (![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 12.28/12.51 inference(modus_ponens,[status(thm)],[4, 3])).
% 12.28/12.51 tff(6,plain,(
% 12.28/12.51 ![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 12.28/12.51 inference(skolemize,[status(sab)],[5])).
% 12.28/12.51 tff(7,plain,
% 12.28/12.51 (![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 12.28/12.51 inference(modus_ponens,[status(thm)],[6, 2])).
% 12.28/12.51 tff(8,plain,
% 12.28/12.51 ((~![Y: $i, X: $i] : product(X, Y, multiply(X, Y))) | product(inverse(elem!0), elem!0, multiply(inverse(elem!0), elem!0))),
% 12.28/12.51 inference(quant_inst,[status(thm)],[])).
% 12.28/12.51 tff(9,plain,
% 12.28/12.51 (product(inverse(elem!0), elem!0, multiply(inverse(elem!0), elem!0))),
% 12.28/12.51 inference(unit_resolution,[status(thm)],[8, 7])).
% 12.28/12.51 tff(10,plain,
% 12.28/12.51 (^[A: $i] : refl(product(inverse(A), A, identity) <=> product(inverse(A), A, identity))),
% 12.28/12.51 inference(bind,[status(th)],[])).
% 12.28/12.51 tff(11,plain,
% 12.28/12.51 (![A: $i] : product(inverse(A), A, identity) <=> ![A: $i] : product(inverse(A), A, identity)),
% 12.28/12.51 inference(quant_intro,[status(thm)],[10])).
% 12.28/12.51 tff(12,plain,
% 12.28/12.51 (![A: $i] : product(inverse(A), A, identity) <=> ![A: $i] : product(inverse(A), A, identity)),
% 12.28/12.51 inference(rewrite,[status(thm)],[])).
% 12.28/12.51 tff(13,axiom,(![A: $i] : product(inverse(A), A, identity)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','left_inverse')).
% 12.28/12.51 tff(14,plain,
% 12.28/12.51 (![A: $i] : product(inverse(A), A, identity)),
% 12.28/12.51 inference(modus_ponens,[status(thm)],[13, 12])).
% 12.28/12.51 tff(15,plain,(
% 12.28/12.51 ![A: $i] : product(inverse(A), A, identity)),
% 12.28/12.51 inference(skolemize,[status(sab)],[14])).
% 12.28/12.51 tff(16,plain,
% 12.28/12.51 (![A: $i] : product(inverse(A), A, identity)),
% 12.28/12.51 inference(modus_ponens,[status(thm)],[15, 11])).
% 12.28/12.51 tff(17,plain,
% 12.28/12.51 ((~![A: $i] : product(inverse(A), A, identity)) | product(inverse(elem!0), elem!0, identity)),
% 12.28/12.51 inference(quant_inst,[status(thm)],[])).
% 12.28/12.51 tff(18,plain,
% 12.28/12.51 (product(inverse(elem!0), elem!0, identity)),
% 12.28/12.51 inference(unit_resolution,[status(thm)],[17, 16])).
% 12.28/12.51 tff(19,plain,
% 12.28/12.51 (^[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))))),
% 12.28/12.51 inference(bind,[status(th)],[])).
% 12.28/12.51 tff(20,plain,
% 12.28/12.51 (![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)))),
% 12.28/12.51 inference(quant_intro,[status(thm)],[19])).
% 12.28/12.51 tff(21,plain,
% 12.28/12.51 (![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)))),
% 12.28/12.51 inference(rewrite,[status(thm)],[])).
% 12.28/12.51 tff(22,plain,
% 12.28/12.51 (^[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))))),
% 12.28/12.51 inference(bind,[status(th)],[])).
% 12.28/12.51 tff(23,plain,
% 12.28/12.51 (![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)))),
% 12.28/12.51 inference(quant_intro,[status(thm)],[22])).
% 12.28/12.51 tff(24,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, Y, Z)) | (~product(X, Y, W))) | (Z = W))), file('/export/starexec/sandbox2/benchmark/Axioms/GRP002-0.ax','total_function2')).
% 12.36/12.51 tff(25,plain,
% 12.36/12.51 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 12.36/12.51 inference(modus_ponens,[status(thm)],[24, 23])).
% 12.36/12.51 tff(26,plain,
% 12.36/12.51 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 12.36/12.51 inference(modus_ponens,[status(thm)],[25, 21])).
% 12.36/12.51 tff(27,plain,(
% 12.36/12.51 ![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 12.36/12.51 inference(skolemize,[status(sab)],[26])).
% 12.36/12.51 tff(28,plain,
% 12.36/12.51 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 12.36/12.51 inference(modus_ponens,[status(thm)],[27, 20])).
% 12.36/12.51 tff(29,plain,
% 12.36/12.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((~product(inverse(elem!0), elem!0, identity)) | (identity = multiply(inverse(elem!0), elem!0)) | (~product(inverse(elem!0), elem!0, multiply(inverse(elem!0), elem!0))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (~product(inverse(elem!0), elem!0, identity)) | (identity = multiply(inverse(elem!0), elem!0)) | (~product(inverse(elem!0), elem!0, multiply(inverse(elem!0), elem!0))))),
% 12.36/12.51 inference(rewrite,[status(thm)],[])).
% 12.36/12.51 tff(30,plain,
% 12.36/12.51 (((identity = multiply(inverse(elem!0), elem!0)) | (~product(inverse(elem!0), elem!0, multiply(inverse(elem!0), elem!0))) | (~product(inverse(elem!0), elem!0, identity))) <=> ((~product(inverse(elem!0), elem!0, identity)) | (identity = multiply(inverse(elem!0), elem!0)) | (~product(inverse(elem!0), elem!0, multiply(inverse(elem!0), elem!0))))),
% 12.36/12.51 inference(rewrite,[status(thm)],[])).
% 12.36/12.51 tff(31,plain,
% 12.36/12.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((identity = multiply(inverse(elem!0), elem!0)) | (~product(inverse(elem!0), elem!0, multiply(inverse(elem!0), elem!0))) | (~product(inverse(elem!0), elem!0, identity)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((~product(inverse(elem!0), elem!0, identity)) | (identity = multiply(inverse(elem!0), elem!0)) | (~product(inverse(elem!0), elem!0, multiply(inverse(elem!0), elem!0)))))),
% 12.36/12.51 inference(monotonicity,[status(thm)],[30])).
% 12.36/12.51 tff(32,plain,
% 12.36/12.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((identity = multiply(inverse(elem!0), elem!0)) | (~product(inverse(elem!0), elem!0, multiply(inverse(elem!0), elem!0))) | (~product(inverse(elem!0), elem!0, identity)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (~product(inverse(elem!0), elem!0, identity)) | (identity = multiply(inverse(elem!0), elem!0)) | (~product(inverse(elem!0), elem!0, multiply(inverse(elem!0), elem!0))))),
% 12.36/12.51 inference(transitivity,[status(thm)],[31, 29])).
% 12.36/12.51 tff(33,plain,
% 12.36/12.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((identity = multiply(inverse(elem!0), elem!0)) | (~product(inverse(elem!0), elem!0, multiply(inverse(elem!0), elem!0))) | (~product(inverse(elem!0), elem!0, identity)))),
% 12.36/12.51 inference(quant_inst,[status(thm)],[])).
% 12.36/12.51 tff(34,plain,
% 12.36/12.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (~product(inverse(elem!0), elem!0, identity)) | (identity = multiply(inverse(elem!0), elem!0)) | (~product(inverse(elem!0), elem!0, multiply(inverse(elem!0), elem!0)))),
% 12.36/12.51 inference(modus_ponens,[status(thm)],[33, 32])).
% 12.36/12.51 tff(35,plain,
% 12.36/12.51 (identity = multiply(inverse(elem!0), elem!0)),
% 12.36/12.51 inference(unit_resolution,[status(thm)],[34, 28, 18, 9])).
% 12.36/12.51 tff(36,plain,
% 12.36/12.51 (multiply(inverse(elem!0), elem!0) = identity),
% 12.36/12.51 inference(symmetry,[status(thm)],[35])).
% 12.36/12.51 tff(37,plain,
% 12.36/12.51 (product(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))) <=> product(identity, multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))),
% 12.36/12.51 inference(monotonicity,[status(thm)],[36])).
% 12.36/12.51 tff(38,plain,
% 12.36/12.51 (product(identity, multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))) <=> product(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))),
% 12.36/12.51 inference(symmetry,[status(thm)],[37])).
% 12.36/12.51 tff(39,plain,
% 12.36/12.51 (^[A: $i] : refl(product(identity, A, A) <=> product(identity, A, A))),
% 12.36/12.51 inference(bind,[status(th)],[])).
% 12.36/12.51 tff(40,plain,
% 12.36/12.51 (![A: $i] : product(identity, A, A) <=> ![A: $i] : product(identity, A, A)),
% 12.36/12.51 inference(quant_intro,[status(thm)],[39])).
% 12.36/12.51 tff(41,plain,
% 12.36/12.51 (![A: $i] : product(identity, A, A) <=> ![A: $i] : product(identity, A, A)),
% 12.36/12.51 inference(rewrite,[status(thm)],[])).
% 12.36/12.51 tff(42,axiom,(![A: $i] : product(identity, A, A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','left_identity')).
% 12.36/12.51 tff(43,plain,
% 12.36/12.51 (![A: $i] : product(identity, A, A)),
% 12.36/12.51 inference(modus_ponens,[status(thm)],[42, 41])).
% 12.36/12.51 tff(44,plain,(
% 12.36/12.51 ![A: $i] : product(identity, A, A)),
% 12.36/12.51 inference(skolemize,[status(sab)],[43])).
% 12.36/12.51 tff(45,plain,
% 12.36/12.51 (![A: $i] : product(identity, A, A)),
% 12.36/12.51 inference(modus_ponens,[status(thm)],[44, 40])).
% 12.36/12.51 tff(46,plain,
% 12.36/12.51 ((~![A: $i] : product(identity, A, A)) | product(identity, multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))),
% 12.36/12.51 inference(quant_inst,[status(thm)],[])).
% 12.36/12.51 tff(47,plain,
% 12.36/12.51 (product(identity, multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))),
% 12.36/12.51 inference(unit_resolution,[status(thm)],[46, 45])).
% 12.36/12.51 tff(48,plain,
% 12.36/12.51 (product(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))),
% 12.36/12.51 inference(modus_ponens,[status(thm)],[47, 38])).
% 12.36/12.51 tff(49,plain,
% 12.36/12.51 ((~![Y: $i, X: $i] : product(X, Y, multiply(X, Y))) | product(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))))),
% 12.36/12.51 inference(quant_inst,[status(thm)],[])).
% 12.36/12.51 tff(50,plain,
% 12.36/12.51 (product(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))))),
% 12.36/12.51 inference(unit_resolution,[status(thm)],[49, 7])).
% 12.36/12.51 tff(51,plain,
% 12.36/12.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)) = multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))) | (~product(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))) | (~product(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)) = multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))) | (~product(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))) | (~product(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))))))),
% 12.36/12.51 inference(rewrite,[status(thm)],[])).
% 12.36/12.51 tff(52,plain,
% 12.36/12.51 (((multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)) = multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))) | (~product(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))))) | (~product(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))))) <=> ((multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)) = multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))) | (~product(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))) | (~product(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))))))),
% 12.36/12.51 inference(rewrite,[status(thm)],[])).
% 12.36/12.51 tff(53,plain,
% 12.36/12.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)) = multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))) | (~product(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))))) | (~product(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)) = multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))) | (~product(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))) | (~product(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))))))),
% 12.36/12.51 inference(monotonicity,[status(thm)],[52])).
% 12.36/12.51 tff(54,plain,
% 12.36/12.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)) = multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))) | (~product(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))))) | (~product(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)) = multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))) | (~product(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))) | (~product(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))))))),
% 12.36/12.51 inference(transitivity,[status(thm)],[53, 51])).
% 12.36/12.51 tff(55,plain,
% 12.36/12.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)) = multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))) | (~product(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))))) | (~product(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))))),
% 12.36/12.51 inference(quant_inst,[status(thm)],[])).
% 12.36/12.51 tff(56,plain,
% 12.36/12.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)) = multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))) | (~product(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))) | (~product(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))))),
% 12.36/12.51 inference(modus_ponens,[status(thm)],[55, 54])).
% 12.36/12.51 tff(57,plain,
% 12.36/12.51 ((multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)) = multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))) | (~product(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))))),
% 12.36/12.51 inference(unit_resolution,[status(thm)],[56, 28, 50])).
% 12.36/12.51 tff(58,plain,
% 12.36/12.51 (multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)) = multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))),
% 12.36/12.51 inference(unit_resolution,[status(thm)],[57, 48])).
% 12.36/12.51 tff(59,plain,
% 12.36/12.51 (multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))) = multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))),
% 12.36/12.51 inference(symmetry,[status(thm)],[58])).
% 12.36/12.51 tff(60,plain,
% 12.36/12.51 (product(multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0)) <=> product(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0))),
% 12.36/12.51 inference(monotonicity,[status(thm)],[59])).
% 12.36/12.51 tff(61,plain,
% 12.36/12.51 (product(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0)) <=> product(multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0))),
% 12.36/12.51 inference(symmetry,[status(thm)],[60])).
% 12.36/12.51 tff(62,plain,
% 12.36/12.51 ((~![Y: $i, X: $i] : product(X, Y, multiply(X, Y))) | product(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))),
% 12.36/12.51 inference(quant_inst,[status(thm)],[])).
% 12.36/12.51 tff(63,plain,
% 12.36/12.51 (product(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))),
% 12.36/12.51 inference(unit_resolution,[status(thm)],[62, 7])).
% 12.36/12.51 tff(64,plain,
% 12.36/12.51 (product(multiply(inverse(elem!0), elem!0), not_right_identity(identity), not_right_identity(identity)) <=> product(identity, not_right_identity(identity), not_right_identity(identity))),
% 12.36/12.51 inference(monotonicity,[status(thm)],[36])).
% 12.36/12.51 tff(65,plain,
% 12.36/12.51 (product(identity, not_right_identity(identity), not_right_identity(identity)) <=> product(multiply(inverse(elem!0), elem!0), not_right_identity(identity), not_right_identity(identity))),
% 12.36/12.51 inference(symmetry,[status(thm)],[64])).
% 12.36/12.51 tff(66,plain,
% 12.36/12.51 ((~![A: $i] : product(identity, A, A)) | product(identity, not_right_identity(identity), not_right_identity(identity))),
% 12.36/12.51 inference(quant_inst,[status(thm)],[])).
% 12.36/12.51 tff(67,plain,
% 12.36/12.51 (product(identity, not_right_identity(identity), not_right_identity(identity))),
% 12.36/12.51 inference(unit_resolution,[status(thm)],[66, 45])).
% 12.36/12.51 tff(68,plain,
% 12.36/12.51 (product(multiply(inverse(elem!0), elem!0), not_right_identity(identity), not_right_identity(identity))),
% 12.36/12.51 inference(modus_ponens,[status(thm)],[67, 65])).
% 12.36/12.51 tff(69,plain,
% 12.36/12.51 ((~![Y: $i, X: $i] : product(X, Y, multiply(X, Y))) | product(multiply(inverse(elem!0), elem!0), not_right_identity(identity), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))),
% 12.36/12.51 inference(quant_inst,[status(thm)],[])).
% 12.36/12.51 tff(70,plain,
% 12.36/12.51 (product(multiply(inverse(elem!0), elem!0), not_right_identity(identity), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))),
% 12.36/12.51 inference(unit_resolution,[status(thm)],[69, 7])).
% 12.36/12.51 tff(71,plain,
% 12.36/12.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((~product(multiply(inverse(elem!0), elem!0), not_right_identity(identity), not_right_identity(identity))) | (not_right_identity(identity) = multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))) | (~product(multiply(inverse(elem!0), elem!0), not_right_identity(identity), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (~product(multiply(inverse(elem!0), elem!0), not_right_identity(identity), not_right_identity(identity))) | (not_right_identity(identity) = multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))) | (~product(multiply(inverse(elem!0), elem!0), not_right_identity(identity), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))))),
% 12.36/12.51 inference(rewrite,[status(thm)],[])).
% 12.36/12.51 tff(72,plain,
% 12.36/12.51 (((not_right_identity(identity) = multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))) | (~product(multiply(inverse(elem!0), elem!0), not_right_identity(identity), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))) | (~product(multiply(inverse(elem!0), elem!0), not_right_identity(identity), not_right_identity(identity)))) <=> ((~product(multiply(inverse(elem!0), elem!0), not_right_identity(identity), not_right_identity(identity))) | (not_right_identity(identity) = multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))) | (~product(multiply(inverse(elem!0), elem!0), not_right_identity(identity), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))))),
% 12.36/12.51 inference(rewrite,[status(thm)],[])).
% 12.36/12.51 tff(73,plain,
% 12.36/12.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((not_right_identity(identity) = multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))) | (~product(multiply(inverse(elem!0), elem!0), not_right_identity(identity), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))) | (~product(multiply(inverse(elem!0), elem!0), not_right_identity(identity), not_right_identity(identity))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((~product(multiply(inverse(elem!0), elem!0), not_right_identity(identity), not_right_identity(identity))) | (not_right_identity(identity) = multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))) | (~product(multiply(inverse(elem!0), elem!0), not_right_identity(identity), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))))))),
% 12.36/12.51 inference(monotonicity,[status(thm)],[72])).
% 12.36/12.51 tff(74,plain,
% 12.36/12.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((not_right_identity(identity) = multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))) | (~product(multiply(inverse(elem!0), elem!0), not_right_identity(identity), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))) | (~product(multiply(inverse(elem!0), elem!0), not_right_identity(identity), not_right_identity(identity))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (~product(multiply(inverse(elem!0), elem!0), not_right_identity(identity), not_right_identity(identity))) | (not_right_identity(identity) = multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))) | (~product(multiply(inverse(elem!0), elem!0), not_right_identity(identity), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))))),
% 12.36/12.51 inference(transitivity,[status(thm)],[73, 71])).
% 12.36/12.51 tff(75,plain,
% 12.36/12.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((not_right_identity(identity) = multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))) | (~product(multiply(inverse(elem!0), elem!0), not_right_identity(identity), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))) | (~product(multiply(inverse(elem!0), elem!0), not_right_identity(identity), not_right_identity(identity))))),
% 12.36/12.51 inference(quant_inst,[status(thm)],[])).
% 12.36/12.51 tff(76,plain,
% 12.36/12.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (~product(multiply(inverse(elem!0), elem!0), not_right_identity(identity), not_right_identity(identity))) | (not_right_identity(identity) = multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))) | (~product(multiply(inverse(elem!0), elem!0), not_right_identity(identity), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))))),
% 12.36/12.51 inference(modus_ponens,[status(thm)],[75, 74])).
% 12.36/12.51 tff(77,plain,
% 12.36/12.51 (not_right_identity(identity) = multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))),
% 12.36/12.51 inference(unit_resolution,[status(thm)],[76, 28, 70, 68])).
% 12.36/12.51 tff(78,plain,
% 12.36/12.51 (multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)) = not_right_identity(identity)),
% 12.36/12.52 inference(symmetry,[status(thm)],[77])).
% 12.36/12.52 tff(79,plain,
% 12.36/12.52 (product(multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))) <=> product(identity, not_right_identity(identity), not_right_identity(identity))),
% 12.36/12.52 inference(monotonicity,[status(thm)],[36, 78, 78])).
% 12.36/12.52 tff(80,plain,
% 12.36/12.52 (product(identity, not_right_identity(identity), not_right_identity(identity)) <=> product(multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))),
% 12.36/12.52 inference(symmetry,[status(thm)],[79])).
% 12.36/12.52 tff(81,plain,
% 12.36/12.52 (product(multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))),
% 12.36/12.52 inference(modus_ponens,[status(thm)],[67, 80])).
% 12.36/12.52 tff(82,plain,
% 12.36/12.52 (product(inverse(not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0)) <=> product(inverse(not_right_identity(identity)), not_right_identity(identity), identity)),
% 12.36/12.52 inference(monotonicity,[status(thm)],[78, 36])).
% 12.36/12.52 tff(83,plain,
% 12.36/12.52 (product(inverse(not_right_identity(identity)), not_right_identity(identity), identity) <=> product(inverse(not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0))),
% 12.36/12.52 inference(symmetry,[status(thm)],[82])).
% 12.36/12.52 tff(84,plain,
% 12.36/12.52 ((~![A: $i] : product(inverse(A), A, identity)) | product(inverse(not_right_identity(identity)), not_right_identity(identity), identity)),
% 12.36/12.52 inference(quant_inst,[status(thm)],[])).
% 12.36/12.52 tff(85,plain,
% 12.36/12.52 (product(inverse(not_right_identity(identity)), not_right_identity(identity), identity)),
% 12.36/12.52 inference(unit_resolution,[status(thm)],[84, 16])).
% 12.36/12.52 tff(86,plain,
% 12.36/12.52 (product(inverse(not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0))),
% 12.36/12.52 inference(modus_ponens,[status(thm)],[85, 83])).
% 12.36/12.52 tff(87,plain,
% 12.36/12.52 (^[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))))),
% 12.36/12.52 inference(bind,[status(th)],[])).
% 12.36/12.52 tff(88,plain,
% 12.36/12.52 (![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)))),
% 12.36/12.52 inference(quant_intro,[status(thm)],[87])).
% 12.36/12.52 tff(89,plain,
% 12.36/12.52 (![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)))),
% 12.36/12.52 inference(rewrite,[status(thm)],[])).
% 12.36/12.52 tff(90,plain,
% 12.36/12.52 (^[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)))))),
% 12.36/12.52 inference(bind,[status(th)],[])).
% 12.36/12.52 tff(91,plain,
% 12.36/12.52 (![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)))),
% 12.36/12.52 inference(quant_intro,[status(thm)],[90])).
% 12.36/12.52 tff(92,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/sandbox2/benchmark/Axioms/GRP002-0.ax','associativity2')).
% 12.36/12.52 tff(93,plain,
% 12.36/12.52 (![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)))),
% 12.36/12.52 inference(modus_ponens,[status(thm)],[92, 91])).
% 12.36/12.52 tff(94,plain,
% 12.36/12.52 (![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)))),
% 12.36/12.52 inference(modus_ponens,[status(thm)],[93, 89])).
% 12.36/12.52 tff(95,plain,(
% 12.36/12.52 ![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)))),
% 12.36/12.52 inference(skolemize,[status(sab)],[94])).
% 12.36/12.52 tff(96,plain,
% 12.36/12.52 (![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)))),
% 12.36/12.52 inference(modus_ponens,[status(thm)],[95, 88])).
% 12.36/12.52 tff(97,plain,
% 12.36/12.52 (((~![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(multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))) | (~product(inverse(not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0))) | (~product(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))) | product(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))) <=> ((~![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(multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))) | (~product(inverse(not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0))) | (~product(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))) | product(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))),
% 12.36/12.52 inference(rewrite,[status(thm)],[])).
% 12.36/12.52 tff(98,plain,
% 12.36/12.52 ((product(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0)) | (~product(multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))) | (~product(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))) | (~product(inverse(not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))) <=> ((~product(multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))) | (~product(inverse(not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0))) | (~product(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))) | product(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))),
% 12.36/12.52 inference(rewrite,[status(thm)],[])).
% 12.36/12.52 tff(99,plain,
% 12.36/12.52 (((~![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(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0)) | (~product(multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))) | (~product(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))) | (~product(inverse(not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0))))) <=> ((~![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(multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))) | (~product(inverse(not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0))) | (~product(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))) | product(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0))))),
% 12.36/12.52 inference(monotonicity,[status(thm)],[98])).
% 12.36/12.52 tff(100,plain,
% 12.36/12.52 (((~![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(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0)) | (~product(multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))) | (~product(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))) | (~product(inverse(not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0))))) <=> ((~![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(multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))) | (~product(inverse(not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0))) | (~product(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))) | product(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))),
% 12.36/12.52 inference(transitivity,[status(thm)],[99, 97])).
% 12.36/12.52 tff(101,plain,
% 12.36/12.52 ((~![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(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0)) | (~product(multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))) | (~product(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))) | (~product(inverse(not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0))))),
% 12.36/12.52 inference(quant_inst,[status(thm)],[])).
% 12.36/12.52 tff(102,plain,
% 12.36/12.52 ((~![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(multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))) | (~product(inverse(not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0))) | (~product(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)))) | product(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0))),
% 12.36/12.52 inference(modus_ponens,[status(thm)],[101, 100])).
% 12.36/12.52 tff(103,plain,
% 12.36/12.52 (product(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0))),
% 12.36/12.52 inference(unit_resolution,[status(thm)],[102, 96, 86, 81, 63])).
% 12.36/12.52 tff(104,plain,
% 12.36/12.52 (product(multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0))),
% 12.36/12.52 inference(modus_ponens,[status(thm)],[103, 61])).
% 12.36/12.52 tff(105,plain,
% 12.36/12.52 (product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0)) <=> product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), identity)),
% 12.36/12.52 inference(monotonicity,[status(thm)],[59, 36])).
% 12.36/12.52 tff(106,plain,
% 12.36/12.52 (product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), identity) <=> product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0))),
% 12.36/12.52 inference(symmetry,[status(thm)],[105])).
% 12.36/12.52 tff(107,plain,
% 12.36/12.52 ((~![A: $i] : product(inverse(A), A, identity)) | product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), identity)),
% 12.36/12.52 inference(quant_inst,[status(thm)],[])).
% 12.36/12.52 tff(108,plain,
% 12.36/12.52 (product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0)), identity)),
% 12.36/12.52 inference(unit_resolution,[status(thm)],[107, 16])).
% 12.36/12.52 tff(109,plain,
% 12.36/12.52 (product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0))),
% 12.36/12.52 inference(modus_ponens,[status(thm)],[108, 106])).
% 12.36/12.52 tff(110,plain,
% 12.36/12.52 (^[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))))),
% 12.36/12.52 inference(bind,[status(th)],[])).
% 12.36/12.52 tff(111,plain,
% 12.36/12.52 (![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)))),
% 12.36/12.52 inference(quant_intro,[status(thm)],[110])).
% 12.36/12.52 tff(112,plain,
% 12.36/12.52 (![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)))),
% 12.36/12.52 inference(rewrite,[status(thm)],[])).
% 12.36/12.52 tff(113,plain,
% 12.36/12.52 (^[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)))))),
% 12.36/12.52 inference(bind,[status(th)],[])).
% 12.36/12.52 tff(114,plain,
% 12.36/12.52 (![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)))),
% 12.36/12.52 inference(quant_intro,[status(thm)],[113])).
% 12.36/12.52 tff(115,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/GRP002-0.ax','associativity1')).
% 12.36/12.52 tff(116,plain,
% 12.36/12.52 (![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)))),
% 12.36/12.52 inference(modus_ponens,[status(thm)],[115, 114])).
% 12.36/12.52 tff(117,plain,
% 12.36/12.52 (![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)))),
% 12.36/12.52 inference(modus_ponens,[status(thm)],[116, 112])).
% 12.36/12.52 tff(118,plain,(
% 12.36/12.52 ![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)))),
% 12.36/12.52 inference(skolemize,[status(sab)],[117])).
% 12.36/12.52 tff(119,plain,
% 12.36/12.52 (![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)))),
% 12.36/12.52 inference(modus_ponens,[status(thm)],[118, 111])).
% 12.36/12.52 tff(120,plain,
% 12.36/12.52 (((~![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(multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))) | (~product(multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0))) | (~product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0))) | product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_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(multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))) | (~product(multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0))) | (~product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0))) | product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))))),
% 12.36/12.52 inference(rewrite,[status(thm)],[])).
% 12.36/12.52 tff(121,plain,
% 12.36/12.52 ((product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))) | (~product(multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))) | (~product(multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0))) | (~product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0)))) <=> ((~product(multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))) | (~product(multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0))) | (~product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0))) | product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))))),
% 12.36/12.52 inference(rewrite,[status(thm)],[])).
% 12.36/12.52 tff(122,plain,
% 12.36/12.52 (((~![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(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))) | (~product(multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))) | (~product(multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0))) | (~product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0))))) <=> ((~![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(multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))) | (~product(multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0))) | (~product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0))) | product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))))),
% 12.36/12.52 inference(monotonicity,[status(thm)],[121])).
% 12.36/12.52 tff(123,plain,
% 12.36/12.52 (((~![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(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))) | (~product(multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))) | (~product(multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0))) | (~product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0))))) <=> ((~![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(multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))) | (~product(multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0))) | (~product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0))) | product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))))),
% 12.36/12.53 inference(transitivity,[status(thm)],[122, 120])).
% 12.36/12.53 tff(124,plain,
% 12.36/12.53 ((~![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(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))) | (~product(multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))) | (~product(multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0))) | (~product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0))))),
% 12.36/12.53 inference(quant_inst,[status(thm)],[])).
% 12.36/12.53 tff(125,plain,
% 12.36/12.53 ((~![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(multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))) | (~product(multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0))) | (~product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0))) | product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))),
% 12.36/12.53 inference(modus_ponens,[status(thm)],[124, 123])).
% 12.36/12.53 tff(126,plain,
% 12.36/12.53 ((~product(multiply(multiply(inverse(elem!0), elem!0), multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0))) | product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))),
% 12.36/12.53 inference(unit_resolution,[status(thm)],[125, 119, 81, 109])).
% 12.36/12.53 tff(127,plain,
% 12.36/12.53 (product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))),
% 12.36/12.53 inference(unit_resolution,[status(thm)],[126, 104])).
% 12.36/12.53 tff(128,plain,
% 12.36/12.53 (product(multiply(inverse(elem!0), elem!0), multiply(inverse(elem!0), elem!0), multiply(inverse(elem!0), elem!0)) <=> product(identity, multiply(inverse(elem!0), elem!0), multiply(inverse(elem!0), elem!0))),
% 12.36/12.53 inference(monotonicity,[status(thm)],[36])).
% 12.36/12.53 tff(129,plain,
% 12.36/12.53 (product(identity, multiply(inverse(elem!0), elem!0), multiply(inverse(elem!0), elem!0)) <=> product(multiply(inverse(elem!0), elem!0), multiply(inverse(elem!0), elem!0), multiply(inverse(elem!0), elem!0))),
% 12.36/12.53 inference(symmetry,[status(thm)],[128])).
% 12.36/12.53 tff(130,plain,
% 12.36/12.53 ((~![A: $i] : product(identity, A, A)) | product(identity, multiply(inverse(elem!0), elem!0), multiply(inverse(elem!0), elem!0))),
% 12.36/12.53 inference(quant_inst,[status(thm)],[])).
% 12.36/12.53 tff(131,plain,
% 12.36/12.53 (product(identity, multiply(inverse(elem!0), elem!0), multiply(inverse(elem!0), elem!0))),
% 12.36/12.53 inference(unit_resolution,[status(thm)],[130, 45])).
% 12.36/12.53 tff(132,plain,
% 12.36/12.53 (product(multiply(inverse(elem!0), elem!0), multiply(inverse(elem!0), elem!0), multiply(inverse(elem!0), elem!0))),
% 12.36/12.53 inference(modus_ponens,[status(thm)],[131, 129])).
% 12.36/12.53 tff(133,plain,
% 12.36/12.53 (product(multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))) <=> product(not_right_identity(identity), identity, not_right_identity(identity))),
% 12.36/12.53 inference(monotonicity,[status(thm)],[78, 36, 78])).
% 12.36/12.53 tff(134,plain,
% 12.36/12.53 (product(not_right_identity(identity), identity, not_right_identity(identity)) <=> product(multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))),
% 12.36/12.53 inference(symmetry,[status(thm)],[133])).
% 12.36/12.53 tff(135,plain,
% 12.36/12.53 ((~product(not_right_identity(identity), identity, not_right_identity(identity))) <=> (~product(multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))))),
% 12.36/12.53 inference(monotonicity,[status(thm)],[134])).
% 12.36/12.53 tff(136,plain,
% 12.36/12.53 (^[A: $i] : refl((~product(not_right_identity(A), A, not_right_identity(A))) <=> (~product(not_right_identity(A), A, not_right_identity(A))))),
% 12.36/12.53 inference(bind,[status(th)],[])).
% 12.36/12.53 tff(137,plain,
% 12.36/12.53 (![A: $i] : (~product(not_right_identity(A), A, not_right_identity(A))) <=> ![A: $i] : (~product(not_right_identity(A), A, not_right_identity(A)))),
% 12.36/12.53 inference(quant_intro,[status(thm)],[136])).
% 12.36/12.53 tff(138,plain,
% 12.36/12.53 (![A: $i] : (~product(not_right_identity(A), A, not_right_identity(A))) <=> ![A: $i] : (~product(not_right_identity(A), A, not_right_identity(A)))),
% 12.36/12.53 inference(rewrite,[status(thm)],[])).
% 12.36/12.53 tff(139,axiom,(![A: $i] : (~product(not_right_identity(A), A, not_right_identity(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_there_is_a_right_identity')).
% 12.36/12.53 tff(140,plain,
% 12.36/12.53 (![A: $i] : (~product(not_right_identity(A), A, not_right_identity(A)))),
% 12.36/12.53 inference(modus_ponens,[status(thm)],[139, 138])).
% 12.36/12.53 tff(141,plain,(
% 12.36/12.53 ![A: $i] : (~product(not_right_identity(A), A, not_right_identity(A)))),
% 12.36/12.53 inference(skolemize,[status(sab)],[140])).
% 12.36/12.53 tff(142,plain,
% 12.36/12.53 (![A: $i] : (~product(not_right_identity(A), A, not_right_identity(A)))),
% 12.36/12.53 inference(modus_ponens,[status(thm)],[141, 137])).
% 12.36/12.53 tff(143,plain,
% 12.36/12.53 ((~![A: $i] : (~product(not_right_identity(A), A, not_right_identity(A)))) | (~product(not_right_identity(identity), identity, not_right_identity(identity)))),
% 12.36/12.53 inference(quant_inst,[status(thm)],[])).
% 12.36/12.53 tff(144,plain,
% 12.36/12.53 (~product(not_right_identity(identity), identity, not_right_identity(identity))),
% 12.36/12.53 inference(unit_resolution,[status(thm)],[143, 142])).
% 12.36/12.53 tff(145,plain,
% 12.36/12.53 (~product(multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))),
% 12.36/12.53 inference(modus_ponens,[status(thm)],[144, 135])).
% 12.36/12.53 tff(146,plain,
% 12.36/12.53 (((~![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(multiply(inverse(elem!0), elem!0), multiply(inverse(elem!0), elem!0), multiply(inverse(elem!0), elem!0))) | product(multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))) | (~product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_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(multiply(inverse(elem!0), elem!0), multiply(inverse(elem!0), elem!0), multiply(inverse(elem!0), elem!0))) | product(multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))) | (~product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))))),
% 12.36/12.53 inference(rewrite,[status(thm)],[])).
% 12.36/12.53 tff(147,plain,
% 12.36/12.53 ((product(multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))) | (~product(multiply(inverse(elem!0), elem!0), multiply(inverse(elem!0), elem!0), multiply(inverse(elem!0), elem!0))) | (~product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))) | (~product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))))) <=> ((~product(multiply(inverse(elem!0), elem!0), multiply(inverse(elem!0), elem!0), multiply(inverse(elem!0), elem!0))) | product(multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))) | (~product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))))),
% 12.36/12.53 inference(rewrite,[status(thm)],[])).
% 12.36/12.53 tff(148,plain,
% 12.36/12.53 (((~![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(multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))) | (~product(multiply(inverse(elem!0), elem!0), multiply(inverse(elem!0), elem!0), multiply(inverse(elem!0), elem!0))) | (~product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))) | (~product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_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(multiply(inverse(elem!0), elem!0), multiply(inverse(elem!0), elem!0), multiply(inverse(elem!0), elem!0))) | product(multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))) | (~product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))))))),
% 12.36/12.53 inference(monotonicity,[status(thm)],[147])).
% 12.36/12.53 tff(149,plain,
% 12.36/12.53 (((~![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(multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))) | (~product(multiply(inverse(elem!0), elem!0), multiply(inverse(elem!0), elem!0), multiply(inverse(elem!0), elem!0))) | (~product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))) | (~product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_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(multiply(inverse(elem!0), elem!0), multiply(inverse(elem!0), elem!0), multiply(inverse(elem!0), elem!0))) | product(multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))) | (~product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))))),
% 12.36/12.53 inference(transitivity,[status(thm)],[148, 146])).
% 12.36/12.53 tff(150,plain,
% 12.36/12.53 ((~![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(multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))) | (~product(multiply(inverse(elem!0), elem!0), multiply(inverse(elem!0), elem!0), multiply(inverse(elem!0), elem!0))) | (~product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))) | (~product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)))))),
% 12.36/12.53 inference(quant_inst,[status(thm)],[])).
% 12.36/12.53 tff(151,plain,
% 12.36/12.53 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (~product(multiply(inverse(elem!0), elem!0), multiply(inverse(elem!0), elem!0), multiply(inverse(elem!0), elem!0))) | product(multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity)), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))) | (~product(inverse(multiply(inverse(not_right_identity(identity)), multiply(inverse(elem!0), elem!0))), multiply(inverse(elem!0), elem!0), multiply(multiply(inverse(elem!0), elem!0), not_right_identity(identity))))),
% 12.36/12.53 inference(modus_ponens,[status(thm)],[150, 149])).
% 12.36/12.53 tff(152,plain,
% 12.36/12.53 ($false),
% 12.36/12.53 inference(unit_resolution,[status(thm)],[151, 96, 145, 132, 127])).
% 12.36/12.53 % SZS output end Proof
% 12.36/12.54 % E exiting
%------------------------------------------------------------------------------