%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP031-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:06:54 AM UTC 2025
% Result : Unsatisfiable 1.99s 2.17s
% Output : Proof 1.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP031-1 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n015.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 15:28:41 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.99/2.17 % SZS status Unsatisfiable
% 1.99/2.17 % SZS output start Proof
% 1.99/2.17 tff(product_type, type, (
% 1.99/2.17 product: ( $i * $i * $i ) > $o)).
% 1.99/2.17 tff(identity_type, type, (
% 1.99/2.17 identity: $i)).
% 1.99/2.17 tff(inverse_type, type, (
% 1.99/2.17 inverse: $i > $i)).
% 1.99/2.17 tff(a_type, type, (
% 1.99/2.17 a: $i)).
% 1.99/2.17 tff(multiply_type, type, (
% 1.99/2.17 multiply: ( $i * $i ) > $i)).
% 1.99/2.17 tff(elem_0_type, type, (
% 1.99/2.17 elem_0: $i)).
% 1.99/2.17 tff(1,plain,
% 1.99/2.17 (^[Y: $i, X: $i] : refl(product(X, Y, multiply(X, Y)) <=> product(X, Y, multiply(X, Y)))),
% 1.99/2.17 inference(bind,[status(th)],[])).
% 1.99/2.17 tff(2,plain,
% 1.99/2.17 (![Y: $i, X: $i] : product(X, Y, multiply(X, Y)) <=> ![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 1.99/2.17 inference(quant_intro,[status(thm)],[1])).
% 1.99/2.17 tff(3,plain,
% 1.99/2.17 (![Y: $i, X: $i] : product(X, Y, multiply(X, Y)) <=> ![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 1.99/2.17 inference(rewrite,[status(thm)],[])).
% 1.99/2.17 tff(4,axiom,(![Y: $i, X: $i] : product(X, Y, multiply(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/GRP002-0.ax','total_function1')).
% 1.99/2.17 tff(5,plain,
% 1.99/2.17 (![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 1.99/2.17 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.99/2.17 tff(6,plain,(
% 1.99/2.17 ![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 1.99/2.17 inference(skolemize,[status(sab)],[5])).
% 1.99/2.17 tff(7,plain,
% 1.99/2.17 (![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 1.99/2.17 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.99/2.17 tff(8,plain,
% 1.99/2.17 ((~![Y: $i, X: $i] : product(X, Y, multiply(X, Y))) | product(inverse(elem!0), elem!0, multiply(inverse(elem!0), elem!0))),
% 1.99/2.17 inference(quant_inst,[status(thm)],[])).
% 1.99/2.17 tff(9,plain,
% 1.99/2.17 (product(inverse(elem!0), elem!0, multiply(inverse(elem!0), elem!0))),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[8, 7])).
% 1.99/2.17 tff(10,plain,
% 1.99/2.17 (^[A: $i] : refl(product(inverse(A), A, identity) <=> product(inverse(A), A, identity))),
% 1.99/2.17 inference(bind,[status(th)],[])).
% 1.99/2.17 tff(11,plain,
% 1.99/2.17 (![A: $i] : product(inverse(A), A, identity) <=> ![A: $i] : product(inverse(A), A, identity)),
% 1.99/2.17 inference(quant_intro,[status(thm)],[10])).
% 1.99/2.17 tff(12,plain,
% 1.99/2.17 (![A: $i] : product(inverse(A), A, identity) <=> ![A: $i] : product(inverse(A), A, identity)),
% 1.99/2.17 inference(rewrite,[status(thm)],[])).
% 1.99/2.17 tff(13,axiom,(![A: $i] : product(inverse(A), A, identity)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','left_inverse')).
% 1.99/2.17 tff(14,plain,
% 1.99/2.17 (![A: $i] : product(inverse(A), A, identity)),
% 1.99/2.17 inference(modus_ponens,[status(thm)],[13, 12])).
% 1.99/2.17 tff(15,plain,(
% 1.99/2.17 ![A: $i] : product(inverse(A), A, identity)),
% 1.99/2.17 inference(skolemize,[status(sab)],[14])).
% 1.99/2.17 tff(16,plain,
% 1.99/2.17 (![A: $i] : product(inverse(A), A, identity)),
% 1.99/2.17 inference(modus_ponens,[status(thm)],[15, 11])).
% 1.99/2.17 tff(17,plain,
% 1.99/2.17 ((~![A: $i] : product(inverse(A), A, identity)) | product(inverse(elem!0), elem!0, identity)),
% 1.99/2.17 inference(quant_inst,[status(thm)],[])).
% 1.99/2.17 tff(18,plain,
% 1.99/2.17 (product(inverse(elem!0), elem!0, identity)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[17, 16])).
% 1.99/2.17 tff(19,plain,
% 1.99/2.17 (^[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))))),
% 1.99/2.17 inference(bind,[status(th)],[])).
% 1.99/2.17 tff(20,plain,
% 1.99/2.17 (![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)))),
% 1.99/2.17 inference(quant_intro,[status(thm)],[19])).
% 1.99/2.17 tff(21,plain,
% 1.99/2.17 (![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)))),
% 1.99/2.17 inference(rewrite,[status(thm)],[])).
% 1.99/2.17 tff(22,plain,
% 1.99/2.17 (^[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))))),
% 1.99/2.17 inference(bind,[status(th)],[])).
% 1.99/2.17 tff(23,plain,
% 1.99/2.17 (![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)))),
% 1.99/2.17 inference(quant_intro,[status(thm)],[22])).
% 1.99/2.17 tff(24,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, Y, Z)) | (~product(X, Y, W))) | (Z = W))), file('/export/starexec/sandbox/benchmark/Axioms/GRP002-0.ax','total_function2')).
% 1.99/2.17 tff(25,plain,
% 1.99/2.17 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 1.99/2.17 inference(modus_ponens,[status(thm)],[24, 23])).
% 1.99/2.17 tff(26,plain,
% 1.99/2.17 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 1.99/2.17 inference(modus_ponens,[status(thm)],[25, 21])).
% 1.99/2.17 tff(27,plain,(
% 1.99/2.17 ![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 1.99/2.17 inference(skolemize,[status(sab)],[26])).
% 1.99/2.17 tff(28,plain,
% 1.99/2.17 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 1.99/2.17 inference(modus_ponens,[status(thm)],[27, 20])).
% 1.99/2.17 tff(29,plain,
% 1.99/2.17 (((~![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))))),
% 1.99/2.17 inference(rewrite,[status(thm)],[])).
% 1.99/2.17 tff(30,plain,
% 1.99/2.17 (((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))))),
% 1.99/2.17 inference(rewrite,[status(thm)],[])).
% 1.99/2.17 tff(31,plain,
% 1.99/2.17 (((~![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)))))),
% 1.99/2.17 inference(monotonicity,[status(thm)],[30])).
% 1.99/2.17 tff(32,plain,
% 1.99/2.17 (((~![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))))),
% 1.99/2.17 inference(transitivity,[status(thm)],[31, 29])).
% 1.99/2.17 tff(33,plain,
% 1.99/2.17 ((~![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)))),
% 1.99/2.17 inference(quant_inst,[status(thm)],[])).
% 1.99/2.17 tff(34,plain,
% 1.99/2.17 ((~![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)))),
% 1.99/2.17 inference(modus_ponens,[status(thm)],[33, 32])).
% 1.99/2.17 tff(35,plain,
% 1.99/2.17 (identity = multiply(inverse(elem!0), elem!0)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[34, 28, 18, 9])).
% 1.99/2.17 tff(36,plain,
% 1.99/2.17 (multiply(inverse(elem!0), elem!0) = identity),
% 1.99/2.17 inference(symmetry,[status(thm)],[35])).
% 1.99/2.17 tff(37,plain,
% 1.99/2.17 (product(multiply(inverse(elem!0), elem!0), multiply(a, inverse(a)), multiply(a, inverse(a))) <=> product(identity, multiply(a, inverse(a)), multiply(a, inverse(a)))),
% 1.99/2.17 inference(monotonicity,[status(thm)],[36])).
% 1.99/2.17 tff(38,plain,
% 1.99/2.17 (product(identity, multiply(a, inverse(a)), multiply(a, inverse(a))) <=> product(multiply(inverse(elem!0), elem!0), multiply(a, inverse(a)), multiply(a, inverse(a)))),
% 1.99/2.17 inference(symmetry,[status(thm)],[37])).
% 1.99/2.17 tff(39,plain,
% 1.99/2.17 (^[A: $i] : refl(product(identity, A, A) <=> product(identity, A, A))),
% 1.99/2.17 inference(bind,[status(th)],[])).
% 1.99/2.17 tff(40,plain,
% 1.99/2.17 (![A: $i] : product(identity, A, A) <=> ![A: $i] : product(identity, A, A)),
% 1.99/2.17 inference(quant_intro,[status(thm)],[39])).
% 1.99/2.17 tff(41,plain,
% 1.99/2.17 (![A: $i] : product(identity, A, A) <=> ![A: $i] : product(identity, A, A)),
% 1.99/2.17 inference(rewrite,[status(thm)],[])).
% 1.99/2.17 tff(42,axiom,(![A: $i] : product(identity, A, A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','left_identity')).
% 1.99/2.17 tff(43,plain,
% 1.99/2.17 (![A: $i] : product(identity, A, A)),
% 1.99/2.17 inference(modus_ponens,[status(thm)],[42, 41])).
% 1.99/2.17 tff(44,plain,(
% 1.99/2.17 ![A: $i] : product(identity, A, A)),
% 1.99/2.17 inference(skolemize,[status(sab)],[43])).
% 1.99/2.17 tff(45,plain,
% 1.99/2.17 (![A: $i] : product(identity, A, A)),
% 1.99/2.17 inference(modus_ponens,[status(thm)],[44, 40])).
% 1.99/2.17 tff(46,plain,
% 1.99/2.17 ((~![A: $i] : product(identity, A, A)) | product(identity, multiply(a, inverse(a)), multiply(a, inverse(a)))),
% 1.99/2.17 inference(quant_inst,[status(thm)],[])).
% 1.99/2.17 tff(47,plain,
% 1.99/2.17 (product(identity, multiply(a, inverse(a)), multiply(a, inverse(a)))),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[46, 45])).
% 1.99/2.17 tff(48,plain,
% 1.99/2.17 (product(multiply(inverse(elem!0), elem!0), multiply(a, inverse(a)), multiply(a, inverse(a)))),
% 1.99/2.17 inference(modus_ponens,[status(thm)],[47, 38])).
% 1.99/2.17 tff(49,plain,
% 1.99/2.17 (product(multiply(inverse(elem!0), elem!0), inverse(a), inverse(a)) <=> product(identity, inverse(a), inverse(a))),
% 1.99/2.17 inference(monotonicity,[status(thm)],[36])).
% 1.99/2.17 tff(50,plain,
% 1.99/2.17 (product(identity, inverse(a), inverse(a)) <=> product(multiply(inverse(elem!0), elem!0), inverse(a), inverse(a))),
% 1.99/2.17 inference(symmetry,[status(thm)],[49])).
% 1.99/2.17 tff(51,plain,
% 1.99/2.17 ((~![A: $i] : product(identity, A, A)) | product(identity, inverse(a), inverse(a))),
% 1.99/2.17 inference(quant_inst,[status(thm)],[])).
% 1.99/2.17 tff(52,plain,
% 1.99/2.17 (product(identity, inverse(a), inverse(a))),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[51, 45])).
% 1.99/2.17 tff(53,plain,
% 1.99/2.17 (product(multiply(inverse(elem!0), elem!0), inverse(a), inverse(a))),
% 1.99/2.17 inference(modus_ponens,[status(thm)],[52, 50])).
% 1.99/2.17 tff(54,plain,
% 1.99/2.17 ((~![Y: $i, X: $i] : product(X, Y, multiply(X, Y))) | product(a, inverse(a), multiply(a, inverse(a)))),
% 1.99/2.17 inference(quant_inst,[status(thm)],[])).
% 1.99/2.17 tff(55,plain,
% 1.99/2.17 (product(a, inverse(a), multiply(a, inverse(a)))),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[54, 7])).
% 1.99/2.17 tff(56,plain,
% 1.99/2.17 (product(inverse(a), a, multiply(inverse(elem!0), elem!0)) <=> product(inverse(a), a, identity)),
% 1.99/2.17 inference(monotonicity,[status(thm)],[36])).
% 1.99/2.17 tff(57,plain,
% 1.99/2.17 (product(inverse(a), a, identity) <=> product(inverse(a), a, multiply(inverse(elem!0), elem!0))),
% 1.99/2.17 inference(symmetry,[status(thm)],[56])).
% 1.99/2.17 tff(58,plain,
% 1.99/2.17 ((~![A: $i] : product(inverse(A), A, identity)) | product(inverse(a), a, identity)),
% 1.99/2.17 inference(quant_inst,[status(thm)],[])).
% 1.99/2.17 tff(59,plain,
% 1.99/2.17 (product(inverse(a), a, identity)),
% 1.99/2.17 inference(unit_resolution,[status(thm)],[58, 16])).
% 1.99/2.17 tff(60,plain,
% 1.99/2.17 (product(inverse(a), a, multiply(inverse(elem!0), elem!0))),
% 1.99/2.17 inference(modus_ponens,[status(thm)],[59, 57])).
% 1.99/2.17 tff(61,plain,
% 1.99/2.17 (^[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))))),
% 1.99/2.17 inference(bind,[status(th)],[])).
% 1.99/2.17 tff(62,plain,
% 1.99/2.17 (![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)))),
% 1.99/2.17 inference(quant_intro,[status(thm)],[61])).
% 1.99/2.17 tff(63,plain,
% 1.99/2.17 (![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)))),
% 1.99/2.18 inference(rewrite,[status(thm)],[])).
% 1.99/2.18 tff(64,plain,
% 1.99/2.18 (^[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)))))),
% 1.99/2.18 inference(bind,[status(th)],[])).
% 1.99/2.18 tff(65,plain,
% 1.99/2.18 (![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)))),
% 1.99/2.18 inference(quant_intro,[status(thm)],[64])).
% 1.99/2.18 tff(66,axiom,(![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(U, Z, W))) | product(X, V, W))), file('/export/starexec/sandbox/benchmark/Axioms/GRP002-0.ax','associativity1')).
% 1.99/2.18 tff(67,plain,
% 1.99/2.18 (![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)))),
% 1.99/2.18 inference(modus_ponens,[status(thm)],[66, 65])).
% 1.99/2.18 tff(68,plain,
% 1.99/2.18 (![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)))),
% 1.99/2.18 inference(modus_ponens,[status(thm)],[67, 63])).
% 1.99/2.18 tff(69,plain,(
% 1.99/2.18 ![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)))),
% 1.99/2.18 inference(skolemize,[status(sab)],[68])).
% 1.99/2.18 tff(70,plain,
% 1.99/2.18 (![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)))),
% 1.99/2.18 inference(modus_ponens,[status(thm)],[69, 62])).
% 1.99/2.18 tff(71,plain,
% 1.99/2.18 (((~![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(a), a, multiply(inverse(elem!0), elem!0))) | (~product(a, inverse(a), multiply(a, inverse(a)))) | product(inverse(a), multiply(a, inverse(a)), inverse(a)) | (~product(multiply(inverse(elem!0), elem!0), inverse(a), inverse(a))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (~product(inverse(a), a, multiply(inverse(elem!0), elem!0))) | (~product(a, inverse(a), multiply(a, inverse(a)))) | product(inverse(a), multiply(a, inverse(a)), inverse(a)) | (~product(multiply(inverse(elem!0), elem!0), inverse(a), inverse(a))))),
% 1.99/2.18 inference(rewrite,[status(thm)],[])).
% 1.99/2.18 tff(72,plain,
% 1.99/2.18 ((product(inverse(a), multiply(a, inverse(a)), inverse(a)) | (~product(multiply(inverse(elem!0), elem!0), inverse(a), inverse(a))) | (~product(a, inverse(a), multiply(a, inverse(a)))) | (~product(inverse(a), a, multiply(inverse(elem!0), elem!0)))) <=> ((~product(inverse(a), a, multiply(inverse(elem!0), elem!0))) | (~product(a, inverse(a), multiply(a, inverse(a)))) | product(inverse(a), multiply(a, inverse(a)), inverse(a)) | (~product(multiply(inverse(elem!0), elem!0), inverse(a), inverse(a))))),
% 1.99/2.18 inference(rewrite,[status(thm)],[])).
% 1.99/2.18 tff(73,plain,
% 1.99/2.18 (((~![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(a), multiply(a, inverse(a)), inverse(a)) | (~product(multiply(inverse(elem!0), elem!0), inverse(a), inverse(a))) | (~product(a, inverse(a), multiply(a, inverse(a)))) | (~product(inverse(a), a, 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(inverse(a), a, multiply(inverse(elem!0), elem!0))) | (~product(a, inverse(a), multiply(a, inverse(a)))) | product(inverse(a), multiply(a, inverse(a)), inverse(a)) | (~product(multiply(inverse(elem!0), elem!0), inverse(a), inverse(a)))))),
% 1.99/2.18 inference(monotonicity,[status(thm)],[72])).
% 1.99/2.18 tff(74,plain,
% 1.99/2.18 (((~![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(a), multiply(a, inverse(a)), inverse(a)) | (~product(multiply(inverse(elem!0), elem!0), inverse(a), inverse(a))) | (~product(a, inverse(a), multiply(a, inverse(a)))) | (~product(inverse(a), a, 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(inverse(a), a, multiply(inverse(elem!0), elem!0))) | (~product(a, inverse(a), multiply(a, inverse(a)))) | product(inverse(a), multiply(a, inverse(a)), inverse(a)) | (~product(multiply(inverse(elem!0), elem!0), inverse(a), inverse(a))))),
% 1.99/2.18 inference(transitivity,[status(thm)],[73, 71])).
% 1.99/2.18 tff(75,plain,
% 1.99/2.18 ((~![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(a), multiply(a, inverse(a)), inverse(a)) | (~product(multiply(inverse(elem!0), elem!0), inverse(a), inverse(a))) | (~product(a, inverse(a), multiply(a, inverse(a)))) | (~product(inverse(a), a, multiply(inverse(elem!0), elem!0))))),
% 1.99/2.18 inference(quant_inst,[status(thm)],[])).
% 1.99/2.18 tff(76,plain,
% 1.99/2.18 ((~![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(a), a, multiply(inverse(elem!0), elem!0))) | (~product(a, inverse(a), multiply(a, inverse(a)))) | product(inverse(a), multiply(a, inverse(a)), inverse(a)) | (~product(multiply(inverse(elem!0), elem!0), inverse(a), inverse(a)))),
% 1.99/2.18 inference(modus_ponens,[status(thm)],[75, 74])).
% 1.99/2.18 tff(77,plain,
% 1.99/2.18 (product(inverse(a), multiply(a, inverse(a)), inverse(a))),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[76, 70, 60, 55, 53])).
% 1.99/2.18 tff(78,plain,
% 1.99/2.18 (product(inverse(inverse(a)), inverse(a), multiply(inverse(elem!0), elem!0)) <=> product(inverse(inverse(a)), inverse(a), identity)),
% 1.99/2.18 inference(monotonicity,[status(thm)],[36])).
% 1.99/2.18 tff(79,plain,
% 1.99/2.18 (product(inverse(inverse(a)), inverse(a), identity) <=> product(inverse(inverse(a)), inverse(a), multiply(inverse(elem!0), elem!0))),
% 1.99/2.18 inference(symmetry,[status(thm)],[78])).
% 1.99/2.18 tff(80,plain,
% 1.99/2.18 ((~![A: $i] : product(inverse(A), A, identity)) | product(inverse(inverse(a)), inverse(a), identity)),
% 1.99/2.18 inference(quant_inst,[status(thm)],[])).
% 1.99/2.18 tff(81,plain,
% 1.99/2.18 (product(inverse(inverse(a)), inverse(a), identity)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[80, 16])).
% 1.99/2.18 tff(82,plain,
% 1.99/2.18 (product(inverse(inverse(a)), inverse(a), multiply(inverse(elem!0), elem!0))),
% 1.99/2.18 inference(modus_ponens,[status(thm)],[81, 79])).
% 1.99/2.18 tff(83,plain,
% 1.99/2.18 (^[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))))),
% 1.99/2.18 inference(bind,[status(th)],[])).
% 1.99/2.18 tff(84,plain,
% 1.99/2.18 (![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)))),
% 1.99/2.18 inference(quant_intro,[status(thm)],[83])).
% 1.99/2.18 tff(85,plain,
% 1.99/2.18 (![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)))),
% 1.99/2.18 inference(rewrite,[status(thm)],[])).
% 1.99/2.18 tff(86,plain,
% 1.99/2.18 (^[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)))))),
% 1.99/2.18 inference(bind,[status(th)],[])).
% 1.99/2.18 tff(87,plain,
% 1.99/2.18 (![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)))),
% 1.99/2.18 inference(quant_intro,[status(thm)],[86])).
% 1.99/2.18 tff(88,axiom,(![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(X, V, W))) | product(U, Z, W))), file('/export/starexec/sandbox/benchmark/Axioms/GRP002-0.ax','associativity2')).
% 1.99/2.18 tff(89,plain,
% 1.99/2.18 (![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)))),
% 1.99/2.18 inference(modus_ponens,[status(thm)],[88, 87])).
% 1.99/2.18 tff(90,plain,
% 1.99/2.18 (![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)))),
% 1.99/2.18 inference(modus_ponens,[status(thm)],[89, 85])).
% 1.99/2.18 tff(91,plain,(
% 1.99/2.18 ![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)))),
% 1.99/2.18 inference(skolemize,[status(sab)],[90])).
% 1.99/2.18 tff(92,plain,
% 1.99/2.18 (![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)))),
% 1.99/2.18 inference(modus_ponens,[status(thm)],[91, 84])).
% 1.99/2.18 tff(93,plain,
% 1.99/2.18 (((~![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(inverse(inverse(a)), inverse(a), multiply(inverse(elem!0), elem!0))) | (~product(inverse(a), multiply(a, inverse(a)), inverse(a))) | product(multiply(inverse(elem!0), elem!0), multiply(a, inverse(a)), 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(inverse(inverse(a)), inverse(a), multiply(inverse(elem!0), elem!0))) | (~product(inverse(a), multiply(a, inverse(a)), inverse(a))) | product(multiply(inverse(elem!0), elem!0), multiply(a, inverse(a)), multiply(inverse(elem!0), elem!0)))),
% 1.99/2.18 inference(rewrite,[status(thm)],[])).
% 1.99/2.18 tff(94,plain,
% 1.99/2.18 ((product(multiply(inverse(elem!0), elem!0), multiply(a, inverse(a)), multiply(inverse(elem!0), elem!0)) | (~product(inverse(a), multiply(a, inverse(a)), inverse(a))) | (~product(inverse(inverse(a)), inverse(a), multiply(inverse(elem!0), elem!0))) | (~product(inverse(inverse(a)), inverse(a), multiply(inverse(elem!0), elem!0)))) <=> ((~product(inverse(inverse(a)), inverse(a), multiply(inverse(elem!0), elem!0))) | (~product(inverse(a), multiply(a, inverse(a)), inverse(a))) | product(multiply(inverse(elem!0), elem!0), multiply(a, inverse(a)), multiply(inverse(elem!0), elem!0)))),
% 1.99/2.18 inference(rewrite,[status(thm)],[])).
% 1.99/2.18 tff(95,plain,
% 1.99/2.18 (((~![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(a, inverse(a)), multiply(inverse(elem!0), elem!0)) | (~product(inverse(a), multiply(a, inverse(a)), inverse(a))) | (~product(inverse(inverse(a)), inverse(a), multiply(inverse(elem!0), elem!0))) | (~product(inverse(inverse(a)), inverse(a), 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(inverse(inverse(a)), inverse(a), multiply(inverse(elem!0), elem!0))) | (~product(inverse(a), multiply(a, inverse(a)), inverse(a))) | product(multiply(inverse(elem!0), elem!0), multiply(a, inverse(a)), multiply(inverse(elem!0), elem!0))))),
% 1.99/2.18 inference(monotonicity,[status(thm)],[94])).
% 1.99/2.18 tff(96,plain,
% 1.99/2.18 (((~![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(a, inverse(a)), multiply(inverse(elem!0), elem!0)) | (~product(inverse(a), multiply(a, inverse(a)), inverse(a))) | (~product(inverse(inverse(a)), inverse(a), multiply(inverse(elem!0), elem!0))) | (~product(inverse(inverse(a)), inverse(a), 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(inverse(inverse(a)), inverse(a), multiply(inverse(elem!0), elem!0))) | (~product(inverse(a), multiply(a, inverse(a)), inverse(a))) | product(multiply(inverse(elem!0), elem!0), multiply(a, inverse(a)), multiply(inverse(elem!0), elem!0)))),
% 1.99/2.18 inference(transitivity,[status(thm)],[95, 93])).
% 1.99/2.18 tff(97,plain,
% 1.99/2.18 ((~![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(a, inverse(a)), multiply(inverse(elem!0), elem!0)) | (~product(inverse(a), multiply(a, inverse(a)), inverse(a))) | (~product(inverse(inverse(a)), inverse(a), multiply(inverse(elem!0), elem!0))) | (~product(inverse(inverse(a)), inverse(a), multiply(inverse(elem!0), elem!0))))),
% 1.99/2.18 inference(quant_inst,[status(thm)],[])).
% 1.99/2.18 tff(98,plain,
% 1.99/2.18 ((~![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(inverse(inverse(a)), inverse(a), multiply(inverse(elem!0), elem!0))) | (~product(inverse(a), multiply(a, inverse(a)), inverse(a))) | product(multiply(inverse(elem!0), elem!0), multiply(a, inverse(a)), multiply(inverse(elem!0), elem!0))),
% 1.99/2.18 inference(modus_ponens,[status(thm)],[97, 96])).
% 1.99/2.18 tff(99,plain,
% 1.99/2.18 (product(multiply(inverse(elem!0), elem!0), multiply(a, inverse(a)), multiply(inverse(elem!0), elem!0))),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[98, 92, 82, 77])).
% 1.99/2.18 tff(100,plain,
% 1.99/2.18 (((~![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), multiply(a, inverse(a)), multiply(a, inverse(a)))) | (multiply(a, inverse(a)) = multiply(inverse(elem!0), elem!0)) | (~product(multiply(inverse(elem!0), elem!0), multiply(a, inverse(a)), 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(multiply(inverse(elem!0), elem!0), multiply(a, inverse(a)), multiply(a, inverse(a)))) | (multiply(a, inverse(a)) = multiply(inverse(elem!0), elem!0)) | (~product(multiply(inverse(elem!0), elem!0), multiply(a, inverse(a)), multiply(inverse(elem!0), elem!0))))),
% 1.99/2.18 inference(rewrite,[status(thm)],[])).
% 1.99/2.18 tff(101,plain,
% 1.99/2.18 (((multiply(a, inverse(a)) = multiply(inverse(elem!0), elem!0)) | (~product(multiply(inverse(elem!0), elem!0), multiply(a, inverse(a)), multiply(inverse(elem!0), elem!0))) | (~product(multiply(inverse(elem!0), elem!0), multiply(a, inverse(a)), multiply(a, inverse(a))))) <=> ((~product(multiply(inverse(elem!0), elem!0), multiply(a, inverse(a)), multiply(a, inverse(a)))) | (multiply(a, inverse(a)) = multiply(inverse(elem!0), elem!0)) | (~product(multiply(inverse(elem!0), elem!0), multiply(a, inverse(a)), multiply(inverse(elem!0), elem!0))))),
% 1.99/2.18 inference(rewrite,[status(thm)],[])).
% 1.99/2.18 tff(102,plain,
% 1.99/2.18 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((multiply(a, inverse(a)) = multiply(inverse(elem!0), elem!0)) | (~product(multiply(inverse(elem!0), elem!0), multiply(a, inverse(a)), multiply(inverse(elem!0), elem!0))) | (~product(multiply(inverse(elem!0), elem!0), multiply(a, inverse(a)), multiply(a, inverse(a)))))) <=> ((~![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), multiply(a, inverse(a)), multiply(a, inverse(a)))) | (multiply(a, inverse(a)) = multiply(inverse(elem!0), elem!0)) | (~product(multiply(inverse(elem!0), elem!0), multiply(a, inverse(a)), multiply(inverse(elem!0), elem!0)))))),
% 1.99/2.18 inference(monotonicity,[status(thm)],[101])).
% 1.99/2.18 tff(103,plain,
% 1.99/2.18 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((multiply(a, inverse(a)) = multiply(inverse(elem!0), elem!0)) | (~product(multiply(inverse(elem!0), elem!0), multiply(a, inverse(a)), multiply(inverse(elem!0), elem!0))) | (~product(multiply(inverse(elem!0), elem!0), multiply(a, inverse(a)), multiply(a, inverse(a)))))) <=> ((~![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), multiply(a, inverse(a)), multiply(a, inverse(a)))) | (multiply(a, inverse(a)) = multiply(inverse(elem!0), elem!0)) | (~product(multiply(inverse(elem!0), elem!0), multiply(a, inverse(a)), multiply(inverse(elem!0), elem!0))))),
% 1.99/2.18 inference(transitivity,[status(thm)],[102, 100])).
% 1.99/2.18 tff(104,plain,
% 1.99/2.18 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((multiply(a, inverse(a)) = multiply(inverse(elem!0), elem!0)) | (~product(multiply(inverse(elem!0), elem!0), multiply(a, inverse(a)), multiply(inverse(elem!0), elem!0))) | (~product(multiply(inverse(elem!0), elem!0), multiply(a, inverse(a)), multiply(a, inverse(a)))))),
% 1.99/2.18 inference(quant_inst,[status(thm)],[])).
% 1.99/2.18 tff(105,plain,
% 1.99/2.18 ((~![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), multiply(a, inverse(a)), multiply(a, inverse(a)))) | (multiply(a, inverse(a)) = multiply(inverse(elem!0), elem!0)) | (~product(multiply(inverse(elem!0), elem!0), multiply(a, inverse(a)), multiply(inverse(elem!0), elem!0)))),
% 1.99/2.18 inference(modus_ponens,[status(thm)],[104, 103])).
% 1.99/2.18 tff(106,plain,
% 1.99/2.18 ((~product(multiply(inverse(elem!0), elem!0), multiply(a, inverse(a)), multiply(a, inverse(a)))) | (multiply(a, inverse(a)) = multiply(inverse(elem!0), elem!0))),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[105, 28, 99])).
% 1.99/2.18 tff(107,plain,
% 1.99/2.18 (multiply(a, inverse(a)) = multiply(inverse(elem!0), elem!0)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[106, 48])).
% 1.99/2.18 tff(108,plain,
% 1.99/2.18 (multiply(inverse(elem!0), elem!0) = multiply(a, inverse(a))),
% 1.99/2.18 inference(symmetry,[status(thm)],[107])).
% 1.99/2.18 tff(109,plain,
% 1.99/2.18 (identity = multiply(a, inverse(a))),
% 1.99/2.18 inference(transitivity,[status(thm)],[35, 108])).
% 1.99/2.18 tff(110,plain,
% 1.99/2.18 (product(a, inverse(a), identity) <=> product(a, inverse(a), multiply(a, inverse(a)))),
% 1.99/2.18 inference(monotonicity,[status(thm)],[109])).
% 1.99/2.18 tff(111,plain,
% 1.99/2.18 (product(a, inverse(a), multiply(a, inverse(a))) <=> product(a, inverse(a), identity)),
% 1.99/2.18 inference(symmetry,[status(thm)],[110])).
% 1.99/2.18 tff(112,plain,
% 1.99/2.18 (product(a, inverse(a), identity)),
% 1.99/2.18 inference(modus_ponens,[status(thm)],[55, 111])).
% 1.99/2.18 tff(113,plain,
% 1.99/2.18 (^[A: $i] : refl((~product(a, A, identity)) <=> (~product(a, A, identity)))),
% 1.99/2.18 inference(bind,[status(th)],[])).
% 1.99/2.18 tff(114,plain,
% 1.99/2.18 (![A: $i] : (~product(a, A, identity)) <=> ![A: $i] : (~product(a, A, identity))),
% 1.99/2.18 inference(quant_intro,[status(thm)],[113])).
% 1.99/2.18 tff(115,plain,
% 1.99/2.18 (![A: $i] : (~product(a, A, identity)) <=> ![A: $i] : (~product(a, A, identity))),
% 1.99/2.18 inference(rewrite,[status(thm)],[])).
% 1.99/2.18 tff(116,axiom,(![A: $i] : (~product(a, A, identity))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_a_has_an_inverse')).
% 1.99/2.18 tff(117,plain,
% 1.99/2.18 (![A: $i] : (~product(a, A, identity))),
% 1.99/2.18 inference(modus_ponens,[status(thm)],[116, 115])).
% 1.99/2.18 tff(118,plain,(
% 1.99/2.18 ![A: $i] : (~product(a, A, identity))),
% 1.99/2.18 inference(skolemize,[status(sab)],[117])).
% 1.99/2.18 tff(119,plain,
% 1.99/2.18 (![A: $i] : (~product(a, A, identity))),
% 1.99/2.18 inference(modus_ponens,[status(thm)],[118, 114])).
% 1.99/2.18 tff(120,plain,
% 1.99/2.18 ((~![A: $i] : (~product(a, A, identity))) | (~product(a, inverse(a), identity))),
% 1.99/2.18 inference(quant_inst,[status(thm)],[])).
% 1.99/2.18 tff(121,plain,
% 1.99/2.18 (~product(a, inverse(a), identity)),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[120, 119])).
% 1.99/2.18 tff(122,plain,
% 1.99/2.18 ($false),
% 1.99/2.18 inference(unit_resolution,[status(thm)],[121, 112])).
% 1.99/2.18 % SZS output end Proof
% 1.99/2.19 % E exiting
%------------------------------------------------------------------------------