%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP310-1 : TPTP v9.0.0. Released v2.5.0.
% 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 05:07:36 AM UTC 2025
% Result : Unsatisfiable 0.23s 0.44s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.15 % Problem : GRP310-1 : TPTP v9.0.0. Released v2.5.0.
% 0.09/0.15 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n015.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu Jun 19 15:56:10 EDT 2025
% 0.15/0.37 % CPUTime :
% 0.23/0.44 % SZS status Unsatisfiable
% 0.23/0.44 % SZS output start Proof
% 0.23/0.44 tff(sk_c7_type, type, (
% 0.23/0.44 sk_c7: $i)).
% 0.23/0.44 tff(multiply_type, type, (
% 0.23/0.44 multiply: ( $i * $i ) > $i)).
% 0.23/0.44 tff(sk_c8_type, type, (
% 0.23/0.44 sk_c8: $i)).
% 0.23/0.44 tff(sk_c5_type, type, (
% 0.23/0.44 sk_c5: $i)).
% 0.23/0.44 tff(sk_c2_type, type, (
% 0.23/0.44 sk_c2: $i)).
% 0.23/0.44 tff(sk_c1_type, type, (
% 0.23/0.44 sk_c1: $i)).
% 0.23/0.44 tff(sk_c6_type, type, (
% 0.23/0.44 sk_c6: $i)).
% 0.23/0.44 tff(inverse_type, type, (
% 0.23/0.44 inverse: $i > $i)).
% 0.23/0.44 tff(sk_c3_type, type, (
% 0.23/0.44 sk_c3: $i)).
% 0.23/0.44 tff(sk_c4_type, type, (
% 0.23/0.44 sk_c4: $i)).
% 0.23/0.44 tff(identity_type, type, (
% 0.23/0.44 identity: $i)).
% 0.23/0.44 tff(1,plain,
% 0.23/0.44 ((sk_c7 = multiply(sk_c8, multiply(sk_c8, sk_c8))) <=> (multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)),
% 0.23/0.44 inference(commutativity,[status(thm)],[])).
% 0.23/0.44 tff(2,plain,
% 0.23/0.44 ((multiply(sk_c8, sk_c7) = sk_c6) <=> (multiply(sk_c8, sk_c7) = sk_c6)),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(3,axiom,(multiply(sk_c8, sk_c7) = sk_c6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_1')).
% 0.23/0.44 tff(4,plain,
% 0.23/0.44 (multiply(sk_c8, sk_c7) = sk_c6),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.23/0.44 tff(5,assumption,(~(multiply(sk_c8, sk_c2) = sk_c7)), introduced(assumption)).
% 0.23/0.44 tff(6,plain,
% 0.23/0.44 (((multiply(sk_c3, sk_c8) = sk_c7) | (multiply(sk_c8, sk_c2) = sk_c7)) <=> ((multiply(sk_c3, sk_c8) = sk_c7) | (multiply(sk_c8, sk_c2) = sk_c7))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(7,plain,
% 0.23/0.44 (((multiply(sk_c8, sk_c2) = sk_c7) | (multiply(sk_c3, sk_c8) = sk_c7)) <=> ((multiply(sk_c3, sk_c8) = sk_c7) | (multiply(sk_c8, sk_c2) = sk_c7))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(8,axiom,((multiply(sk_c8, sk_c2) = sk_c7) | (multiply(sk_c3, sk_c8) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_12')).
% 0.23/0.44 tff(9,plain,
% 0.23/0.44 ((multiply(sk_c3, sk_c8) = sk_c7) | (multiply(sk_c8, sk_c2) = sk_c7)),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.23/0.44 tff(10,plain,
% 0.23/0.44 ((multiply(sk_c3, sk_c8) = sk_c7) | (multiply(sk_c8, sk_c2) = sk_c7)),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.23/0.44 tff(11,plain,
% 0.23/0.44 (multiply(sk_c3, sk_c8) = sk_c7),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[10, 5])).
% 0.23/0.44 tff(12,plain,
% 0.23/0.44 (sk_c7 = multiply(sk_c3, sk_c8)),
% 0.23/0.44 inference(symmetry,[status(thm)],[11])).
% 0.23/0.44 tff(13,plain,
% 0.23/0.44 (multiply(sk_c8, sk_c7) = multiply(sk_c8, multiply(sk_c3, sk_c8))),
% 0.23/0.44 inference(monotonicity,[status(thm)],[12])).
% 0.23/0.44 tff(14,plain,
% 0.23/0.44 (multiply(sk_c8, multiply(sk_c3, sk_c8)) = multiply(sk_c8, sk_c7)),
% 0.23/0.44 inference(symmetry,[status(thm)],[13])).
% 0.23/0.44 tff(15,plain,
% 0.23/0.44 (^[Z: $i, Y: $i, X: $i] : refl((multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))) <=> (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(16,plain,
% 0.23/0.44 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[15])).
% 0.23/0.44 tff(17,plain,
% 0.23/0.44 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(18,axiom,(![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax','associativity')).
% 0.23/0.44 tff(19,plain,
% 0.23/0.44 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.23/0.44 tff(20,plain,(
% 0.23/0.44 ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.23/0.44 inference(skolemize,[status(sab)],[19])).
% 0.23/0.44 tff(21,plain,
% 0.23/0.44 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.23/0.44 tff(22,plain,
% 0.23/0.44 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c3), sk_c8) = multiply(sk_c8, multiply(sk_c3, sk_c8)))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(23,plain,
% 0.23/0.44 (multiply(multiply(sk_c8, sk_c3), sk_c8) = multiply(sk_c8, multiply(sk_c3, sk_c8))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.23/0.44 tff(24,plain,
% 0.23/0.44 (((inverse(sk_c4) = sk_c8) | (multiply(sk_c8, sk_c2) = sk_c7)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c8, sk_c2) = sk_c7))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(25,plain,
% 0.23/0.44 (((multiply(sk_c8, sk_c2) = sk_c7) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c8, sk_c2) = sk_c7))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(26,axiom,((multiply(sk_c8, sk_c2) = sk_c7) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_16')).
% 0.23/0.44 tff(27,plain,
% 0.23/0.44 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c8, sk_c2) = sk_c7)),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.23/0.44 tff(28,plain,
% 0.23/0.44 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c8, sk_c2) = sk_c7)),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.23/0.44 tff(29,plain,
% 0.23/0.44 (inverse(sk_c4) = sk_c8),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[28, 5])).
% 0.23/0.44 tff(30,plain,
% 0.23/0.44 (sk_c8 = inverse(sk_c4)),
% 0.23/0.44 inference(symmetry,[status(thm)],[29])).
% 0.23/0.44 tff(31,plain,
% 0.23/0.44 (multiply(sk_c8, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.23/0.44 inference(monotonicity,[status(thm)],[30])).
% 0.23/0.44 tff(32,plain,
% 0.23/0.44 (multiply(inverse(sk_c4), sk_c4) = multiply(sk_c8, sk_c4)),
% 0.23/0.44 inference(symmetry,[status(thm)],[31])).
% 0.23/0.44 tff(33,plain,
% 0.23/0.44 (^[X: $i] : refl((multiply(inverse(X), X) = identity) <=> (multiply(inverse(X), X) = identity))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(34,plain,
% 0.23/0.44 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.23/0.44 inference(quant_intro,[status(thm)],[33])).
% 0.23/0.44 tff(35,plain,
% 0.23/0.44 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(36,axiom,(![X: $i] : (multiply(inverse(X), X) = identity)), file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax','left_inverse')).
% 0.23/0.44 tff(37,plain,
% 0.23/0.44 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.23/0.44 tff(38,plain,(
% 0.23/0.44 ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.23/0.44 inference(skolemize,[status(sab)],[37])).
% 0.23/0.44 tff(39,plain,
% 0.23/0.44 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.23/0.44 tff(40,plain,
% 0.23/0.44 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c4), sk_c4) = identity)),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(41,plain,
% 0.23/0.44 (multiply(inverse(sk_c4), sk_c4) = identity),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.23/0.44 tff(42,plain,
% 0.23/0.44 (identity = multiply(inverse(sk_c4), sk_c4)),
% 0.23/0.44 inference(symmetry,[status(thm)],[41])).
% 0.23/0.44 tff(43,plain,
% 0.23/0.44 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c3), sk_c3) = identity)),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(44,plain,
% 0.23/0.44 (multiply(inverse(sk_c3), sk_c3) = identity),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[43, 39])).
% 0.23/0.44 tff(45,assumption,(~(inverse(sk_c3) = sk_c8)), introduced(assumption)).
% 0.23/0.44 tff(46,plain,
% 0.23/0.44 (((inverse(sk_c3) = sk_c8) | (multiply(sk_c8, sk_c2) = sk_c7)) <=> ((inverse(sk_c3) = sk_c8) | (multiply(sk_c8, sk_c2) = sk_c7))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(47,plain,
% 0.23/0.44 (((multiply(sk_c8, sk_c2) = sk_c7) | (inverse(sk_c3) = sk_c8)) <=> ((inverse(sk_c3) = sk_c8) | (multiply(sk_c8, sk_c2) = sk_c7))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(48,axiom,((multiply(sk_c8, sk_c2) = sk_c7) | (inverse(sk_c3) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_13')).
% 0.23/0.44 tff(49,plain,
% 0.23/0.44 ((inverse(sk_c3) = sk_c8) | (multiply(sk_c8, sk_c2) = sk_c7)),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.23/0.44 tff(50,plain,
% 0.23/0.44 ((inverse(sk_c3) = sk_c8) | (multiply(sk_c8, sk_c2) = sk_c7)),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[49, 46])).
% 0.23/0.44 tff(51,plain,
% 0.23/0.44 (multiply(sk_c8, sk_c2) = sk_c7),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[50, 45])).
% 0.23/0.44 tff(52,plain,
% 0.23/0.44 (((inverse(sk_c3) = sk_c8) | (multiply(sk_c1, sk_c8) = sk_c2)) <=> ((inverse(sk_c3) = sk_c8) | (multiply(sk_c1, sk_c8) = sk_c2))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(53,plain,
% 0.23/0.44 (((multiply(sk_c1, sk_c8) = sk_c2) | (inverse(sk_c3) = sk_c8)) <=> ((inverse(sk_c3) = sk_c8) | (multiply(sk_c1, sk_c8) = sk_c2))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(54,axiom,((multiply(sk_c1, sk_c8) = sk_c2) | (inverse(sk_c3) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_18')).
% 0.23/0.44 tff(55,plain,
% 0.23/0.44 ((inverse(sk_c3) = sk_c8) | (multiply(sk_c1, sk_c8) = sk_c2)),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.23/0.44 tff(56,plain,
% 0.23/0.44 ((inverse(sk_c3) = sk_c8) | (multiply(sk_c1, sk_c8) = sk_c2)),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[55, 52])).
% 0.23/0.44 tff(57,plain,
% 0.23/0.44 (multiply(sk_c1, sk_c8) = sk_c2),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[56, 45])).
% 0.23/0.44 tff(58,plain,
% 0.23/0.44 (sk_c2 = multiply(sk_c1, sk_c8)),
% 0.23/0.44 inference(symmetry,[status(thm)],[57])).
% 0.23/0.44 tff(59,plain,
% 0.23/0.44 (multiply(sk_c8, sk_c2) = multiply(sk_c8, multiply(sk_c1, sk_c8))),
% 0.23/0.44 inference(monotonicity,[status(thm)],[58])).
% 0.23/0.44 tff(60,plain,
% 0.23/0.44 (multiply(sk_c8, multiply(sk_c1, sk_c8)) = multiply(sk_c8, sk_c2)),
% 0.23/0.44 inference(symmetry,[status(thm)],[59])).
% 0.23/0.44 tff(61,plain,
% 0.23/0.44 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c1), sk_c8) = multiply(sk_c8, multiply(sk_c1, sk_c8)))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(62,plain,
% 0.23/0.44 (multiply(multiply(sk_c8, sk_c1), sk_c8) = multiply(sk_c8, multiply(sk_c1, sk_c8))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[61, 21])).
% 0.23/0.44 tff(63,plain,
% 0.23/0.44 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c1), sk_c1) = identity)),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(64,plain,
% 0.23/0.44 (multiply(inverse(sk_c1), sk_c1) = identity),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[63, 39])).
% 0.23/0.44 tff(65,plain,
% 0.23/0.44 (((inverse(sk_c1) = sk_c8) | (inverse(sk_c3) = sk_c8)) <=> ((inverse(sk_c1) = sk_c8) | (inverse(sk_c3) = sk_c8))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(66,axiom,((inverse(sk_c1) = sk_c8) | (inverse(sk_c3) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_23')).
% 0.23/0.44 tff(67,plain,
% 0.23/0.44 ((inverse(sk_c1) = sk_c8) | (inverse(sk_c3) = sk_c8)),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.23/0.44 tff(68,plain,
% 0.23/0.44 (inverse(sk_c1) = sk_c8),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[67, 45])).
% 0.23/0.44 tff(69,plain,
% 0.23/0.44 (sk_c8 = inverse(sk_c1)),
% 0.23/0.44 inference(symmetry,[status(thm)],[68])).
% 0.23/0.44 tff(70,plain,
% 0.23/0.44 (multiply(sk_c8, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.23/0.44 inference(monotonicity,[status(thm)],[69])).
% 0.23/0.44 tff(71,plain,
% 0.23/0.44 (multiply(sk_c8, sk_c1) = identity),
% 0.23/0.44 inference(transitivity,[status(thm)],[70, 64])).
% 0.23/0.44 tff(72,plain,
% 0.23/0.44 (multiply(multiply(sk_c8, sk_c1), sk_c8) = multiply(identity, sk_c8)),
% 0.23/0.44 inference(monotonicity,[status(thm)],[71])).
% 0.23/0.44 tff(73,plain,
% 0.23/0.44 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c1), sk_c8)),
% 0.23/0.44 inference(symmetry,[status(thm)],[72])).
% 0.23/0.44 tff(74,plain,
% 0.23/0.44 (^[X: $i] : refl((multiply(identity, X) = X) <=> (multiply(identity, X) = X))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(75,plain,
% 0.23/0.44 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.23/0.44 inference(quant_intro,[status(thm)],[74])).
% 0.23/0.44 tff(76,plain,
% 0.23/0.44 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(77,axiom,(![X: $i] : (multiply(identity, X) = X)), file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax','left_identity')).
% 0.23/0.44 tff(78,plain,
% 0.23/0.44 (![X: $i] : (multiply(identity, X) = X)),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.23/0.44 tff(79,plain,(
% 0.23/0.44 ![X: $i] : (multiply(identity, X) = X)),
% 0.23/0.44 inference(skolemize,[status(sab)],[78])).
% 0.23/0.44 tff(80,plain,
% 0.23/0.44 (![X: $i] : (multiply(identity, X) = X)),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.23/0.44 tff(81,plain,
% 0.23/0.44 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c8) = sk_c8)),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(82,plain,
% 0.23/0.44 (multiply(identity, sk_c8) = sk_c8),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.23/0.45 tff(83,plain,
% 0.23/0.45 (sk_c8 = multiply(identity, sk_c8)),
% 0.23/0.45 inference(symmetry,[status(thm)],[82])).
% 0.23/0.45 tff(84,plain,
% 0.23/0.45 (((inverse(sk_c3) = sk_c8) | (multiply(sk_c6, sk_c7) = sk_c8)) <=> ((inverse(sk_c3) = sk_c8) | (multiply(sk_c6, sk_c7) = sk_c8))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(85,plain,
% 0.23/0.45 (((multiply(sk_c6, sk_c7) = sk_c8) | (inverse(sk_c3) = sk_c8)) <=> ((inverse(sk_c3) = sk_c8) | (multiply(sk_c6, sk_c7) = sk_c8))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(86,axiom,((multiply(sk_c6, sk_c7) = sk_c8) | (inverse(sk_c3) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_8')).
% 0.23/0.45 tff(87,plain,
% 0.23/0.45 ((inverse(sk_c3) = sk_c8) | (multiply(sk_c6, sk_c7) = sk_c8)),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.23/0.45 tff(88,plain,
% 0.23/0.45 ((inverse(sk_c3) = sk_c8) | (multiply(sk_c6, sk_c7) = sk_c8)),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[87, 84])).
% 0.23/0.45 tff(89,plain,
% 0.23/0.45 (multiply(sk_c6, sk_c7) = sk_c8),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[88, 45])).
% 0.23/0.45 tff(90,plain,
% 0.23/0.45 (multiply(sk_c6, multiply(sk_c8, sk_c2)) = multiply(sk_c6, sk_c7)),
% 0.23/0.45 inference(monotonicity,[status(thm)],[51])).
% 0.23/0.45 tff(91,plain,
% 0.23/0.45 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c8), sk_c2) = multiply(sk_c6, multiply(sk_c8, sk_c2)))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(92,plain,
% 0.23/0.45 (multiply(multiply(sk_c6, sk_c8), sk_c2) = multiply(sk_c6, multiply(sk_c8, sk_c2))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[91, 21])).
% 0.23/0.45 tff(93,plain,
% 0.23/0.45 (((inverse(sk_c8) = sk_c6) | (inverse(sk_c3) = sk_c8)) <=> ((inverse(sk_c8) = sk_c6) | (inverse(sk_c3) = sk_c8))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(94,axiom,((inverse(sk_c8) = sk_c6) | (inverse(sk_c3) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_3')).
% 0.23/0.45 tff(95,plain,
% 0.23/0.45 ((inverse(sk_c8) = sk_c6) | (inverse(sk_c3) = sk_c8)),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.23/0.45 tff(96,plain,
% 0.23/0.45 ((inverse(sk_c8) = sk_c6) | (inverse(sk_c3) = sk_c8)),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[95, 93])).
% 0.23/0.45 tff(97,plain,
% 0.23/0.45 ((inverse(sk_c8) = sk_c6) | (inverse(sk_c3) = sk_c8)),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[96, 93])).
% 0.23/0.45 tff(98,plain,
% 0.23/0.45 ((inverse(sk_c8) = sk_c6) | (inverse(sk_c3) = sk_c8)),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.23/0.45 tff(99,plain,
% 0.23/0.45 ((inverse(sk_c8) = sk_c6) | (inverse(sk_c3) = sk_c8)),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[98, 93])).
% 0.23/0.45 tff(100,plain,
% 0.23/0.45 (inverse(sk_c8) = sk_c6),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[99, 45])).
% 0.23/0.45 tff(101,plain,
% 0.23/0.45 (sk_c6 = inverse(sk_c8)),
% 0.23/0.45 inference(symmetry,[status(thm)],[100])).
% 0.23/0.45 tff(102,plain,
% 0.23/0.45 (multiply(sk_c6, sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.23/0.45 inference(monotonicity,[status(thm)],[101])).
% 0.23/0.45 tff(103,plain,
% 0.23/0.45 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c6, sk_c8)),
% 0.23/0.45 inference(symmetry,[status(thm)],[102])).
% 0.23/0.45 tff(104,plain,
% 0.23/0.45 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c8), sk_c8) = identity)),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(105,plain,
% 0.23/0.45 (multiply(inverse(sk_c8), sk_c8) = identity),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[104, 39])).
% 0.23/0.45 tff(106,plain,
% 0.23/0.45 (identity = multiply(inverse(sk_c8), sk_c8)),
% 0.23/0.45 inference(symmetry,[status(thm)],[105])).
% 0.23/0.45 tff(107,plain,
% 0.23/0.45 (identity = multiply(sk_c6, sk_c8)),
% 0.23/0.45 inference(transitivity,[status(thm)],[106, 103])).
% 0.23/0.45 tff(108,plain,
% 0.23/0.45 (multiply(identity, sk_c2) = multiply(multiply(sk_c6, sk_c8), sk_c2)),
% 0.23/0.45 inference(monotonicity,[status(thm)],[107])).
% 0.23/0.45 tff(109,plain,
% 0.23/0.45 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c2) = sk_c2)),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(110,plain,
% 0.23/0.45 (multiply(identity, sk_c2) = sk_c2),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[109, 80])).
% 0.23/0.45 tff(111,plain,
% 0.23/0.45 (sk_c2 = multiply(identity, sk_c2)),
% 0.23/0.45 inference(symmetry,[status(thm)],[110])).
% 0.23/0.45 tff(112,plain,
% 0.23/0.45 (multiply(sk_c1, sk_c8) = sk_c7),
% 0.23/0.45 inference(transitivity,[status(thm)],[57, 111, 108, 92, 90, 89, 83, 73, 62, 60, 51])).
% 0.23/0.45 tff(113,plain,
% 0.23/0.45 (multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7),
% 0.23/0.45 inference(transitivity,[status(thm)],[60, 51])).
% 0.23/0.45 tff(114,plain,
% 0.23/0.45 (^[X4: $i, X5: $i, X1: $i] : refl(((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8))) <=> ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(115,plain,
% 0.23/0.45 (![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8))) <=> ![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[114])).
% 0.23/0.45 tff(116,plain,
% 0.23/0.45 (![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8))) <=> ![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(117,plain,
% 0.23/0.45 (^[X4: $i, X5: $i, X1: $i] : rewrite(((~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) <=> ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(118,plain,
% 0.23/0.45 (![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) <=> ![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[117])).
% 0.23/0.45 tff(119,plain,
% 0.23/0.45 (![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) <=> ![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)))),
% 0.23/0.45 inference(elim_unused_vars,[status(thm)],[])).
% 0.23/0.45 tff(120,plain,
% 0.23/0.45 (![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = X3)) | (~(multiply(sk_c8, X3) = sk_c7))) <=> ![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)))),
% 0.23/0.45 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.23/0.45 tff(121,plain,
% 0.23/0.45 (![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = X3)) | (~(multiply(sk_c8, X3) = sk_c7))) <=> ![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)))),
% 0.23/0.45 inference(transitivity,[status(thm)],[120, 119])).
% 0.23/0.45 tff(122,plain,
% 0.23/0.45 (![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = X3)) | (~(multiply(sk_c8, X3) = sk_c7))) <=> ![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))),
% 0.23/0.45 inference(transitivity,[status(thm)],[121, 118])).
% 0.23/0.45 tff(123,plain,
% 0.23/0.45 (^[X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6))) <=> ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)))), ((((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c8))) <=> (((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c8))))), rewrite((((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c8))) <=> ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)))), ((((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c8))) <=> ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8))))), (((((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X3) = sk_c7))) <=> (((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X3) = sk_c7))))), rewrite((((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X3) = sk_c7))) <=> ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(sk_c8, X3) = sk_c7)))), (((((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X3) = sk_c7))) <=> ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(sk_c8, X3) = sk_c7))))), ((((((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X3) = sk_c7))) | (~(multiply(X4, sk_c8) = X3))) <=> (((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(sk_c8, X3) = sk_c7))) | (~(multiply(X4, sk_c8) = X3))))), rewrite((((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(sk_c8, X3) = sk_c7))) | (~(multiply(X4, sk_c8) = X3))) <=> ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(X4, sk_c8) = X3)) | (~(multiply(sk_c8, X3) = sk_c7)))), ((((((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X3) = sk_c7))) | (~(multiply(X4, sk_c8) = X3))) <=> ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(X4, sk_c8) = X3)) | (~(multiply(sk_c8, X3) = sk_c7))))), (((((((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X3) = sk_c7))) | (~(multiply(X4, sk_c8) = X3))) | (~(inverse(X4) = sk_c8))) <=> (((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(X4, sk_c8) = X3)) | (~(multiply(sk_c8, X3) = sk_c7))) | (~(inverse(X4) = sk_c8))))), rewrite((((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(X4, sk_c8) = X3)) | (~(multiply(sk_c8, X3) = sk_c7))) | (~(inverse(X4) = sk_c8))) <=> ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = X3)) | (~(multiply(sk_c8, X3) = sk_c7)))), (((((((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X3) = sk_c7))) | (~(multiply(X4, sk_c8) = X3))) | (~(inverse(X4) = sk_c8))) <=> ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = X3)) | (~(multiply(sk_c8, X3) = sk_c7))))), ((((((((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X3) = sk_c7))) | (~(multiply(X4, sk_c8) = X3))) | (~(inverse(X4) = sk_c8))) | (~(multiply(X1, sk_c8) = sk_c7))) <=> (((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = X3)) | (~(multiply(sk_c8, X3) = sk_c7))) | (~(multiply(X1, sk_c8) = sk_c7))))), rewrite((((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = X3)) | (~(multiply(sk_c8, X3) = sk_c7))) | (~(multiply(X1, sk_c8) = sk_c7))) <=> ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = X3)) | (~(multiply(sk_c8, X3) = sk_c7)))), ((((((((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X3) = sk_c7))) | (~(multiply(X4, sk_c8) = X3))) | (~(inverse(X4) = sk_c8))) | (~(multiply(X1, sk_c8) = sk_c7))) <=> ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = X3)) | (~(multiply(sk_c8, X3) = sk_c7))))), (((((((((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X3) = sk_c7))) | (~(multiply(X4, sk_c8) = X3))) | (~(inverse(X4) = sk_c8))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) <=> (((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = X3)) | (~(multiply(sk_c8, X3) = sk_c7))) | (~(inverse(X1) = sk_c8))))), rewrite((((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = X3)) | (~(multiply(sk_c8, X3) = sk_c7))) | (~(inverse(X1) = sk_c8))) <=> ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = X3)) | (~(multiply(sk_c8, X3) = sk_c7)))), (((((((((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X3) = sk_c7))) | (~(multiply(X4, sk_c8) = X3))) | (~(inverse(X4) = sk_c8))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) <=> ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = X3)) | (~(multiply(sk_c8, X3) = sk_c7))))), ((((((((((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X3) = sk_c7))) | (~(multiply(X4, sk_c8) = X3))) | (~(inverse(X4) = sk_c8))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) <=> (((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = X3)) | (~(multiply(sk_c8, X3) = sk_c7))) | (~(multiply(sk_c8, X2) = sk_c7))))), rewrite((((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = X3)) | (~(multiply(sk_c8, X3) = sk_c7))) | (~(multiply(sk_c8, X2) = sk_c7))) <=> ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = X3)) | (~(multiply(sk_c8, X3) = sk_c7)))), ((((((((((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X3) = sk_c7))) | (~(multiply(X4, sk_c8) = X3))) | (~(inverse(X4) = sk_c8))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) <=> ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = X3)) | (~(multiply(sk_c8, X3) = sk_c7))))), (((((((((((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X3) = sk_c7))) | (~(multiply(X4, sk_c8) = X3))) | (~(inverse(X4) = sk_c8))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X5, sk_c8) = X2))) <=> (((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = X3)) | (~(multiply(sk_c8, X3) = sk_c7))) | (~(multiply(X5, sk_c8) = X2))))), rewrite((((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = X3)) | (~(multiply(sk_c8, X3) = sk_c7))) | (~(multiply(X5, sk_c8) = X2))) <=> ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(X5, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = X3)) | (~(multiply(sk_c8, X3) = sk_c7)))), (((((((((((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X3) = sk_c7))) | (~(multiply(X4, sk_c8) = X3))) | (~(inverse(X4) = sk_c8))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X5, sk_c8) = X2))) <=> ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(X5, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = X3)) | (~(multiply(sk_c8, X3) = sk_c7))))), ((((((((((((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X3) = sk_c7))) | (~(multiply(X4, sk_c8) = X3))) | (~(inverse(X4) = sk_c8))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X5, sk_c8) = X2))) | (~(inverse(X5) = sk_c8))) <=> (((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(X5, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = X3)) | (~(multiply(sk_c8, X3) = sk_c7))) | (~(inverse(X5) = sk_c8))))), rewrite((((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(X5, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = X3)) | (~(multiply(sk_c8, X3) = sk_c7))) | (~(inverse(X5) = sk_c8))) <=> ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = X3)) | (~(multiply(sk_c8, X3) = sk_c7)))), ((((((((((((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X3) = sk_c7))) | (~(multiply(X4, sk_c8) = X3))) | (~(inverse(X4) = sk_c8))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X5, sk_c8) = X2))) | (~(inverse(X5) = sk_c8))) <=> ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = X3)) | (~(multiply(sk_c8, X3) = sk_c7)))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(124,plain,
% 0.23/0.47 (![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : (((((((((((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X3) = sk_c7))) | (~(multiply(X4, sk_c8) = X3))) | (~(inverse(X4) = sk_c8))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X5, sk_c8) = X2))) | (~(inverse(X5) = sk_c8))) <=> ![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = X3)) | (~(multiply(sk_c8, X3) = sk_c7)))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[123])).
% 0.23/0.47 tff(125,plain,
% 0.23/0.47 (![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : (((((((((((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X3) = sk_c7))) | (~(multiply(X4, sk_c8) = X3))) | (~(inverse(X4) = sk_c8))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X5, sk_c8) = X2))) | (~(inverse(X5) = sk_c8))) <=> ![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))),
% 0.23/0.47 inference(transitivity,[status(thm)],[124, 122])).
% 0.23/0.47 tff(126,axiom,(![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : (((((((((((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c6, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X3) = sk_c7))) | (~(multiply(X4, sk_c8) = X3))) | (~(inverse(X4) = sk_c8))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X5, sk_c8) = X2))) | (~(inverse(X5) = sk_c8)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_27')).
% 0.23/0.47 tff(127,plain,
% 0.23/0.47 (![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.23/0.47 tff(128,plain,
% 0.23/0.47 (![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[127, 116])).
% 0.23/0.47 tff(129,plain,(
% 0.23/0.47 ![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))),
% 0.23/0.47 inference(skolemize,[status(sab)],[128])).
% 0.23/0.47 tff(130,plain,
% 0.23/0.47 (![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[129, 115])).
% 0.23/0.47 tff(131,plain,
% 0.23/0.47 (((~![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)))) <=> ((~![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(132,plain,
% 0.23/0.47 (((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8))) <=> ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(133,plain,
% 0.23/0.47 (((~![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)))) <=> ((~![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7))))),
% 0.23/0.47 inference(monotonicity,[status(thm)],[132])).
% 0.23/0.47 tff(134,plain,
% 0.23/0.47 (((~![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)))) <=> ((~![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)))),
% 0.23/0.48 inference(transitivity,[status(thm)],[133, 131])).
% 0.23/0.48 tff(135,plain,
% 0.23/0.48 ((~![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)))),
% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(136,plain,
% 0.23/0.48 ((~![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.23/0.48 tff(137,plain,
% 0.23/0.48 ((~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[136, 4, 100, 89, 68, 130])).
% 0.23/0.48 tff(138,plain,
% 0.23/0.48 (~(multiply(sk_c1, sk_c8) = sk_c7)),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[137, 113])).
% 0.23/0.48 tff(139,plain,
% 0.23/0.48 ($false),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[138, 112])).
% 0.23/0.48 tff(140,plain,(inverse(sk_c3) = sk_c8), inference(lemma,lemma(discharge,[]))).
% 0.23/0.48 tff(141,plain,
% 0.23/0.48 (sk_c8 = inverse(sk_c3)),
% 0.23/0.48 inference(symmetry,[status(thm)],[140])).
% 0.23/0.48 tff(142,plain,
% 0.23/0.48 (multiply(sk_c8, sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.23/0.48 inference(monotonicity,[status(thm)],[141])).
% 0.23/0.48 tff(143,plain,
% 0.23/0.48 (multiply(sk_c8, sk_c3) = multiply(sk_c8, sk_c4)),
% 0.23/0.48 inference(transitivity,[status(thm)],[142, 44, 42, 32])).
% 0.23/0.48 tff(144,plain,
% 0.23/0.48 (multiply(multiply(sk_c8, sk_c3), sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.23/0.48 inference(monotonicity,[status(thm)],[143])).
% 0.23/0.48 tff(145,plain,
% 0.23/0.48 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(multiply(sk_c8, sk_c3), sk_c8)),
% 0.23/0.48 inference(symmetry,[status(thm)],[144])).
% 0.23/0.48 tff(146,plain,
% 0.23/0.48 (identity = multiply(sk_c8, sk_c4)),
% 0.23/0.48 inference(transitivity,[status(thm)],[42, 32])).
% 0.23/0.48 tff(147,plain,
% 0.23/0.48 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.23/0.48 inference(monotonicity,[status(thm)],[146])).
% 0.23/0.48 tff(148,plain,
% 0.23/0.48 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c3) = sk_c3)),
% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(149,plain,
% 0.23/0.48 (multiply(identity, sk_c3) = sk_c3),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[148, 80])).
% 0.23/0.48 tff(150,plain,
% 0.23/0.48 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(identity, sk_c8)),
% 0.23/0.48 inference(symmetry,[status(thm)],[147])).
% 0.23/0.48 tff(151,plain,
% 0.23/0.48 (multiply(sk_c8, multiply(sk_c3, sk_c8)) = multiply(multiply(sk_c8, sk_c3), sk_c8)),
% 0.23/0.48 inference(symmetry,[status(thm)],[23])).
% 0.23/0.48 tff(152,plain,
% 0.23/0.48 (sk_c6 = multiply(sk_c8, sk_c7)),
% 0.23/0.48 inference(symmetry,[status(thm)],[4])).
% 0.23/0.48 tff(153,plain,
% 0.23/0.48 (sk_c6 = sk_c8),
% 0.23/0.48 inference(transitivity,[status(thm)],[152, 13, 151, 144, 150, 82])).
% 0.23/0.48 tff(154,plain,
% 0.23/0.48 (multiply(sk_c6, identity) = multiply(sk_c8, identity)),
% 0.23/0.48 inference(monotonicity,[status(thm)],[153])).
% 0.23/0.48 tff(155,plain,
% 0.23/0.48 (multiply(sk_c8, identity) = multiply(sk_c6, identity)),
% 0.23/0.48 inference(symmetry,[status(thm)],[154])).
% 0.23/0.48 tff(156,plain,
% 0.23/0.48 (multiply(sk_c6, sk_c4) = multiply(sk_c8, sk_c4)),
% 0.23/0.48 inference(monotonicity,[status(thm)],[153])).
% 0.23/0.48 tff(157,plain,
% 0.23/0.48 (multiply(sk_c8, sk_c4) = multiply(sk_c6, sk_c4)),
% 0.23/0.48 inference(symmetry,[status(thm)],[156])).
% 0.23/0.48 tff(158,plain,
% 0.23/0.48 (identity = multiply(sk_c6, sk_c4)),
% 0.23/0.48 inference(transitivity,[status(thm)],[42, 32, 157])).
% 0.23/0.48 tff(159,plain,
% 0.23/0.48 (sk_c8 = sk_c6),
% 0.23/0.48 inference(transitivity,[status(thm)],[83, 147, 145, 23, 14, 4])).
% 0.23/0.48 tff(160,plain,
% 0.23/0.48 (multiply(sk_c8, identity) = multiply(sk_c6, multiply(sk_c6, sk_c4))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[159, 158])).
% 0.23/0.48 tff(161,plain,
% 0.23/0.48 (multiply(sk_c6, multiply(sk_c6, sk_c4)) = multiply(sk_c8, identity)),
% 0.23/0.48 inference(symmetry,[status(thm)],[160])).
% 0.23/0.48 tff(162,plain,
% 0.23/0.48 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c6), sk_c4) = multiply(sk_c6, multiply(sk_c6, sk_c4)))),
% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(163,plain,
% 0.23/0.48 (multiply(multiply(sk_c6, sk_c6), sk_c4) = multiply(sk_c6, multiply(sk_c6, sk_c4))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[162, 21])).
% 0.23/0.48 tff(164,plain,
% 0.23/0.48 (multiply(sk_c6, sk_c7) = multiply(sk_c8, sk_c7)),
% 0.23/0.48 inference(monotonicity,[status(thm)],[153])).
% 0.23/0.48 tff(165,plain,
% 0.23/0.48 (((multiply(sk_c8, sk_c2) = sk_c7) | (multiply(sk_c8, sk_c5) = sk_c7)) <=> ((multiply(sk_c8, sk_c2) = sk_c7) | (multiply(sk_c8, sk_c5) = sk_c7))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(166,axiom,((multiply(sk_c8, sk_c2) = sk_c7) | (multiply(sk_c8, sk_c5) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_14')).
% 0.23/0.48 tff(167,plain,
% 0.23/0.48 ((multiply(sk_c8, sk_c2) = sk_c7) | (multiply(sk_c8, sk_c5) = sk_c7)),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.23/0.48 tff(168,plain,
% 0.23/0.48 (multiply(sk_c8, sk_c5) = sk_c7),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[167, 5])).
% 0.23/0.48 tff(169,plain,
% 0.23/0.48 (((multiply(sk_c4, sk_c8) = sk_c5) | (multiply(sk_c8, sk_c2) = sk_c7)) <=> ((multiply(sk_c4, sk_c8) = sk_c5) | (multiply(sk_c8, sk_c2) = sk_c7))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(170,plain,
% 0.23/0.48 (((multiply(sk_c8, sk_c2) = sk_c7) | (multiply(sk_c4, sk_c8) = sk_c5)) <=> ((multiply(sk_c4, sk_c8) = sk_c5) | (multiply(sk_c8, sk_c2) = sk_c7))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(171,axiom,((multiply(sk_c8, sk_c2) = sk_c7) | (multiply(sk_c4, sk_c8) = sk_c5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_15')).
% 0.23/0.48 tff(172,plain,
% 0.23/0.48 ((multiply(sk_c4, sk_c8) = sk_c5) | (multiply(sk_c8, sk_c2) = sk_c7)),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.23/0.48 tff(173,plain,
% 0.23/0.48 ((multiply(sk_c4, sk_c8) = sk_c5) | (multiply(sk_c8, sk_c2) = sk_c7)),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[172, 169])).
% 0.23/0.48 tff(174,plain,
% 0.23/0.48 (multiply(sk_c4, sk_c8) = sk_c5),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[173, 5])).
% 0.23/0.48 tff(175,plain,
% 0.23/0.48 (sk_c5 = multiply(sk_c4, sk_c8)),
% 0.23/0.48 inference(symmetry,[status(thm)],[174])).
% 0.23/0.48 tff(176,plain,
% 0.23/0.48 (multiply(sk_c8, sk_c5) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[175])).
% 0.23/0.48 tff(177,plain,
% 0.23/0.48 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = multiply(sk_c8, sk_c5)),
% 0.23/0.48 inference(symmetry,[status(thm)],[176])).
% 0.23/0.48 tff(178,plain,
% 0.23/0.48 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(sk_c8, multiply(sk_c4, sk_c8)))),
% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(179,plain,
% 0.23/0.48 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[178, 21])).
% 0.23/0.48 tff(180,plain,
% 0.23/0.48 (sk_c6 = sk_c7),
% 0.23/0.48 inference(transitivity,[status(thm)],[152, 13, 151, 144, 179, 177, 168])).
% 0.23/0.48 tff(181,plain,
% 0.23/0.48 (multiply(sk_c6, sk_c6) = multiply(sk_c6, sk_c7)),
% 0.23/0.48 inference(monotonicity,[status(thm)],[180])).
% 0.23/0.48 tff(182,plain,
% 0.23/0.48 (multiply(sk_c6, sk_c6) = sk_c8),
% 0.23/0.48 inference(transitivity,[status(thm)],[181, 164, 13, 151, 144, 150, 82])).
% 0.23/0.48 tff(183,plain,
% 0.23/0.48 (multiply(multiply(sk_c6, sk_c6), sk_c4) = multiply(sk_c8, sk_c4)),
% 0.23/0.48 inference(monotonicity,[status(thm)],[182])).
% 0.23/0.48 tff(184,plain,
% 0.23/0.48 (multiply(sk_c8, sk_c4) = multiply(multiply(sk_c6, sk_c6), sk_c4)),
% 0.23/0.48 inference(symmetry,[status(thm)],[183])).
% 0.23/0.48 tff(185,plain,
% 0.23/0.48 (identity = multiply(sk_c6, identity)),
% 0.23/0.48 inference(transitivity,[status(thm)],[42, 32, 184, 163, 161, 155])).
% 0.23/0.48 tff(186,plain,
% 0.23/0.48 (multiply(identity, sk_c3) = multiply(multiply(sk_c6, identity), sk_c3)),
% 0.23/0.48 inference(monotonicity,[status(thm)],[185])).
% 0.23/0.48 tff(187,plain,
% 0.23/0.48 (multiply(multiply(sk_c6, identity), sk_c3) = multiply(identity, sk_c3)),
% 0.23/0.48 inference(symmetry,[status(thm)],[186])).
% 0.23/0.48 tff(188,plain,
% 0.23/0.48 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, identity), sk_c3) = multiply(sk_c6, multiply(identity, sk_c3)))),
% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(189,plain,
% 0.23/0.48 (multiply(multiply(sk_c6, identity), sk_c3) = multiply(sk_c6, multiply(identity, sk_c3))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[188, 21])).
% 0.23/0.48 tff(190,plain,
% 0.23/0.48 (multiply(sk_c6, multiply(identity, sk_c3)) = multiply(multiply(sk_c6, identity), sk_c3)),
% 0.23/0.48 inference(symmetry,[status(thm)],[189])).
% 0.23/0.48 tff(191,plain,
% 0.23/0.48 (sk_c6 = inverse(sk_c3)),
% 0.23/0.48 inference(transitivity,[status(thm)],[152, 13, 151, 144, 150, 82, 141])).
% 0.23/0.48 tff(192,plain,
% 0.23/0.48 (multiply(sk_c6, multiply(identity, sk_c3)) = multiply(inverse(sk_c3), sk_c3)),
% 0.23/0.48 inference(monotonicity,[status(thm)],[191, 149])).
% 0.23/0.48 tff(193,plain,
% 0.23/0.48 (multiply(inverse(sk_c3), sk_c3) = multiply(sk_c6, multiply(identity, sk_c3))),
% 0.23/0.48 inference(symmetry,[status(thm)],[192])).
% 0.23/0.48 tff(194,plain,
% 0.23/0.48 (identity = multiply(inverse(sk_c3), sk_c3)),
% 0.23/0.48 inference(symmetry,[status(thm)],[44])).
% 0.23/0.48 tff(195,plain,
% 0.23/0.48 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c6), sk_c6) = identity)),
% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(196,plain,
% 0.23/0.48 (multiply(inverse(sk_c6), sk_c6) = identity),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[195, 39])).
% 0.23/0.48 tff(197,plain,
% 0.23/0.48 (multiply(sk_c6, sk_c6) = sk_c6),
% 0.23/0.48 inference(transitivity,[status(thm)],[181, 164, 4])).
% 0.23/0.48 tff(198,plain,
% 0.23/0.48 (inverse(sk_c6) = inverse(sk_c8)),
% 0.23/0.48 inference(monotonicity,[status(thm)],[153])).
% 0.23/0.48 tff(199,plain,
% 0.23/0.48 (inverse(sk_c8) = inverse(sk_c6)),
% 0.23/0.48 inference(symmetry,[status(thm)],[198])).
% 0.23/0.48 tff(200,plain,
% 0.23/0.48 (multiply(inverse(sk_c8), multiply(sk_c6, sk_c6)) = multiply(inverse(sk_c6), sk_c6)),
% 0.23/0.48 inference(monotonicity,[status(thm)],[199, 197])).
% 0.23/0.48 tff(201,plain,
% 0.23/0.48 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(inverse(sk_c8), sk_c6), sk_c6) = multiply(inverse(sk_c8), multiply(sk_c6, sk_c6)))),
% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(202,plain,
% 0.23/0.48 (multiply(multiply(inverse(sk_c8), sk_c6), sk_c6) = multiply(inverse(sk_c8), multiply(sk_c6, sk_c6))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[201, 21])).
% 0.23/0.48 tff(203,plain,
% 0.23/0.48 (multiply(inverse(sk_c8), sk_c6) = multiply(inverse(sk_c6), sk_c6)),
% 0.23/0.48 inference(monotonicity,[status(thm)],[199])).
% 0.23/0.48 tff(204,plain,
% 0.23/0.48 (multiply(inverse(sk_c6), sk_c6) = multiply(inverse(sk_c8), sk_c6)),
% 0.23/0.48 inference(symmetry,[status(thm)],[203])).
% 0.23/0.48 tff(205,plain,
% 0.23/0.48 (identity = multiply(inverse(sk_c6), sk_c6)),
% 0.23/0.48 inference(symmetry,[status(thm)],[196])).
% 0.23/0.48 tff(206,plain,
% 0.23/0.48 (multiply(sk_c8, sk_c4) = multiply(inverse(sk_c8), sk_c6)),
% 0.23/0.48 inference(transitivity,[status(thm)],[31, 41, 205, 204])).
% 0.23/0.48 tff(207,plain,
% 0.23/0.48 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(multiply(inverse(sk_c8), sk_c6), sk_c6)),
% 0.23/0.48 inference(monotonicity,[status(thm)],[206, 159])).
% 0.23/0.48 tff(208,plain,
% 0.23/0.48 (sk_c8 = sk_c3),
% 0.23/0.48 inference(transitivity,[status(thm)],[83, 147, 207, 202, 200, 196, 194, 193, 190, 187, 149])).
% 0.23/0.48 tff(209,plain,
% 0.23/0.48 (inverse(sk_c8) = inverse(sk_c3)),
% 0.23/0.48 inference(monotonicity,[status(thm)],[208])).
% 0.23/0.48 tff(210,plain,
% 0.23/0.48 (inverse(sk_c8) = sk_c6),
% 0.23/0.48 inference(transitivity,[status(thm)],[209, 140, 83, 147, 145, 23, 14, 4])).
% 0.23/0.48 tff(211,plain,
% 0.23/0.48 (multiply(sk_c8, multiply(sk_c3, sk_c8)) = sk_c7),
% 0.23/0.48 inference(transitivity,[status(thm)],[151, 144, 179, 177, 168])).
% 0.23/0.48 tff(212,plain,
% 0.23/0.48 (multiply(sk_c6, sk_c7) = sk_c8),
% 0.23/0.48 inference(transitivity,[status(thm)],[164, 13, 151, 144, 150, 82])).
% 0.23/0.48 tff(213,plain,
% 0.23/0.48 (((~![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c3, sk_c8)) = sk_c7)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(inverse(sk_c3) = sk_c8)))) <=> ((~![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c3, sk_c8)) = sk_c7)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(inverse(sk_c3) = sk_c8)))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(214,plain,
% 0.23/0.48 (((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(sk_c3) = sk_c8)) | (~(inverse(sk_c3) = sk_c8)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c3, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c3, sk_c8)) = sk_c7)) | (~(inverse(sk_c3) = sk_c8))) <=> ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c3, sk_c8)) = sk_c7)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(inverse(sk_c3) = sk_c8)))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(215,plain,
% 0.23/0.48 (((~![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(sk_c3) = sk_c8)) | (~(inverse(sk_c3) = sk_c8)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c3, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c3, sk_c8)) = sk_c7)) | (~(inverse(sk_c3) = sk_c8)))) <=> ((~![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c3, sk_c8)) = sk_c7)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(inverse(sk_c3) = sk_c8))))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[214])).
% 0.23/0.48 tff(216,plain,
% 0.23/0.48 (((~![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(sk_c3) = sk_c8)) | (~(inverse(sk_c3) = sk_c8)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c3, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c3, sk_c8)) = sk_c7)) | (~(inverse(sk_c3) = sk_c8)))) <=> ((~![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c3, sk_c8)) = sk_c7)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(inverse(sk_c3) = sk_c8)))),
% 0.23/0.49 inference(transitivity,[status(thm)],[215, 213])).
% 0.23/0.49 tff(217,plain,
% 0.23/0.49 ((~![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(sk_c3) = sk_c8)) | (~(inverse(sk_c3) = sk_c8)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c3, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c3, sk_c8)) = sk_c7)) | (~(inverse(sk_c3) = sk_c8)))),
% 0.23/0.49 inference(quant_inst,[status(thm)],[])).
% 0.23/0.49 tff(218,plain,
% 0.23/0.49 ((~![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c3, sk_c8)) = sk_c7)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(inverse(sk_c3) = sk_c8))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.23/0.49 tff(219,plain,
% 0.23/0.49 ((~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c3, sk_c8)) = sk_c7)) | (~(multiply(sk_c3, sk_c8) = sk_c7))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[218, 4, 140, 130])).
% 0.23/0.49 tff(220,plain,
% 0.23/0.49 (~(inverse(sk_c8) = sk_c6)),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[219, 212, 11, 211])).
% 0.23/0.49 tff(221,plain,
% 0.23/0.49 ($false),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[220, 210])).
% 0.23/0.49 tff(222,plain,(multiply(sk_c8, sk_c2) = sk_c7), inference(lemma,lemma(discharge,[]))).
% 0.23/0.49 tff(223,assumption,(~(inverse(sk_c8) = sk_c6)), introduced(assumption)).
% 0.23/0.49 tff(224,plain,
% 0.23/0.49 (((inverse(sk_c8) = sk_c6) | (multiply(sk_c3, sk_c8) = sk_c7)) <=> ((inverse(sk_c8) = sk_c6) | (multiply(sk_c3, sk_c8) = sk_c7))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(225,axiom,((inverse(sk_c8) = sk_c6) | (multiply(sk_c3, sk_c8) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_2')).
% 0.23/0.49 tff(226,plain,
% 0.23/0.49 ((inverse(sk_c8) = sk_c6) | (multiply(sk_c3, sk_c8) = sk_c7)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.23/0.49 tff(227,plain,
% 0.23/0.49 (multiply(sk_c3, sk_c8) = sk_c7),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[226, 223])).
% 0.23/0.49 tff(228,plain,
% 0.23/0.49 (multiply(sk_c8, multiply(sk_c3, sk_c8)) = multiply(sk_c8, sk_c7)),
% 0.23/0.49 inference(monotonicity,[status(thm)],[227])).
% 0.23/0.49 tff(229,plain,
% 0.23/0.49 (multiply(inverse(sk_c3), sk_c3) = multiply(sk_c8, sk_c3)),
% 0.23/0.49 inference(symmetry,[status(thm)],[142])).
% 0.23/0.49 tff(230,plain,
% 0.23/0.49 (((inverse(sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(231,axiom,((inverse(sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_6')).
% 0.23/0.49 tff(232,plain,
% 0.23/0.49 ((inverse(sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.23/0.49 tff(233,plain,
% 0.23/0.49 ((inverse(sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[232, 230])).
% 0.23/0.49 tff(234,plain,
% 0.23/0.49 ((inverse(sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[233, 230])).
% 0.23/0.49 tff(235,plain,
% 0.23/0.49 ((inverse(sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[234, 230])).
% 0.23/0.49 tff(236,plain,
% 0.23/0.49 ((inverse(sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[235, 230])).
% 0.23/0.49 tff(237,plain,
% 0.23/0.49 (inverse(sk_c4) = sk_c8),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[236, 223])).
% 0.23/0.49 tff(238,plain,
% 0.23/0.49 (sk_c8 = inverse(sk_c4)),
% 0.23/0.49 inference(symmetry,[status(thm)],[237])).
% 0.23/0.49 tff(239,plain,
% 0.23/0.49 (multiply(sk_c8, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.23/0.49 inference(monotonicity,[status(thm)],[238])).
% 0.23/0.49 tff(240,plain,
% 0.23/0.49 (multiply(sk_c8, sk_c4) = multiply(sk_c8, sk_c3)),
% 0.23/0.49 inference(transitivity,[status(thm)],[239, 41, 194, 229])).
% 0.23/0.49 tff(241,plain,
% 0.23/0.49 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(multiply(sk_c8, sk_c3), sk_c8)),
% 0.23/0.49 inference(monotonicity,[status(thm)],[240])).
% 0.23/0.49 tff(242,plain,
% 0.23/0.49 (multiply(inverse(sk_c4), sk_c4) = multiply(sk_c8, sk_c4)),
% 0.23/0.49 inference(symmetry,[status(thm)],[239])).
% 0.23/0.49 tff(243,plain,
% 0.23/0.49 (identity = multiply(sk_c8, sk_c4)),
% 0.23/0.49 inference(transitivity,[status(thm)],[42, 242])).
% 0.23/0.49 tff(244,plain,
% 0.23/0.49 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.23/0.49 inference(monotonicity,[status(thm)],[243])).
% 0.23/0.49 tff(245,plain,
% 0.23/0.49 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(identity, sk_c8)),
% 0.23/0.49 inference(symmetry,[status(thm)],[244])).
% 0.23/0.49 tff(246,plain,
% 0.23/0.49 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c8, sk_c4)),
% 0.23/0.49 inference(transitivity,[status(thm)],[105, 42, 242])).
% 0.23/0.49 tff(247,plain,
% 0.23/0.49 (multiply(multiply(inverse(sk_c8), sk_c8), sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.23/0.49 inference(monotonicity,[status(thm)],[246])).
% 0.23/0.49 tff(248,plain,
% 0.23/0.49 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(inverse(sk_c8), sk_c8), sk_c8) = multiply(inverse(sk_c8), multiply(sk_c8, sk_c8)))),
% 0.23/0.49 inference(quant_inst,[status(thm)],[])).
% 0.23/0.49 tff(249,plain,
% 0.23/0.49 (multiply(multiply(inverse(sk_c8), sk_c8), sk_c8) = multiply(inverse(sk_c8), multiply(sk_c8, sk_c8))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[248, 21])).
% 0.23/0.49 tff(250,plain,
% 0.23/0.49 (multiply(inverse(sk_c8), multiply(sk_c8, sk_c8)) = multiply(multiply(inverse(sk_c8), sk_c8), sk_c8)),
% 0.23/0.49 inference(symmetry,[status(thm)],[249])).
% 0.23/0.49 tff(251,plain,
% 0.23/0.49 (((inverse(sk_c8) = sk_c6) | (multiply(sk_c8, sk_c5) = sk_c7)) <=> ((inverse(sk_c8) = sk_c6) | (multiply(sk_c8, sk_c5) = sk_c7))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(252,axiom,((inverse(sk_c8) = sk_c6) | (multiply(sk_c8, sk_c5) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_4')).
% 0.23/0.49 tff(253,plain,
% 0.23/0.49 ((inverse(sk_c8) = sk_c6) | (multiply(sk_c8, sk_c5) = sk_c7)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.23/0.49 tff(254,plain,
% 0.23/0.49 (multiply(sk_c8, sk_c5) = sk_c7),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[253, 223])).
% 0.23/0.49 tff(255,plain,
% 0.23/0.49 (((inverse(sk_c8) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c5)) <=> ((inverse(sk_c8) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c5))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(256,axiom,((inverse(sk_c8) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_5')).
% 0.23/0.49 tff(257,plain,
% 0.23/0.49 ((inverse(sk_c8) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c5)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.23/0.49 tff(258,plain,
% 0.23/0.49 (multiply(sk_c4, sk_c8) = sk_c5),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[257, 223])).
% 0.23/0.49 tff(259,plain,
% 0.23/0.49 (sk_c5 = multiply(sk_c4, sk_c8)),
% 0.23/0.49 inference(symmetry,[status(thm)],[258])).
% 0.23/0.49 tff(260,plain,
% 0.23/0.49 (multiply(sk_c8, sk_c5) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[259])).
% 0.23/0.49 tff(261,plain,
% 0.23/0.49 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = multiply(sk_c8, sk_c5)),
% 0.23/0.49 inference(symmetry,[status(thm)],[260])).
% 0.23/0.49 tff(262,plain,
% 0.23/0.49 (sk_c8 = sk_c7),
% 0.23/0.49 inference(transitivity,[status(thm)],[83, 244, 179, 261, 254])).
% 0.23/0.49 tff(263,plain,
% 0.23/0.49 (sk_c8 = sk_c6),
% 0.23/0.49 inference(transitivity,[status(thm)],[83, 244, 241, 23, 228, 4])).
% 0.23/0.49 tff(264,plain,
% 0.23/0.49 (multiply(sk_c8, sk_c8) = multiply(sk_c6, sk_c7)),
% 0.23/0.49 inference(monotonicity,[status(thm)],[263, 262])).
% 0.23/0.49 tff(265,plain,
% 0.23/0.49 (multiply(sk_c6, sk_c7) = multiply(sk_c8, sk_c8)),
% 0.23/0.49 inference(symmetry,[status(thm)],[264])).
% 0.23/0.49 tff(266,plain,
% 0.23/0.49 (multiply(multiply(sk_c8, sk_c3), sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.23/0.49 inference(symmetry,[status(thm)],[241])).
% 0.23/0.49 tff(267,plain,
% 0.23/0.49 (multiply(sk_c8, sk_c7) = multiply(sk_c8, multiply(sk_c3, sk_c8))),
% 0.23/0.49 inference(symmetry,[status(thm)],[228])).
% 0.23/0.49 tff(268,plain,
% 0.23/0.49 (sk_c6 = sk_c8),
% 0.23/0.49 inference(transitivity,[status(thm)],[152, 267, 151, 266, 245, 82])).
% 0.23/0.49 tff(269,plain,
% 0.23/0.49 (multiply(sk_c6, sk_c7) = multiply(sk_c8, sk_c7)),
% 0.23/0.49 inference(monotonicity,[status(thm)],[268])).
% 0.23/0.49 tff(270,plain,
% 0.23/0.49 (multiply(sk_c8, sk_c7) = multiply(sk_c6, sk_c7)),
% 0.23/0.49 inference(symmetry,[status(thm)],[269])).
% 0.23/0.49 tff(271,plain,
% 0.23/0.49 (sk_c8 = multiply(sk_c8, sk_c8)),
% 0.23/0.49 inference(transitivity,[status(thm)],[83, 244, 241, 23, 228, 270, 265])).
% 0.23/0.49 tff(272,plain,
% 0.23/0.49 (multiply(inverse(sk_c8), sk_c8) = multiply(inverse(sk_c8), multiply(sk_c8, sk_c8))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[271])).
% 0.23/0.49 tff(273,plain,
% 0.23/0.49 (identity = inverse(sk_c3)),
% 0.23/0.49 inference(transitivity,[status(thm)],[106, 272, 250, 247, 245, 82, 141])).
% 0.23/0.49 tff(274,plain,
% 0.23/0.49 (multiply(identity, sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.23/0.49 inference(monotonicity,[status(thm)],[273])).
% 0.23/0.49 tff(275,plain,
% 0.23/0.49 (multiply(inverse(sk_c3), sk_c3) = multiply(identity, sk_c3)),
% 0.23/0.49 inference(symmetry,[status(thm)],[274])).
% 0.23/0.49 tff(276,plain,
% 0.23/0.49 (multiply(inverse(sk_c8), multiply(sk_c8, sk_c8)) = multiply(inverse(sk_c8), sk_c8)),
% 0.23/0.49 inference(symmetry,[status(thm)],[272])).
% 0.23/0.49 tff(277,plain,
% 0.23/0.49 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(multiply(inverse(sk_c8), sk_c8), sk_c8)),
% 0.23/0.49 inference(symmetry,[status(thm)],[247])).
% 0.23/0.49 tff(278,plain,
% 0.23/0.49 (sk_c8 = sk_c3),
% 0.23/0.49 inference(transitivity,[status(thm)],[83, 244, 277, 249, 276, 105, 194, 275, 149])).
% 0.23/0.49 tff(279,plain,
% 0.23/0.49 (inverse(sk_c8) = inverse(sk_c3)),
% 0.23/0.49 inference(monotonicity,[status(thm)],[278])).
% 0.23/0.49 tff(280,plain,
% 0.23/0.49 (inverse(sk_c8) = sk_c6),
% 0.23/0.49 inference(transitivity,[status(thm)],[279, 140, 83, 244, 241, 23, 228, 4])).
% 0.23/0.49 tff(281,plain,
% 0.23/0.49 ($false),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[223, 280])).
% 0.23/0.49 tff(282,plain,(inverse(sk_c8) = sk_c6), inference(lemma,lemma(discharge,[]))).
% 0.23/0.49 tff(283,plain,
% 0.23/0.49 (sk_c6 = inverse(sk_c8)),
% 0.23/0.49 inference(symmetry,[status(thm)],[282])).
% 0.23/0.49 tff(284,plain,
% 0.23/0.49 (multiply(sk_c6, sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.23/0.49 inference(monotonicity,[status(thm)],[283])).
% 0.23/0.49 tff(285,plain,
% 0.23/0.49 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c6, sk_c8)),
% 0.23/0.49 inference(symmetry,[status(thm)],[284])).
% 0.23/0.49 tff(286,plain,
% 0.23/0.49 (identity = multiply(sk_c6, sk_c8)),
% 0.23/0.49 inference(transitivity,[status(thm)],[106, 285])).
% 0.23/0.49 tff(287,plain,
% 0.23/0.49 (multiply(identity, sk_c2) = multiply(multiply(sk_c6, sk_c8), sk_c2)),
% 0.23/0.49 inference(monotonicity,[status(thm)],[286])).
% 0.23/0.49 tff(288,plain,
% 0.23/0.49 (multiply(multiply(sk_c6, sk_c8), sk_c2) = multiply(identity, sk_c2)),
% 0.23/0.49 inference(symmetry,[status(thm)],[287])).
% 0.23/0.49 tff(289,plain,
% 0.23/0.49 (multiply(sk_c6, multiply(sk_c8, sk_c2)) = multiply(multiply(sk_c6, sk_c8), sk_c2)),
% 0.23/0.49 inference(symmetry,[status(thm)],[92])).
% 0.23/0.49 tff(290,plain,
% 0.23/0.49 (sk_c7 = multiply(sk_c8, sk_c2)),
% 0.23/0.49 inference(symmetry,[status(thm)],[222])).
% 0.23/0.49 tff(291,plain,
% 0.23/0.49 (multiply(sk_c6, sk_c7) = multiply(sk_c6, multiply(sk_c8, sk_c2))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[290])).
% 0.23/0.49 tff(292,assumption,(~(inverse(sk_c4) = sk_c8)), introduced(assumption)).
% 0.23/0.49 tff(293,plain,
% 0.23/0.49 (((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c8) = sk_c2)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c8) = sk_c2))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(294,plain,
% 0.23/0.49 (((multiply(sk_c1, sk_c8) = sk_c2) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c8) = sk_c2))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(295,axiom,((multiply(sk_c1, sk_c8) = sk_c2) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_21')).
% 0.23/0.49 tff(296,plain,
% 0.23/0.49 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c8) = sk_c2)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.23/0.49 tff(297,plain,
% 0.23/0.49 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c8) = sk_c2)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[296, 293])).
% 0.23/0.49 tff(298,plain,
% 0.23/0.49 (multiply(sk_c1, sk_c8) = sk_c2),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[297, 292])).
% 0.23/0.49 tff(299,plain,
% 0.23/0.49 (sk_c2 = multiply(sk_c1, sk_c8)),
% 0.23/0.49 inference(symmetry,[status(thm)],[298])).
% 0.23/0.49 tff(300,plain,
% 0.23/0.49 (multiply(sk_c8, sk_c2) = multiply(sk_c8, multiply(sk_c1, sk_c8))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[299])).
% 0.23/0.49 tff(301,plain,
% 0.23/0.49 (multiply(sk_c8, multiply(sk_c1, sk_c8)) = multiply(sk_c8, sk_c2)),
% 0.23/0.49 inference(symmetry,[status(thm)],[300])).
% 0.23/0.49 tff(302,plain,
% 0.23/0.49 (((inverse(sk_c1) = sk_c8) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c1) = sk_c8) | (inverse(sk_c4) = sk_c8))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(303,axiom,((inverse(sk_c1) = sk_c8) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_26')).
% 0.23/0.49 tff(304,plain,
% 0.23/0.49 ((inverse(sk_c1) = sk_c8) | (inverse(sk_c4) = sk_c8)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[303, 302])).
% 0.23/0.49 tff(305,plain,
% 0.23/0.49 (inverse(sk_c1) = sk_c8),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[304, 292])).
% 0.23/0.49 tff(306,plain,
% 0.23/0.49 (sk_c8 = inverse(sk_c1)),
% 0.23/0.49 inference(symmetry,[status(thm)],[305])).
% 0.23/0.49 tff(307,plain,
% 0.23/0.49 (multiply(sk_c8, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.23/0.49 inference(monotonicity,[status(thm)],[306])).
% 0.23/0.49 tff(308,plain,
% 0.23/0.49 (multiply(sk_c8, sk_c1) = identity),
% 0.23/0.49 inference(transitivity,[status(thm)],[307, 64])).
% 0.23/0.49 tff(309,plain,
% 0.23/0.49 (multiply(multiply(sk_c8, sk_c1), sk_c8) = multiply(identity, sk_c8)),
% 0.23/0.49 inference(monotonicity,[status(thm)],[308])).
% 0.23/0.49 tff(310,plain,
% 0.23/0.49 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c1), sk_c8)),
% 0.23/0.49 inference(symmetry,[status(thm)],[309])).
% 0.23/0.49 tff(311,plain,
% 0.23/0.49 (((inverse(sk_c4) = sk_c8) | (multiply(sk_c6, sk_c7) = sk_c8)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c6, sk_c7) = sk_c8))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(312,plain,
% 0.23/0.49 (((multiply(sk_c6, sk_c7) = sk_c8) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c6, sk_c7) = sk_c8))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(313,axiom,((multiply(sk_c6, sk_c7) = sk_c8) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_11')).
% 0.23/0.49 tff(314,plain,
% 0.23/0.49 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c6, sk_c7) = sk_c8)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.23/0.49 tff(315,plain,
% 0.23/0.49 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c6, sk_c7) = sk_c8)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[314, 311])).
% 0.23/0.49 tff(316,plain,
% 0.23/0.49 (multiply(sk_c6, sk_c7) = sk_c8),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[315, 292])).
% 0.23/0.49 tff(317,plain,
% 0.23/0.49 (multiply(sk_c6, multiply(sk_c8, sk_c2)) = multiply(sk_c6, sk_c7)),
% 0.23/0.49 inference(monotonicity,[status(thm)],[222])).
% 0.23/0.49 tff(318,plain,
% 0.23/0.49 (multiply(sk_c1, sk_c8) = sk_c7),
% 0.23/0.49 inference(transitivity,[status(thm)],[298, 111, 287, 92, 317, 316, 83, 310, 62, 301, 222])).
% 0.23/0.49 tff(319,plain,
% 0.23/0.49 (multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7),
% 0.23/0.49 inference(transitivity,[status(thm)],[301, 222])).
% 0.23/0.49 tff(320,plain,
% 0.23/0.49 ((~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[136, 4, 282, 316, 305, 130])).
% 0.23/0.49 tff(321,plain,
% 0.23/0.49 (~(multiply(sk_c1, sk_c8) = sk_c7)),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[320, 319])).
% 0.23/0.49 tff(322,plain,
% 0.23/0.49 ($false),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[321, 318])).
% 0.23/0.49 tff(323,plain,(inverse(sk_c4) = sk_c8), inference(lemma,lemma(discharge,[]))).
% 0.23/0.49 tff(324,plain,
% 0.23/0.49 (sk_c8 = inverse(sk_c4)),
% 0.23/0.49 inference(symmetry,[status(thm)],[323])).
% 0.23/0.49 tff(325,plain,
% 0.23/0.49 (multiply(sk_c8, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.23/0.49 inference(monotonicity,[status(thm)],[324])).
% 0.23/0.49 tff(326,plain,
% 0.23/0.49 (multiply(inverse(sk_c4), sk_c4) = multiply(sk_c8, sk_c4)),
% 0.23/0.49 inference(symmetry,[status(thm)],[325])).
% 0.23/0.49 tff(327,plain,
% 0.23/0.49 (identity = multiply(sk_c8, sk_c4)),
% 0.23/0.49 inference(transitivity,[status(thm)],[42, 326])).
% 0.23/0.49 tff(328,plain,
% 0.23/0.49 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.23/0.49 inference(monotonicity,[status(thm)],[327])).
% 0.23/0.49 tff(329,plain,
% 0.23/0.49 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(identity, sk_c8)),
% 0.23/0.49 inference(symmetry,[status(thm)],[328])).
% 0.23/0.49 tff(330,plain,
% 0.23/0.49 (multiply(sk_c8, sk_c4) = multiply(sk_c8, sk_c3)),
% 0.23/0.49 inference(transitivity,[status(thm)],[325, 41, 194, 229])).
% 0.23/0.49 tff(331,plain,
% 0.23/0.49 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(multiply(sk_c8, sk_c3), sk_c8)),
% 0.23/0.49 inference(monotonicity,[status(thm)],[330])).
% 0.23/0.49 tff(332,plain,
% 0.23/0.49 (multiply(multiply(sk_c8, sk_c3), sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.23/0.49 inference(symmetry,[status(thm)],[331])).
% 0.23/0.49 tff(333,assumption,(~(multiply(sk_c6, sk_c7) = sk_c8)), introduced(assumption)).
% 0.23/0.49 tff(334,plain,
% 0.23/0.49 (((multiply(sk_c3, sk_c8) = sk_c7) | (multiply(sk_c6, sk_c7) = sk_c8)) <=> ((multiply(sk_c3, sk_c8) = sk_c7) | (multiply(sk_c6, sk_c7) = sk_c8))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(335,plain,
% 0.23/0.49 (((multiply(sk_c6, sk_c7) = sk_c8) | (multiply(sk_c3, sk_c8) = sk_c7)) <=> ((multiply(sk_c3, sk_c8) = sk_c7) | (multiply(sk_c6, sk_c7) = sk_c8))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(336,axiom,((multiply(sk_c6, sk_c7) = sk_c8) | (multiply(sk_c3, sk_c8) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_7')).
% 0.23/0.49 tff(337,plain,
% 0.23/0.49 ((multiply(sk_c3, sk_c8) = sk_c7) | (multiply(sk_c6, sk_c7) = sk_c8)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[336, 335])).
% 0.23/0.49 tff(338,plain,
% 0.23/0.49 ((multiply(sk_c3, sk_c8) = sk_c7) | (multiply(sk_c6, sk_c7) = sk_c8)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[337, 334])).
% 0.23/0.49 tff(339,plain,
% 0.23/0.49 (multiply(sk_c3, sk_c8) = sk_c7),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[338, 333])).
% 0.23/0.49 tff(340,plain,
% 0.23/0.49 (multiply(sk_c8, multiply(sk_c3, sk_c8)) = multiply(sk_c8, sk_c7)),
% 0.23/0.49 inference(monotonicity,[status(thm)],[339])).
% 0.23/0.49 tff(341,plain,
% 0.23/0.49 (multiply(sk_c8, sk_c7) = multiply(sk_c8, multiply(sk_c3, sk_c8))),
% 0.23/0.49 inference(symmetry,[status(thm)],[340])).
% 0.23/0.49 tff(342,plain,
% 0.23/0.49 (sk_c8 = sk_c6),
% 0.23/0.49 inference(transitivity,[status(thm)],[83, 328, 331, 23, 340, 4])).
% 0.23/0.49 tff(343,plain,
% 0.23/0.49 (multiply(sk_c8, sk_c7) = multiply(sk_c6, sk_c7)),
% 0.23/0.49 inference(monotonicity,[status(thm)],[342])).
% 0.23/0.49 tff(344,plain,
% 0.23/0.49 (multiply(sk_c6, sk_c7) = multiply(sk_c8, sk_c7)),
% 0.23/0.49 inference(symmetry,[status(thm)],[343])).
% 0.23/0.49 tff(345,plain,
% 0.23/0.49 (multiply(sk_c6, sk_c7) = sk_c8),
% 0.23/0.49 inference(transitivity,[status(thm)],[344, 341, 151, 332, 329, 82])).
% 0.23/0.49 tff(346,plain,
% 0.23/0.49 ($false),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[333, 345])).
% 0.23/0.49 tff(347,plain,(multiply(sk_c6, sk_c7) = sk_c8), inference(lemma,lemma(discharge,[]))).
% 0.23/0.49 tff(348,plain,
% 0.23/0.49 (sk_c8 = multiply(sk_c6, sk_c7)),
% 0.23/0.49 inference(symmetry,[status(thm)],[347])).
% 0.23/0.49 tff(349,plain,
% 0.23/0.49 (sk_c8 = sk_c2),
% 0.23/0.49 inference(transitivity,[status(thm)],[348, 291, 289, 288, 110])).
% 0.23/0.49 tff(350,plain,
% 0.23/0.49 (multiply(sk_c8, sk_c8) = multiply(sk_c8, sk_c2)),
% 0.23/0.49 inference(monotonicity,[status(thm)],[349])).
% 0.23/0.49 tff(351,plain,
% 0.23/0.49 (multiply(sk_c8, sk_c8) = sk_c7),
% 0.23/0.49 inference(transitivity,[status(thm)],[350, 222])).
% 0.23/0.49 tff(352,plain,
% 0.23/0.49 (multiply(sk_c8, multiply(sk_c8, sk_c8)) = multiply(sk_c8, sk_c7)),
% 0.23/0.49 inference(monotonicity,[status(thm)],[351])).
% 0.23/0.49 tff(353,plain,
% 0.23/0.49 (multiply(sk_c8, sk_c7) = multiply(sk_c8, multiply(sk_c8, sk_c8))),
% 0.23/0.49 inference(symmetry,[status(thm)],[352])).
% 0.23/0.49 tff(354,plain,
% 0.23/0.50 (multiply(sk_c8, sk_c7) = multiply(sk_c8, multiply(sk_c8, sk_c2))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[290])).
% 0.23/0.50 tff(355,plain,
% 0.23/0.50 (multiply(sk_c8, multiply(sk_c8, sk_c2)) = multiply(sk_c8, sk_c7)),
% 0.23/0.50 inference(symmetry,[status(thm)],[354])).
% 0.23/0.50 tff(356,plain,
% 0.23/0.50 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c8), sk_c2) = multiply(sk_c8, multiply(sk_c8, sk_c2)))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(357,plain,
% 0.23/0.50 (multiply(multiply(sk_c8, sk_c8), sk_c2) = multiply(sk_c8, multiply(sk_c8, sk_c2))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[356, 21])).
% 0.23/0.50 tff(358,plain,
% 0.23/0.50 (multiply(sk_c8, sk_c2) = multiply(sk_c8, sk_c8)),
% 0.23/0.50 inference(symmetry,[status(thm)],[350])).
% 0.23/0.50 tff(359,plain,
% 0.23/0.50 (sk_c2 = sk_c8),
% 0.23/0.50 inference(transitivity,[status(thm)],[111, 287, 92, 317, 347])).
% 0.23/0.50 tff(360,plain,
% 0.23/0.50 (multiply(sk_c8, sk_c2) = multiply(sk_c8, sk_c8)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[359])).
% 0.23/0.50 tff(361,plain,
% 0.23/0.50 (multiply(sk_c8, sk_c8) = multiply(sk_c8, sk_c2)),
% 0.23/0.50 inference(symmetry,[status(thm)],[360])).
% 0.23/0.50 tff(362,plain,
% 0.23/0.50 (multiply(sk_c6, sk_c7) = multiply(sk_c6, multiply(sk_c8, sk_c2))),
% 0.23/0.50 inference(symmetry,[status(thm)],[317])).
% 0.23/0.50 tff(363,plain,
% 0.23/0.50 (sk_c8 = sk_c2),
% 0.23/0.50 inference(transitivity,[status(thm)],[348, 362, 289, 288, 110])).
% 0.23/0.50 tff(364,assumption,(~(multiply(sk_c3, sk_c8) = sk_c7)), introduced(assumption)).
% 0.23/0.50 tff(365,plain,
% 0.23/0.50 (((inverse(sk_c1) = sk_c8) | (multiply(sk_c3, sk_c8) = sk_c7)) <=> ((inverse(sk_c1) = sk_c8) | (multiply(sk_c3, sk_c8) = sk_c7))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(366,axiom,((inverse(sk_c1) = sk_c8) | (multiply(sk_c3, sk_c8) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_22')).
% 0.23/0.50 tff(367,plain,
% 0.23/0.50 ((inverse(sk_c1) = sk_c8) | (multiply(sk_c3, sk_c8) = sk_c7)),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[366, 365])).
% 0.23/0.50 tff(368,plain,
% 0.23/0.50 (inverse(sk_c1) = sk_c8),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[367, 364])).
% 0.23/0.50 tff(369,plain,
% 0.23/0.50 (sk_c8 = inverse(sk_c1)),
% 0.23/0.50 inference(symmetry,[status(thm)],[368])).
% 0.23/0.50 tff(370,plain,
% 0.23/0.50 (multiply(sk_c8, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[369])).
% 0.23/0.50 tff(371,plain,
% 0.23/0.50 (multiply(sk_c8, sk_c1) = multiply(sk_c6, sk_c8)),
% 0.23/0.50 inference(transitivity,[status(thm)],[370, 64, 106, 285])).
% 0.23/0.50 tff(372,plain,
% 0.23/0.50 (multiply(multiply(sk_c8, sk_c1), sk_c8) = multiply(multiply(sk_c6, sk_c8), sk_c2)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[371, 363])).
% 0.23/0.50 tff(373,plain,
% 0.23/0.50 (multiply(sk_c8, multiply(sk_c1, sk_c8)) = multiply(multiply(sk_c8, sk_c1), sk_c8)),
% 0.23/0.50 inference(symmetry,[status(thm)],[62])).
% 0.23/0.50 tff(374,plain,
% 0.23/0.50 (((multiply(sk_c1, sk_c8) = sk_c2) | (multiply(sk_c3, sk_c8) = sk_c7)) <=> ((multiply(sk_c1, sk_c8) = sk_c2) | (multiply(sk_c3, sk_c8) = sk_c7))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(375,axiom,((multiply(sk_c1, sk_c8) = sk_c2) | (multiply(sk_c3, sk_c8) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_17')).
% 0.23/0.50 tff(376,plain,
% 0.23/0.50 ((multiply(sk_c1, sk_c8) = sk_c2) | (multiply(sk_c3, sk_c8) = sk_c7)),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[375, 374])).
% 0.23/0.50 tff(377,plain,
% 0.23/0.50 (multiply(sk_c1, sk_c8) = sk_c2),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[376, 364])).
% 0.23/0.50 tff(378,plain,
% 0.23/0.50 (sk_c2 = multiply(sk_c1, sk_c8)),
% 0.23/0.50 inference(symmetry,[status(thm)],[377])).
% 0.23/0.50 tff(379,plain,
% 0.23/0.50 (sk_c8 = multiply(sk_c1, sk_c8)),
% 0.23/0.50 inference(transitivity,[status(thm)],[348, 362, 289, 288, 110, 378])).
% 0.23/0.50 tff(380,plain,
% 0.23/0.50 (multiply(sk_c8, sk_c8) = multiply(sk_c8, multiply(sk_c1, sk_c8))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[379])).
% 0.23/0.50 tff(381,plain,
% 0.23/0.50 (sk_c7 = sk_c8),
% 0.23/0.50 inference(transitivity,[status(thm)],[290, 360, 380, 373, 372, 92, 317, 347])).
% 0.23/0.50 tff(382,plain,
% 0.23/0.50 (multiply(sk_c7, sk_c7) = multiply(sk_c8, sk_c8)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[381, 381])).
% 0.23/0.50 tff(383,plain,
% 0.23/0.50 (multiply(sk_c7, multiply(sk_c8, sk_c2)) = multiply(sk_c7, sk_c7)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[222])).
% 0.23/0.50 tff(384,plain,
% 0.23/0.50 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c8), sk_c2) = multiply(sk_c7, multiply(sk_c8, sk_c2)))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(385,plain,
% 0.23/0.50 (multiply(multiply(sk_c7, sk_c8), sk_c2) = multiply(sk_c7, multiply(sk_c8, sk_c2))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[384, 21])).
% 0.23/0.50 tff(386,plain,
% 0.23/0.50 (multiply(multiply(sk_c8, sk_c2), sk_c8) = multiply(sk_c7, sk_c8)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[222])).
% 0.23/0.50 tff(387,plain,
% 0.23/0.50 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c2), sk_c8) = multiply(sk_c8, multiply(sk_c2, sk_c8)))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(388,plain,
% 0.23/0.50 (multiply(multiply(sk_c8, sk_c2), sk_c8) = multiply(sk_c8, multiply(sk_c2, sk_c8))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[387, 21])).
% 0.23/0.50 tff(389,plain,
% 0.23/0.50 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = multiply(multiply(sk_c8, sk_c2), sk_c8)),
% 0.23/0.50 inference(symmetry,[status(thm)],[388])).
% 0.23/0.50 tff(390,plain,
% 0.23/0.50 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = multiply(sk_c7, sk_c8)),
% 0.23/0.50 inference(transitivity,[status(thm)],[389, 386])).
% 0.23/0.50 tff(391,plain,
% 0.23/0.50 (multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), sk_c2) = multiply(multiply(sk_c7, sk_c8), sk_c2)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[390])).
% 0.23/0.50 tff(392,plain,
% 0.23/0.50 (multiply(multiply(sk_c6, sk_c7), multiply(sk_c2, sk_c8)) = multiply(sk_c8, multiply(sk_c2, sk_c8))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[347])).
% 0.23/0.50 tff(393,plain,
% 0.23/0.50 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c7), multiply(sk_c2, sk_c8)) = multiply(sk_c6, multiply(sk_c7, multiply(sk_c2, sk_c8))))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(394,plain,
% 0.23/0.50 (multiply(multiply(sk_c6, sk_c7), multiply(sk_c2, sk_c8)) = multiply(sk_c6, multiply(sk_c7, multiply(sk_c2, sk_c8)))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[393, 21])).
% 0.23/0.50 tff(395,plain,
% 0.23/0.50 (multiply(sk_c6, multiply(sk_c7, multiply(sk_c2, sk_c8))) = multiply(multiply(sk_c6, sk_c7), multiply(sk_c2, sk_c8))),
% 0.23/0.50 inference(symmetry,[status(thm)],[394])).
% 0.23/0.50 tff(396,plain,
% 0.23/0.50 (sk_c7 = multiply(sk_c8, sk_c8)),
% 0.23/0.50 inference(transitivity,[status(thm)],[290, 360])).
% 0.23/0.50 tff(397,plain,
% 0.23/0.50 (multiply(sk_c7, multiply(sk_c2, sk_c8)) = multiply(multiply(sk_c8, sk_c8), multiply(sk_c2, sk_c8))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[396])).
% 0.23/0.50 tff(398,plain,
% 0.23/0.50 (multiply(multiply(sk_c8, sk_c8), multiply(sk_c2, sk_c8)) = multiply(sk_c7, multiply(sk_c2, sk_c8))),
% 0.23/0.50 inference(symmetry,[status(thm)],[397])).
% 0.23/0.50 tff(399,plain,
% 0.23/0.50 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c8, sk_c8), sk_c2), sk_c8) = multiply(multiply(sk_c8, sk_c8), multiply(sk_c2, sk_c8)))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(400,plain,
% 0.23/0.50 (multiply(multiply(multiply(sk_c8, sk_c8), sk_c2), sk_c8) = multiply(multiply(sk_c8, sk_c8), multiply(sk_c2, sk_c8))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[399, 21])).
% 0.23/0.50 tff(401,plain,
% 0.23/0.50 (multiply(sk_c8, multiply(sk_c8, sk_c2)) = multiply(multiply(sk_c8, sk_c8), sk_c2)),
% 0.23/0.50 inference(symmetry,[status(thm)],[357])).
% 0.23/0.50 tff(402,plain,
% 0.23/0.50 (inverse(sk_c8) = multiply(multiply(sk_c8, sk_c8), sk_c2)),
% 0.23/0.50 inference(transitivity,[status(thm)],[282, 152, 354, 401])).
% 0.23/0.50 tff(403,plain,
% 0.23/0.50 (multiply(inverse(sk_c8), sk_c8) = multiply(multiply(multiply(sk_c8, sk_c8), sk_c2), sk_c8)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[402])).
% 0.23/0.50 tff(404,plain,
% 0.23/0.50 (identity = multiply(sk_c7, multiply(sk_c2, sk_c8))),
% 0.23/0.50 inference(transitivity,[status(thm)],[106, 403, 400, 398])).
% 0.23/0.50 tff(405,plain,
% 0.23/0.50 (multiply(sk_c6, identity) = multiply(sk_c6, multiply(sk_c7, multiply(sk_c2, sk_c8)))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[404])).
% 0.23/0.50 tff(406,plain,
% 0.23/0.50 (multiply(sk_c8, sk_c3) = identity),
% 0.23/0.50 inference(transitivity,[status(thm)],[142, 44])).
% 0.23/0.50 tff(407,plain,
% 0.23/0.50 (multiply(sk_c7, sk_c8) = multiply(multiply(sk_c8, sk_c8), sk_c2)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[396, 363])).
% 0.23/0.50 tff(408,plain,
% 0.23/0.50 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c6),
% 0.23/0.50 inference(transitivity,[status(thm)],[389, 386, 407, 357, 355, 4])).
% 0.23/0.50 tff(409,plain,
% 0.23/0.50 (multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), multiply(sk_c8, sk_c3)) = multiply(sk_c6, identity)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[408, 406])).
% 0.23/0.50 tff(410,plain,
% 0.23/0.50 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), sk_c8), sk_c3) = multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), multiply(sk_c8, sk_c3)))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(411,plain,
% 0.23/0.50 (multiply(multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), sk_c8), sk_c3) = multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), multiply(sk_c8, sk_c3))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[410, 21])).
% 0.23/0.50 tff(412,plain,
% 0.23/0.50 (multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), sk_c8) = multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), sk_c2)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[363])).
% 0.23/0.50 tff(413,plain,
% 0.23/0.50 (multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), sk_c2) = multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), sk_c8)),
% 0.23/0.50 inference(symmetry,[status(thm)],[412])).
% 0.23/0.50 tff(414,plain,
% 0.23/0.50 (multiply(multiply(sk_c7, sk_c8), sk_c2) = multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), sk_c2)),
% 0.23/0.50 inference(symmetry,[status(thm)],[391])).
% 0.23/0.50 tff(415,plain,
% 0.23/0.50 (multiply(sk_c7, multiply(sk_c8, sk_c2)) = multiply(multiply(sk_c7, sk_c8), sk_c2)),
% 0.23/0.50 inference(symmetry,[status(thm)],[385])).
% 0.23/0.50 tff(416,plain,
% 0.23/0.50 (multiply(sk_c7, sk_c7) = multiply(sk_c7, multiply(sk_c8, sk_c2))),
% 0.23/0.50 inference(symmetry,[status(thm)],[383])).
% 0.23/0.50 tff(417,plain,
% 0.23/0.50 (multiply(sk_c7, sk_c7) = multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), sk_c8)),
% 0.23/0.50 inference(transitivity,[status(thm)],[416, 415, 414, 413])).
% 0.23/0.50 tff(418,plain,
% 0.23/0.50 (multiply(multiply(sk_c7, sk_c7), sk_c3) = multiply(multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), sk_c8), sk_c3)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[417])).
% 0.23/0.50 tff(419,plain,
% 0.23/0.50 (multiply(sk_c2, sk_c8) = multiply(sk_c8, sk_c8)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[359])).
% 0.23/0.50 tff(420,plain,
% 0.23/0.50 (multiply(sk_c2, sk_c8) = sk_c7),
% 0.23/0.50 inference(transitivity,[status(thm)],[419, 361, 222])).
% 0.23/0.50 tff(421,plain,
% 0.23/0.50 (multiply(sk_c8, sk_c8) = sk_c7),
% 0.23/0.50 inference(transitivity,[status(thm)],[361, 222])).
% 0.23/0.50 tff(422,plain,
% 0.23/0.50 (multiply(multiply(sk_c8, sk_c8), multiply(sk_c2, sk_c8)) = multiply(sk_c7, sk_c7)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[421, 420])).
% 0.23/0.50 tff(423,plain,
% 0.23/0.50 (identity = multiply(sk_c7, sk_c7)),
% 0.23/0.50 inference(transitivity,[status(thm)],[106, 403, 400, 422])).
% 0.23/0.50 tff(424,plain,
% 0.23/0.50 (multiply(identity, sk_c3) = multiply(multiply(sk_c7, sk_c7), sk_c3)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[423])).
% 0.23/0.50 tff(425,plain,
% 0.23/0.50 (sk_c3 = multiply(identity, sk_c3)),
% 0.23/0.50 inference(symmetry,[status(thm)],[149])).
% 0.23/0.50 tff(426,plain,
% 0.23/0.50 (sk_c3 = multiply(sk_c8, multiply(sk_c2, sk_c8))),
% 0.23/0.50 inference(transitivity,[status(thm)],[425, 424, 418, 411, 409, 405, 395, 392])).
% 0.23/0.50 tff(427,plain,
% 0.23/0.50 (multiply(sk_c3, sk_c8) = multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), sk_c2)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[426, 363])).
% 0.23/0.50 tff(428,plain,
% 0.23/0.50 (multiply(sk_c3, sk_c8) = sk_c7),
% 0.23/0.50 inference(transitivity,[status(thm)],[427, 391, 385, 383, 382, 361, 222])).
% 0.23/0.50 tff(429,plain,
% 0.23/0.50 ($false),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[364, 428])).
% 0.23/0.50 tff(430,plain,(multiply(sk_c3, sk_c8) = sk_c7), inference(lemma,lemma(discharge,[]))).
% 0.23/0.50 tff(431,plain,
% 0.23/0.50 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = multiply(multiply(sk_c6, sk_c7), multiply(sk_c2, sk_c8))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[348])).
% 0.23/0.50 tff(432,plain,
% 0.23/0.50 (multiply(multiply(sk_c6, sk_c7), multiply(sk_c2, sk_c8)) = multiply(sk_c8, multiply(sk_c2, sk_c8))),
% 0.23/0.50 inference(symmetry,[status(thm)],[431])).
% 0.23/0.50 tff(433,plain,
% 0.23/0.50 (multiply(multiply(sk_c8, sk_c8), sk_c2) = inverse(sk_c8)),
% 0.23/0.50 inference(transitivity,[status(thm)],[357, 355, 4, 283])).
% 0.23/0.50 tff(434,plain,
% 0.23/0.50 (multiply(multiply(multiply(sk_c8, sk_c8), sk_c2), sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[433])).
% 0.23/0.50 tff(435,plain,
% 0.23/0.50 (multiply(multiply(sk_c8, sk_c8), multiply(sk_c2, sk_c8)) = multiply(multiply(multiply(sk_c8, sk_c8), sk_c2), sk_c8)),
% 0.23/0.50 inference(symmetry,[status(thm)],[400])).
% 0.23/0.50 tff(436,plain,
% 0.23/0.50 (sk_c7 = multiply(sk_c8, sk_c8)),
% 0.23/0.50 inference(transitivity,[status(thm)],[290, 358])).
% 0.23/0.50 tff(437,plain,
% 0.23/0.50 (multiply(sk_c7, multiply(sk_c2, sk_c8)) = multiply(multiply(sk_c8, sk_c8), multiply(sk_c2, sk_c8))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[436])).
% 0.23/0.50 tff(438,plain,
% 0.23/0.50 (multiply(sk_c7, multiply(sk_c2, sk_c8)) = identity),
% 0.23/0.50 inference(transitivity,[status(thm)],[437, 435, 434, 105])).
% 0.23/0.50 tff(439,plain,
% 0.23/0.50 (multiply(sk_c6, multiply(sk_c7, multiply(sk_c2, sk_c8))) = multiply(sk_c6, identity)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[438])).
% 0.23/0.50 tff(440,plain,
% 0.23/0.50 (multiply(sk_c6, identity) = multiply(sk_c6, multiply(sk_c7, multiply(sk_c2, sk_c8)))),
% 0.23/0.50 inference(symmetry,[status(thm)],[439])).
% 0.23/0.50 tff(441,plain,
% 0.23/0.50 (multiply(sk_c6, multiply(sk_c8, sk_c2)) = multiply(sk_c6, sk_c7)),
% 0.23/0.50 inference(symmetry,[status(thm)],[291])).
% 0.23/0.50 tff(442,plain,
% 0.23/0.50 (sk_c2 = sk_c8),
% 0.23/0.50 inference(transitivity,[status(thm)],[111, 287, 92, 441, 347])).
% 0.23/0.50 tff(443,plain,
% 0.23/0.50 (multiply(multiply(sk_c8, sk_c8), sk_c2) = multiply(sk_c7, sk_c8)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[351, 442])).
% 0.23/0.50 tff(444,plain,
% 0.23/0.50 (multiply(sk_c7, sk_c8) = multiply(multiply(sk_c8, sk_c8), sk_c2)),
% 0.23/0.50 inference(symmetry,[status(thm)],[443])).
% 0.23/0.50 tff(445,plain,
% 0.23/0.50 (multiply(sk_c7, sk_c8) = multiply(multiply(sk_c8, sk_c2), sk_c8)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[290])).
% 0.23/0.50 tff(446,plain,
% 0.23/0.50 (multiply(multiply(sk_c8, sk_c2), sk_c8) = multiply(sk_c7, sk_c8)),
% 0.23/0.50 inference(symmetry,[status(thm)],[445])).
% 0.23/0.50 tff(447,plain,
% 0.23/0.50 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c6),
% 0.23/0.50 inference(transitivity,[status(thm)],[389, 446, 444, 357, 355, 4])).
% 0.23/0.50 tff(448,plain,
% 0.23/0.50 (multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), multiply(sk_c8, sk_c3)) = multiply(sk_c6, identity)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[447, 406])).
% 0.23/0.50 tff(449,plain,
% 0.23/0.50 (multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), sk_c8) = multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), sk_c2)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[349])).
% 0.23/0.50 tff(450,plain,
% 0.23/0.50 (multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), sk_c2) = multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), sk_c8)),
% 0.23/0.50 inference(symmetry,[status(thm)],[449])).
% 0.23/0.50 tff(451,plain,
% 0.23/0.50 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = multiply(sk_c7, sk_c8)),
% 0.23/0.50 inference(transitivity,[status(thm)],[389, 446])).
% 0.23/0.50 tff(452,plain,
% 0.23/0.50 (multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), sk_c2) = multiply(multiply(sk_c7, sk_c8), sk_c2)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[451])).
% 0.23/0.50 tff(453,plain,
% 0.23/0.50 (multiply(multiply(sk_c7, sk_c8), sk_c2) = multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), sk_c2)),
% 0.23/0.50 inference(symmetry,[status(thm)],[452])).
% 0.23/0.50 tff(454,plain,
% 0.23/0.50 (multiply(sk_c7, sk_c7) = multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), sk_c8)),
% 0.23/0.50 inference(transitivity,[status(thm)],[416, 415, 453, 450])).
% 0.23/0.50 tff(455,plain,
% 0.23/0.50 (multiply(multiply(sk_c7, sk_c7), sk_c3) = multiply(multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), sk_c8), sk_c3)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[454])).
% 0.23/0.50 tff(456,plain,
% 0.23/0.50 (multiply(sk_c2, sk_c8) = multiply(sk_c8, sk_c8)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[442])).
% 0.23/0.50 tff(457,plain,
% 0.23/0.50 (multiply(sk_c8, sk_c8) = multiply(sk_c2, sk_c8)),
% 0.23/0.50 inference(symmetry,[status(thm)],[456])).
% 0.23/0.50 tff(458,plain,
% 0.23/0.50 (sk_c7 = multiply(sk_c2, sk_c8)),
% 0.23/0.50 inference(transitivity,[status(thm)],[290, 358, 457])).
% 0.23/0.50 tff(459,plain,
% 0.23/0.50 (multiply(sk_c7, sk_c7) = multiply(multiply(sk_c8, sk_c8), multiply(sk_c2, sk_c8))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[436, 458])).
% 0.23/0.50 tff(460,plain,
% 0.23/0.50 (multiply(multiply(sk_c8, sk_c8), multiply(sk_c2, sk_c8)) = multiply(sk_c7, sk_c7)),
% 0.23/0.50 inference(symmetry,[status(thm)],[459])).
% 0.23/0.50 tff(461,plain,
% 0.23/0.50 (multiply(inverse(sk_c8), sk_c8) = multiply(multiply(multiply(sk_c8, sk_c8), sk_c2), sk_c8)),
% 0.23/0.50 inference(symmetry,[status(thm)],[434])).
% 0.23/0.50 tff(462,plain,
% 0.23/0.50 (identity = multiply(sk_c7, sk_c7)),
% 0.23/0.50 inference(transitivity,[status(thm)],[106, 461, 400, 460])).
% 0.23/0.50 tff(463,plain,
% 0.23/0.50 (multiply(identity, sk_c3) = multiply(multiply(sk_c7, sk_c7), sk_c3)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[462])).
% 0.23/0.50 tff(464,plain,
% 0.23/0.50 (sk_c3 = multiply(sk_c8, multiply(sk_c2, sk_c8))),
% 0.23/0.50 inference(transitivity,[status(thm)],[425, 463, 455, 411, 448, 440, 395, 432])).
% 0.23/0.50 tff(465,plain,
% 0.23/0.50 (multiply(sk_c3, sk_c8) = multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), sk_c2)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[464, 349])).
% 0.23/0.50 tff(466,plain,
% 0.23/0.50 (multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), sk_c2) = multiply(sk_c3, sk_c8)),
% 0.23/0.50 inference(symmetry,[status(thm)],[465])).
% 0.23/0.50 tff(467,plain,
% 0.23/0.50 (multiply(sk_c6, sk_c8) = multiply(sk_c8, sk_c8)),
% 0.23/0.50 inference(transitivity,[status(thm)],[284, 461, 400, 460, 416, 415, 453, 466, 430, 290, 358])).
% 0.23/0.50 tff(468,plain,
% 0.23/0.50 (multiply(multiply(sk_c6, sk_c8), sk_c2) = multiply(multiply(sk_c8, sk_c8), sk_c2)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[467])).
% 0.23/0.50 tff(469,plain,
% 0.23/0.50 (sk_c2 = multiply(sk_c8, multiply(sk_c8, sk_c8))),
% 0.23/0.50 inference(transitivity,[status(thm)],[111, 287, 468, 357, 355, 353])).
% 0.23/0.50 tff(470,plain,
% 0.23/0.50 (multiply(multiply(sk_c6, sk_c7), sk_c8) = multiply(sk_c8, sk_c8)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[347])).
% 0.23/0.50 tff(471,plain,
% 0.23/0.50 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c7), sk_c8) = multiply(sk_c6, multiply(sk_c7, sk_c8)))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(472,plain,
% 0.23/0.50 (multiply(multiply(sk_c6, sk_c7), sk_c8) = multiply(sk_c6, multiply(sk_c7, sk_c8))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[471, 21])).
% 0.23/0.50 tff(473,plain,
% 0.23/0.50 (multiply(sk_c6, multiply(sk_c7, sk_c8)) = multiply(multiply(sk_c6, sk_c7), sk_c8)),
% 0.23/0.50 inference(symmetry,[status(thm)],[472])).
% 0.23/0.50 tff(474,plain,
% 0.23/0.50 (multiply(sk_c7, sk_c2) = multiply(sk_c7, sk_c8)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[442])).
% 0.23/0.50 tff(475,plain,
% 0.23/0.50 (multiply(sk_c7, sk_c2) = sk_c6),
% 0.23/0.50 inference(transitivity,[status(thm)],[474, 444, 357, 355, 4])).
% 0.23/0.50 tff(476,plain,
% 0.23/0.50 (multiply(multiply(sk_c7, sk_c2), multiply(sk_c8, multiply(sk_c2, sk_c8))) = multiply(sk_c6, multiply(sk_c7, sk_c8))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[475, 451])).
% 0.23/0.50 tff(477,plain,
% 0.23/0.50 (sk_c8 = multiply(sk_c8, multiply(sk_c2, sk_c8))),
% 0.23/0.50 inference(transitivity,[status(thm)],[348, 291, 289, 468, 443, 445, 388])).
% 0.23/0.50 tff(478,plain,
% 0.23/0.50 (multiply(sk_c7, sk_c8) = multiply(sk_c7, sk_c2)),
% 0.23/0.50 inference(symmetry,[status(thm)],[474])).
% 0.23/0.50 tff(479,assumption,(~(inverse(sk_c1) = sk_c8)), introduced(assumption)).
% 0.23/0.50 tff(480,plain,
% 0.23/0.50 (((inverse(sk_c1) = sk_c8) | (multiply(sk_c8, sk_c5) = sk_c7)) <=> ((inverse(sk_c1) = sk_c8) | (multiply(sk_c8, sk_c5) = sk_c7))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(481,axiom,((inverse(sk_c1) = sk_c8) | (multiply(sk_c8, sk_c5) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_24')).
% 0.23/0.50 tff(482,plain,
% 0.23/0.50 ((inverse(sk_c1) = sk_c8) | (multiply(sk_c8, sk_c5) = sk_c7)),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[481, 480])).
% 0.23/0.50 tff(483,plain,
% 0.23/0.50 (multiply(sk_c8, sk_c5) = sk_c7),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[482, 479])).
% 0.23/0.50 tff(484,plain,
% 0.23/0.50 (((inverse(sk_c1) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c5)) <=> ((inverse(sk_c1) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c5))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(485,axiom,((inverse(sk_c1) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_25')).
% 0.23/0.50 tff(486,plain,
% 0.23/0.50 ((inverse(sk_c1) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c5)),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[485, 484])).
% 0.23/0.50 tff(487,plain,
% 0.23/0.50 (multiply(sk_c4, sk_c8) = sk_c5),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[486, 479])).
% 0.23/0.50 tff(488,plain,
% 0.23/0.50 (multiply(sk_c8, sk_c4) = identity),
% 0.23/0.50 inference(transitivity,[status(thm)],[325, 41])).
% 0.23/0.50 tff(489,plain,
% 0.23/0.50 (multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), multiply(sk_c8, sk_c4)) = multiply(sk_c6, identity)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[447, 488])).
% 0.23/0.50 tff(490,plain,
% 0.23/0.50 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), sk_c8), sk_c4) = multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), multiply(sk_c8, sk_c4)))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(491,plain,
% 0.23/0.50 (multiply(multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), sk_c8), sk_c4) = multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), multiply(sk_c8, sk_c4))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[490, 21])).
% 0.23/0.50 tff(492,plain,
% 0.23/0.50 (multiply(multiply(sk_c7, sk_c7), sk_c4) = multiply(multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), sk_c8), sk_c4)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[454])).
% 0.23/0.50 tff(493,plain,
% 0.23/0.50 (multiply(identity, sk_c4) = multiply(multiply(sk_c7, sk_c7), sk_c4)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[462])).
% 0.23/0.50 tff(494,plain,
% 0.23/0.50 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c4) = sk_c4)),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(495,plain,
% 0.23/0.50 (multiply(identity, sk_c4) = sk_c4),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[494, 80])).
% 0.23/0.50 tff(496,plain,
% 0.23/0.50 (sk_c4 = multiply(identity, sk_c4)),
% 0.23/0.50 inference(symmetry,[status(thm)],[495])).
% 0.23/0.50 tff(497,plain,
% 0.23/0.50 (sk_c4 = multiply(sk_c8, multiply(sk_c2, sk_c8))),
% 0.23/0.50 inference(transitivity,[status(thm)],[496, 493, 492, 491, 489, 440, 395, 432])).
% 0.23/0.50 tff(498,plain,
% 0.23/0.50 (multiply(sk_c4, sk_c8) = multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), sk_c2)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[497, 349])).
% 0.23/0.50 tff(499,plain,
% 0.23/0.50 (multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), sk_c2) = multiply(sk_c4, sk_c8)),
% 0.23/0.50 inference(symmetry,[status(thm)],[498])).
% 0.23/0.50 tff(500,plain,
% 0.23/0.50 (identity = sk_c5),
% 0.23/0.50 inference(transitivity,[status(thm)],[106, 461, 400, 460, 416, 415, 453, 499, 487])).
% 0.23/0.50 tff(501,plain,
% 0.23/0.50 (multiply(multiply(sk_c8, sk_c8), sk_c2) = multiply(multiply(sk_c6, sk_c8), sk_c2)),
% 0.23/0.50 inference(symmetry,[status(thm)],[468])).
% 0.23/0.50 tff(502,plain,
% 0.23/0.50 (sk_c6 = sk_c8),
% 0.23/0.50 inference(transitivity,[status(thm)],[152, 354, 401, 501, 92, 441, 347])).
% 0.23/0.50 tff(503,plain,
% 0.23/0.50 (multiply(sk_c6, identity) = multiply(sk_c8, sk_c5)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[502, 500])).
% 0.23/0.50 tff(504,plain,
% 0.23/0.50 (multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7),
% 0.23/0.50 inference(transitivity,[status(thm)],[352, 354, 401, 443, 445, 388, 431, 394, 439, 503, 483])).
% 0.23/0.50 tff(505,plain,
% 0.23/0.50 (multiply(sk_c4, sk_c2) = multiply(sk_c4, sk_c8)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[442])).
% 0.23/0.50 tff(506,plain,
% 0.23/0.50 (multiply(sk_c4, sk_c8) = multiply(sk_c4, sk_c2)),
% 0.23/0.50 inference(symmetry,[status(thm)],[505])).
% 0.23/0.50 tff(507,plain,
% 0.23/0.50 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = multiply(sk_c8, multiply(sk_c4, sk_c2))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[506])).
% 0.23/0.50 tff(508,plain,
% 0.23/0.50 (multiply(sk_c8, multiply(sk_c4, sk_c2)) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.23/0.50 inference(symmetry,[status(thm)],[507])).
% 0.23/0.50 tff(509,plain,
% 0.23/0.50 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c4), sk_c2) = multiply(sk_c8, multiply(sk_c4, sk_c2)))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(510,plain,
% 0.23/0.50 (multiply(multiply(sk_c8, sk_c4), sk_c2) = multiply(sk_c8, multiply(sk_c4, sk_c2))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[509, 21])).
% 0.23/0.50 tff(511,plain,
% 0.23/0.50 (multiply(sk_c8, sk_c4) = multiply(sk_c6, sk_c8)),
% 0.23/0.50 inference(transitivity,[status(thm)],[325, 41, 106, 285])).
% 0.23/0.50 tff(512,plain,
% 0.23/0.50 (multiply(multiply(sk_c8, sk_c4), sk_c2) = multiply(multiply(sk_c6, sk_c8), sk_c2)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[511])).
% 0.23/0.50 tff(513,plain,
% 0.23/0.50 (multiply(multiply(sk_c6, sk_c8), sk_c2) = multiply(multiply(sk_c8, sk_c4), sk_c2)),
% 0.23/0.50 inference(symmetry,[status(thm)],[512])).
% 0.23/0.50 tff(514,plain,
% 0.23/0.50 (multiply(sk_c8, multiply(sk_c8, sk_c8)) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.23/0.50 inference(transitivity,[status(thm)],[352, 354, 401, 501, 513, 510, 508])).
% 0.23/0.50 tff(515,plain,
% 0.23/0.50 ((multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7) <=> (multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)),
% 0.23/0.51 inference(monotonicity,[status(thm)],[514])).
% 0.23/0.51 tff(516,plain,
% 0.23/0.51 ((multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7) <=> (multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)),
% 0.23/0.51 inference(symmetry,[status(thm)],[515])).
% 0.23/0.51 tff(517,plain,
% 0.23/0.51 ((~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) <=> (~(multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[516])).
% 0.23/0.51 tff(518,plain,
% 0.23/0.51 (((~![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(sk_c3) = sk_c8)))) <=> ((~![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(sk_c3) = sk_c8)))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(519,plain,
% 0.23/0.51 (((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(inverse(sk_c3) = sk_c8)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c8))) <=> ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(sk_c3) = sk_c8)))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(520,plain,
% 0.23/0.51 (((~![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(inverse(sk_c3) = sk_c8)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)))) <=> ((~![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(sk_c3) = sk_c8))))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[519])).
% 0.23/0.51 tff(521,plain,
% 0.23/0.51 (((~![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(inverse(sk_c3) = sk_c8)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)))) <=> ((~![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(sk_c3) = sk_c8)))),
% 0.23/0.51 inference(transitivity,[status(thm)],[520, 518])).
% 0.23/0.51 tff(522,plain,
% 0.23/0.51 ((~![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(inverse(sk_c3) = sk_c8)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)))),
% 0.23/0.51 inference(quant_inst,[status(thm)],[])).
% 0.23/0.51 tff(523,plain,
% 0.23/0.51 ((~![X4: $i, X5: $i, X1: $i] : ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(X4, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c8)))) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(sk_c3) = sk_c8))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[522, 521])).
% 0.23/0.51 tff(524,plain,
% 0.23/0.51 ((~(multiply(sk_c6, sk_c7) = sk_c8)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[523, 4, 282, 140, 323, 130])).
% 0.23/0.51 tff(525,plain,
% 0.23/0.51 ((~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[524, 347])).
% 0.23/0.51 tff(526,plain,
% 0.23/0.51 (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[525, 430])).
% 0.23/0.51 tff(527,plain,
% 0.23/0.51 (~(multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[526, 517])).
% 0.23/0.51 tff(528,plain,
% 0.23/0.51 ($false),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[527, 504])).
% 0.23/0.51 tff(529,plain,(inverse(sk_c1) = sk_c8), inference(lemma,lemma(discharge,[]))).
% 0.23/0.51 tff(530,plain,
% 0.23/0.51 (sk_c8 = inverse(sk_c1)),
% 0.23/0.51 inference(symmetry,[status(thm)],[529])).
% 0.23/0.51 tff(531,plain,
% 0.23/0.51 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = inverse(sk_c1)),
% 0.23/0.51 inference(transitivity,[status(thm)],[389, 446, 444, 501, 92, 441, 347, 530])).
% 0.23/0.51 tff(532,plain,
% 0.23/0.51 (multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.23/0.51 inference(monotonicity,[status(thm)],[531])).
% 0.23/0.51 tff(533,plain,
% 0.23/0.51 (multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), sk_c1) = identity),
% 0.23/0.51 inference(transitivity,[status(thm)],[532, 64])).
% 0.23/0.51 tff(534,plain,
% 0.23/0.51 (multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), sk_c1)) = multiply(sk_c6, identity)),
% 0.23/0.51 inference(monotonicity,[status(thm)],[447, 533])).
% 0.23/0.51 tff(535,plain,
% 0.23/0.51 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), multiply(sk_c8, multiply(sk_c2, sk_c8))), sk_c1) = multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), sk_c1)))),
% 0.23/0.51 inference(quant_inst,[status(thm)],[])).
% 0.23/0.51 tff(536,plain,
% 0.23/0.51 (multiply(multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), multiply(sk_c8, multiply(sk_c2, sk_c8))), sk_c1) = multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), sk_c1))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[535, 21])).
% 0.23/0.51 tff(537,plain,
% 0.23/0.51 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = multiply(sk_c7, sk_c2)),
% 0.23/0.51 inference(transitivity,[status(thm)],[389, 446, 478])).
% 0.23/0.51 tff(538,plain,
% 0.23/0.51 (multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), multiply(sk_c8, multiply(sk_c2, sk_c8))) = multiply(multiply(sk_c7, sk_c2), multiply(sk_c8, multiply(sk_c2, sk_c8)))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[537])).
% 0.23/0.51 tff(539,plain,
% 0.23/0.51 (multiply(multiply(sk_c7, sk_c2), multiply(sk_c8, multiply(sk_c2, sk_c8))) = multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), multiply(sk_c8, multiply(sk_c2, sk_c8)))),
% 0.23/0.51 inference(symmetry,[status(thm)],[538])).
% 0.23/0.51 tff(540,plain,
% 0.23/0.51 (multiply(sk_c6, multiply(sk_c7, sk_c8)) = multiply(multiply(sk_c7, sk_c2), multiply(sk_c8, multiply(sk_c2, sk_c8)))),
% 0.23/0.51 inference(symmetry,[status(thm)],[476])).
% 0.23/0.51 tff(541,plain,
% 0.23/0.51 (multiply(sk_c8, sk_c8) = multiply(multiply(sk_c6, sk_c7), sk_c8)),
% 0.23/0.51 inference(symmetry,[status(thm)],[470])).
% 0.23/0.51 tff(542,plain,
% 0.23/0.51 (identity = multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), multiply(sk_c8, multiply(sk_c2, sk_c8)))),
% 0.23/0.51 inference(transitivity,[status(thm)],[106, 461, 400, 460, 416, 415, 453, 466, 430, 290, 358, 541, 472, 540, 539])).
% 0.23/0.51 tff(543,plain,
% 0.23/0.51 (multiply(identity, sk_c1) = multiply(multiply(multiply(sk_c8, multiply(sk_c2, sk_c8)), multiply(sk_c8, multiply(sk_c2, sk_c8))), sk_c1)),
% 0.23/0.51 inference(monotonicity,[status(thm)],[542])).
% 0.23/0.51 tff(544,plain,
% 0.23/0.51 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c1) = sk_c1)),
% 0.23/0.51 inference(quant_inst,[status(thm)],[])).
% 0.23/0.51 tff(545,plain,
% 0.23/0.51 (multiply(identity, sk_c1) = sk_c1),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[544, 80])).
% 0.23/0.51 tff(546,plain,
% 0.23/0.51 (sk_c1 = multiply(identity, sk_c1)),
% 0.23/0.51 inference(symmetry,[status(thm)],[545])).
% 0.23/0.51 tff(547,plain,
% 0.23/0.51 (sk_c1 = multiply(sk_c7, sk_c2)),
% 0.23/0.51 inference(transitivity,[status(thm)],[546, 543, 536, 534, 440, 395, 432, 389, 446, 478])).
% 0.23/0.51 tff(548,plain,
% 0.23/0.51 (multiply(sk_c1, sk_c8) = multiply(multiply(sk_c7, sk_c2), multiply(sk_c8, multiply(sk_c2, sk_c8)))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[547, 477])).
% 0.23/0.51 tff(549,plain,
% 0.23/0.51 (multiply(sk_c1, sk_c8) = sk_c7),
% 0.23/0.51 inference(transitivity,[status(thm)],[548, 476, 473, 470, 350, 222])).
% 0.23/0.51 tff(550,plain,
% 0.23/0.51 ((multiply(sk_c1, sk_c8) = sk_c2) <=> (sk_c7 = multiply(sk_c8, multiply(sk_c8, sk_c8)))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[549, 469])).
% 0.23/0.51 tff(551,plain,
% 0.23/0.51 ((multiply(sk_c1, sk_c8) = sk_c2) <=> (multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)),
% 0.23/0.51 inference(transitivity,[status(thm)],[550, 1])).
% 0.23/0.51 tff(552,plain,
% 0.23/0.51 ((multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7) <=> (multiply(sk_c1, sk_c8) = sk_c2)),
% 0.23/0.51 inference(symmetry,[status(thm)],[551])).
% 0.23/0.51 tff(553,plain,
% 0.23/0.51 ((~(multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7)) <=> (~(multiply(sk_c1, sk_c8) = sk_c2))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[552])).
% 0.23/0.51 tff(554,plain,
% 0.23/0.51 (~(multiply(sk_c1, sk_c8) = sk_c2)),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[527, 553])).
% 0.23/0.51 tff(555,plain,
% 0.23/0.51 (((multiply(sk_c1, sk_c8) = sk_c2) | (multiply(sk_c8, sk_c5) = sk_c7)) <=> ((multiply(sk_c1, sk_c8) = sk_c2) | (multiply(sk_c8, sk_c5) = sk_c7))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(556,axiom,((multiply(sk_c1, sk_c8) = sk_c2) | (multiply(sk_c8, sk_c5) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_19')).
% 0.23/0.51 tff(557,plain,
% 0.23/0.51 ((multiply(sk_c1, sk_c8) = sk_c2) | (multiply(sk_c8, sk_c5) = sk_c7)),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[556, 555])).
% 0.23/0.51 tff(558,plain,
% 0.23/0.51 (multiply(sk_c8, sk_c5) = sk_c7),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[557, 554])).
% 0.23/0.51 tff(559,plain,
% 0.23/0.51 (((multiply(sk_c1, sk_c8) = sk_c2) | (multiply(sk_c4, sk_c8) = sk_c5)) <=> ((multiply(sk_c1, sk_c8) = sk_c2) | (multiply(sk_c4, sk_c8) = sk_c5))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(560,axiom,((multiply(sk_c1, sk_c8) = sk_c2) | (multiply(sk_c4, sk_c8) = sk_c5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_20')).
% 0.23/0.51 tff(561,plain,
% 0.23/0.51 ((multiply(sk_c1, sk_c8) = sk_c2) | (multiply(sk_c4, sk_c8) = sk_c5)),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[560, 559])).
% 0.23/0.51 tff(562,plain,
% 0.23/0.51 (multiply(sk_c4, sk_c8) = sk_c5),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[561, 554])).
% 0.23/0.51 tff(563,plain,
% 0.23/0.51 (identity = sk_c5),
% 0.23/0.51 inference(transitivity,[status(thm)],[106, 461, 400, 460, 416, 415, 453, 499, 562])).
% 0.23/0.51 tff(564,plain,
% 0.23/0.51 (multiply(sk_c6, identity) = multiply(sk_c8, sk_c5)),
% 0.23/0.51 inference(monotonicity,[status(thm)],[502, 563])).
% 0.23/0.51 tff(565,plain,
% 0.23/0.51 (multiply(sk_c8, multiply(sk_c8, sk_c8)) = sk_c7),
% 0.23/0.51 inference(transitivity,[status(thm)],[352, 354, 401, 443, 445, 388, 431, 394, 439, 564, 558])).
% 0.23/0.51 tff(566,plain,
% 0.23/0.51 ($false),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[527, 565])).
% 0.23/0.51 % SZS output end Proof
% 0.23/0.51 % E exiting
%------------------------------------------------------------------------------