%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP241-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:07:31 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP241-1 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 15:50:02 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.42 % SZS status Unsatisfiable
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 tff(sk_c8_type, type, (
% 0.20/0.42 sk_c8: $i)).
% 0.20/0.42 tff(inverse_type, type, (
% 0.20/0.42 inverse: $i > $i)).
% 0.20/0.42 tff(sk_c1_type, type, (
% 0.20/0.42 sk_c1: $i)).
% 0.20/0.42 tff(multiply_type, type, (
% 0.20/0.42 multiply: ( $i * $i ) > $i)).
% 0.20/0.42 tff(identity_type, type, (
% 0.20/0.42 identity: $i)).
% 0.20/0.42 tff(sk_c5_type, type, (
% 0.20/0.42 sk_c5: $i)).
% 0.20/0.42 tff(sk_c7_type, type, (
% 0.20/0.42 sk_c7: $i)).
% 0.20/0.42 tff(sk_c2_type, type, (
% 0.20/0.42 sk_c2: $i)).
% 0.20/0.42 tff(sk_c3_type, type, (
% 0.20/0.42 sk_c3: $i)).
% 0.20/0.42 tff(sk_c6_type, type, (
% 0.20/0.42 sk_c6: $i)).
% 0.20/0.42 tff(sk_c4_type, type, (
% 0.20/0.42 sk_c4: $i)).
% 0.20/0.42 tff(1,plain,
% 0.20/0.42 (^[X: $i] : refl((multiply(identity, X) = X) <=> (multiply(identity, X) = X))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(2,plain,
% 0.20/0.42 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.20/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.42 tff(3,plain,
% 0.20/0.42 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(4,axiom,(![X: $i] : (multiply(identity, X) = X)), file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax','left_identity')).
% 0.20/0.42 tff(5,plain,
% 0.20/0.42 (![X: $i] : (multiply(identity, X) = X)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.42 tff(6,plain,(
% 0.20/0.42 ![X: $i] : (multiply(identity, X) = X)),
% 0.20/0.42 inference(skolemize,[status(sab)],[5])).
% 0.20/0.42 tff(7,plain,
% 0.20/0.42 (![X: $i] : (multiply(identity, X) = X)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c8) = sk_c8)),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 (multiply(identity, sk_c8) = sk_c8),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.42 tff(10,assumption,(~(inverse(sk_c5) = sk_c8)), introduced(assumption)).
% 0.20/0.42 tff(11,plain,
% 0.20/0.42 (((inverse(sk_c5) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7)) <=> ((inverse(sk_c5) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 (((multiply(sk_c8, sk_c3) = sk_c7) | (inverse(sk_c5) = sk_c8)) <=> ((inverse(sk_c5) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(13,axiom,((multiply(sk_c8, sk_c3) = sk_c7) | (inverse(sk_c5) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_25')).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 ((inverse(sk_c5) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 ((inverse(sk_c5) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 (multiply(sk_c8, sk_c3) = sk_c7),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[15, 10])).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 (((inverse(sk_c5) = sk_c8) | (multiply(sk_c2, sk_c8) = sk_c3)) <=> ((inverse(sk_c5) = sk_c8) | (multiply(sk_c2, sk_c8) = sk_c3))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 (((multiply(sk_c2, sk_c8) = sk_c3) | (inverse(sk_c5) = sk_c8)) <=> ((inverse(sk_c5) = sk_c8) | (multiply(sk_c2, sk_c8) = sk_c3))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(19,axiom,((multiply(sk_c2, sk_c8) = sk_c3) | (inverse(sk_c5) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_30')).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 ((inverse(sk_c5) = sk_c8) | (multiply(sk_c2, sk_c8) = sk_c3)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 ((inverse(sk_c5) = sk_c8) | (multiply(sk_c2, sk_c8) = sk_c3)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[20, 17])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 (multiply(sk_c2, sk_c8) = sk_c3),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[21, 10])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = multiply(sk_c8, sk_c3)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[22])).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 (^[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))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(27,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')).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.42 tff(29,plain,(
% 0.20/0.42 ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[28])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 ((~![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)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 (multiply(multiply(sk_c8, sk_c2), sk_c8) = multiply(sk_c8, multiply(sk_c2, sk_c8))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.20/0.42 tff(33,assumption,(~(inverse(sk_c2) = sk_c8)), introduced(assumption)).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (((inverse(sk_c2) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7)) <=> ((inverse(sk_c2) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(35,axiom,((inverse(sk_c2) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_33')).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 ((inverse(sk_c2) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (multiply(sk_c8, sk_c6) = sk_c7),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[36, 33])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (((inverse(sk_c2) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6)) <=> ((inverse(sk_c2) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(39,axiom,((inverse(sk_c2) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_34')).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 ((inverse(sk_c2) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 (multiply(sk_c5, sk_c8) = sk_c6),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[40, 33])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 (sk_c6 = multiply(sk_c5, sk_c8)),
% 0.20/0.42 inference(symmetry,[status(thm)],[41])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 (multiply(sk_c8, sk_c6) = multiply(sk_c8, multiply(sk_c5, sk_c8))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[42])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 (multiply(sk_c8, multiply(sk_c5, sk_c8)) = multiply(sk_c8, sk_c6)),
% 0.20/0.42 inference(symmetry,[status(thm)],[43])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c5), sk_c8) = multiply(sk_c8, multiply(sk_c5, sk_c8)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (multiply(multiply(sk_c8, sk_c5), sk_c8) = multiply(sk_c8, multiply(sk_c5, sk_c8))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[45, 30])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 (^[X: $i] : refl((multiply(inverse(X), X) = identity) <=> (multiply(inverse(X), X) = identity))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.20/0.42 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(50,axiom,(![X: $i] : (multiply(inverse(X), X) = identity)), file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax','left_inverse')).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.43 tff(52,plain,(
% 0.20/0.43 ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.20/0.43 inference(skolemize,[status(sab)],[51])).
% 0.20/0.43 tff(53,plain,
% 0.20/0.43 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.20/0.43 tff(54,plain,
% 0.20/0.43 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c5), sk_c5) = identity)),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(55,plain,
% 0.20/0.43 (multiply(inverse(sk_c5), sk_c5) = identity),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.20/0.43 tff(56,plain,
% 0.20/0.43 (((inverse(sk_c2) = sk_c8) | (inverse(sk_c5) = sk_c8)) <=> ((inverse(sk_c2) = sk_c8) | (inverse(sk_c5) = sk_c8))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(57,axiom,((inverse(sk_c2) = sk_c8) | (inverse(sk_c5) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_35')).
% 0.20/0.43 tff(58,plain,
% 0.20/0.43 ((inverse(sk_c2) = sk_c8) | (inverse(sk_c5) = sk_c8)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.43 tff(59,plain,
% 0.20/0.43 (inverse(sk_c5) = sk_c8),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[58, 33])).
% 0.20/0.43 tff(60,plain,
% 0.20/0.43 (sk_c8 = inverse(sk_c5)),
% 0.20/0.43 inference(symmetry,[status(thm)],[59])).
% 0.20/0.43 tff(61,plain,
% 0.20/0.43 (multiply(sk_c8, sk_c5) = multiply(inverse(sk_c5), sk_c5)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[60])).
% 0.20/0.43 tff(62,plain,
% 0.20/0.43 (multiply(sk_c8, sk_c5) = identity),
% 0.20/0.43 inference(transitivity,[status(thm)],[61, 55])).
% 0.20/0.43 tff(63,plain,
% 0.20/0.43 (multiply(multiply(sk_c8, sk_c5), sk_c8) = multiply(identity, sk_c8)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[62])).
% 0.20/0.43 tff(64,plain,
% 0.20/0.43 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c5), sk_c8)),
% 0.20/0.43 inference(symmetry,[status(thm)],[63])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 (sk_c8 = multiply(identity, sk_c8)),
% 0.20/0.43 inference(symmetry,[status(thm)],[9])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 (sk_c8 = sk_c7),
% 0.20/0.43 inference(transitivity,[status(thm)],[65, 64, 46, 44, 37])).
% 0.20/0.43 tff(67,plain,
% 0.20/0.43 (multiply(sk_c8, multiply(sk_c5, sk_c8)) = multiply(multiply(sk_c8, sk_c5), sk_c8)),
% 0.20/0.43 inference(symmetry,[status(thm)],[46])).
% 0.20/0.43 tff(68,plain,
% 0.20/0.43 (sk_c7 = multiply(sk_c8, sk_c6)),
% 0.20/0.43 inference(symmetry,[status(thm)],[37])).
% 0.20/0.43 tff(69,plain,
% 0.20/0.43 (sk_c7 = sk_c8),
% 0.20/0.43 inference(transitivity,[status(thm)],[68, 43, 67, 63, 9])).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 (inverse(sk_c7) = inverse(sk_c8)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[69])).
% 0.20/0.43 tff(71,plain,
% 0.20/0.43 ((inverse(sk_c7) = sk_c8) <=> (inverse(sk_c8) = sk_c7)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[70, 66])).
% 0.20/0.43 tff(72,plain,
% 0.20/0.43 ((inverse(sk_c8) = sk_c7) <=> (inverse(sk_c7) = sk_c8)),
% 0.20/0.43 inference(symmetry,[status(thm)],[71])).
% 0.20/0.43 tff(73,plain,
% 0.20/0.43 (((inverse(sk_c2) = sk_c8) | (multiply(sk_c4, sk_c7) = sk_c8)) <=> ((inverse(sk_c2) = sk_c8) | (multiply(sk_c4, sk_c7) = sk_c8))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(74,axiom,((inverse(sk_c2) = sk_c8) | (multiply(sk_c4, sk_c7) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_32')).
% 0.20/0.43 tff(75,plain,
% 0.20/0.43 ((inverse(sk_c2) = sk_c8) | (multiply(sk_c4, sk_c7) = sk_c8)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.43 tff(76,plain,
% 0.20/0.43 (multiply(sk_c4, sk_c7) = sk_c8),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[75, 33])).
% 0.20/0.43 tff(77,plain,
% 0.20/0.43 (((inverse(sk_c2) = sk_c8) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c2) = sk_c8) | (inverse(sk_c4) = sk_c8))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(78,axiom,((inverse(sk_c2) = sk_c8) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_31')).
% 0.20/0.43 tff(79,plain,
% 0.20/0.43 ((inverse(sk_c2) = sk_c8) | (inverse(sk_c4) = sk_c8)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.43 tff(80,plain,
% 0.20/0.43 (inverse(sk_c4) = sk_c8),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[79, 33])).
% 0.20/0.43 tff(81,assumption,(multiply(sk_c8, sk_c6) = sk_c7), introduced(assumption)).
% 0.20/0.43 tff(82,assumption,(multiply(sk_c5, sk_c8) = sk_c6), introduced(assumption)).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 (sk_c6 = multiply(sk_c5, sk_c8)),
% 0.20/0.43 inference(symmetry,[status(thm)],[82])).
% 0.20/0.43 tff(84,plain,
% 0.20/0.43 (multiply(sk_c8, sk_c6) = multiply(sk_c8, multiply(sk_c5, sk_c8))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[83])).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 (multiply(sk_c8, multiply(sk_c5, sk_c8)) = multiply(sk_c8, sk_c6)),
% 0.20/0.43 inference(symmetry,[status(thm)],[84])).
% 0.20/0.43 tff(86,assumption,(inverse(sk_c5) = sk_c8), introduced(assumption)).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 (sk_c8 = inverse(sk_c5)),
% 0.20/0.43 inference(symmetry,[status(thm)],[86])).
% 0.20/0.43 tff(88,plain,
% 0.20/0.43 (multiply(sk_c8, sk_c5) = multiply(inverse(sk_c5), sk_c5)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[87])).
% 0.20/0.43 tff(89,plain,
% 0.20/0.43 (multiply(sk_c8, sk_c5) = identity),
% 0.20/0.43 inference(transitivity,[status(thm)],[88, 55])).
% 0.20/0.43 tff(90,plain,
% 0.20/0.43 (multiply(multiply(sk_c8, sk_c5), sk_c8) = multiply(identity, sk_c8)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[89])).
% 0.20/0.43 tff(91,plain,
% 0.20/0.43 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c5), sk_c8)),
% 0.20/0.43 inference(symmetry,[status(thm)],[90])).
% 0.20/0.43 tff(92,assumption,(inverse(sk_c4) = sk_c8), introduced(assumption)).
% 0.20/0.43 tff(93,plain,
% 0.20/0.43 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c4) = sk_c4)),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(94,plain,
% 0.20/0.43 (multiply(identity, sk_c4) = sk_c4),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[93, 7])).
% 0.20/0.43 tff(95,plain,
% 0.20/0.43 (multiply(inverse(sk_c5), sk_c5) = multiply(sk_c8, sk_c5)),
% 0.20/0.43 inference(symmetry,[status(thm)],[88])).
% 0.20/0.43 tff(96,plain,
% 0.20/0.43 (identity = multiply(inverse(sk_c5), sk_c5)),
% 0.20/0.43 inference(symmetry,[status(thm)],[55])).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 (identity = multiply(sk_c8, sk_c5)),
% 0.20/0.43 inference(transitivity,[status(thm)],[96, 95])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 (multiply(identity, sk_c4) = multiply(multiply(sk_c8, sk_c5), sk_c4)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[97])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 (multiply(multiply(sk_c8, sk_c5), sk_c4) = multiply(identity, sk_c4)),
% 0.20/0.43 inference(symmetry,[status(thm)],[98])).
% 0.20/0.43 tff(100,plain,
% 0.20/0.43 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c5), sk_c4) = multiply(sk_c8, multiply(sk_c5, sk_c4)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 (multiply(multiply(sk_c8, sk_c5), sk_c4) = multiply(sk_c8, multiply(sk_c5, sk_c4))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[100, 30])).
% 0.20/0.43 tff(102,plain,
% 0.20/0.43 (multiply(sk_c8, multiply(sk_c5, sk_c4)) = multiply(multiply(sk_c8, sk_c5), sk_c4)),
% 0.20/0.43 inference(symmetry,[status(thm)],[101])).
% 0.20/0.43 tff(103,plain,
% 0.20/0.43 (sk_c8 = sk_c7),
% 0.20/0.43 inference(transitivity,[status(thm)],[65, 91, 46, 85, 81])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 (multiply(sk_c4, sk_c8) = multiply(sk_c4, sk_c7)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[103])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 (multiply(sk_c4, sk_c7) = multiply(sk_c4, sk_c8)),
% 0.20/0.43 inference(symmetry,[status(thm)],[104])).
% 0.20/0.43 tff(106,assumption,(multiply(sk_c4, sk_c7) = sk_c8), introduced(assumption)).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 (sk_c8 = multiply(sk_c4, sk_c7)),
% 0.20/0.43 inference(symmetry,[status(thm)],[106])).
% 0.20/0.43 tff(108,plain,
% 0.20/0.43 (sk_c8 = multiply(sk_c4, sk_c8)),
% 0.20/0.43 inference(transitivity,[status(thm)],[107, 105])).
% 0.20/0.43 tff(109,plain,
% 0.20/0.43 (multiply(sk_c8, sk_c8) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[108])).
% 0.20/0.43 tff(110,plain,
% 0.20/0.43 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = multiply(sk_c8, sk_c8)),
% 0.20/0.43 inference(symmetry,[status(thm)],[109])).
% 0.20/0.43 tff(111,plain,
% 0.20/0.43 ((~![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)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(112,plain,
% 0.20/0.43 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[111, 30])).
% 0.20/0.43 tff(113,plain,
% 0.20/0.43 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c4), sk_c4) = identity)),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(114,plain,
% 0.20/0.43 (multiply(inverse(sk_c4), sk_c4) = identity),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[113, 53])).
% 0.20/0.43 tff(115,plain,
% 0.20/0.43 (sk_c8 = inverse(sk_c4)),
% 0.20/0.43 inference(symmetry,[status(thm)],[92])).
% 0.20/0.43 tff(116,plain,
% 0.20/0.43 (multiply(sk_c8, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[115])).
% 0.20/0.43 tff(117,plain,
% 0.20/0.43 (multiply(sk_c8, sk_c4) = multiply(sk_c8, sk_c5)),
% 0.20/0.43 inference(transitivity,[status(thm)],[116, 114, 96, 95])).
% 0.20/0.43 tff(118,plain,
% 0.20/0.43 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(multiply(sk_c8, sk_c5), sk_c8)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[117])).
% 0.20/0.43 tff(119,plain,
% 0.20/0.43 (multiply(multiply(sk_c8, sk_c5), sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.20/0.43 inference(symmetry,[status(thm)],[118])).
% 0.20/0.43 tff(120,plain,
% 0.20/0.43 (sk_c8 = multiply(sk_c8, sk_c8)),
% 0.20/0.43 inference(transitivity,[status(thm)],[65, 91, 119, 112, 110])).
% 0.20/0.43 tff(121,plain,
% 0.20/0.43 (multiply(sk_c8, multiply(sk_c5, sk_c4)) = multiply(multiply(sk_c8, sk_c8), multiply(sk_c5, sk_c4))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[120])).
% 0.20/0.43 tff(122,plain,
% 0.20/0.43 (multiply(multiply(sk_c8, sk_c8), multiply(sk_c5, sk_c4)) = multiply(sk_c8, multiply(sk_c5, sk_c4))),
% 0.20/0.43 inference(symmetry,[status(thm)],[121])).
% 0.20/0.43 tff(123,plain,
% 0.20/0.43 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c8), multiply(sk_c5, sk_c4)) = multiply(sk_c8, multiply(sk_c8, multiply(sk_c5, sk_c4))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(124,plain,
% 0.20/0.43 (multiply(multiply(sk_c8, sk_c8), multiply(sk_c5, sk_c4)) = multiply(sk_c8, multiply(sk_c8, multiply(sk_c5, sk_c4)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[123, 30])).
% 0.20/0.43 tff(125,plain,
% 0.20/0.43 (multiply(sk_c8, multiply(sk_c8, multiply(sk_c5, sk_c4))) = multiply(multiply(sk_c8, sk_c8), multiply(sk_c5, sk_c4))),
% 0.20/0.43 inference(symmetry,[status(thm)],[124])).
% 0.20/0.43 tff(126,plain,
% 0.20/0.43 (multiply(sk_c8, multiply(sk_c5, sk_c4)) = sk_c4),
% 0.20/0.43 inference(transitivity,[status(thm)],[102, 99, 94])).
% 0.20/0.43 tff(127,plain,
% 0.20/0.43 (multiply(sk_c8, multiply(sk_c8, multiply(sk_c5, sk_c4))) = multiply(inverse(sk_c4), sk_c4)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[115, 126])).
% 0.20/0.43 tff(128,plain,
% 0.20/0.43 (multiply(inverse(sk_c4), sk_c4) = multiply(sk_c8, multiply(sk_c8, multiply(sk_c5, sk_c4)))),
% 0.20/0.43 inference(symmetry,[status(thm)],[127])).
% 0.20/0.43 tff(129,plain,
% 0.20/0.43 (identity = multiply(inverse(sk_c4), sk_c4)),
% 0.20/0.43 inference(symmetry,[status(thm)],[114])).
% 0.20/0.43 tff(130,plain,
% 0.20/0.43 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c8), sk_c8) = identity)),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(131,plain,
% 0.20/0.43 (multiply(inverse(sk_c8), sk_c8) = identity),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[130, 53])).
% 0.20/0.43 tff(132,plain,
% 0.20/0.43 (multiply(inverse(sk_c8), sk_c8) = multiply(inverse(sk_c8), multiply(sk_c8, sk_c8))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[120])).
% 0.20/0.43 tff(133,plain,
% 0.20/0.43 (multiply(inverse(sk_c8), multiply(sk_c8, sk_c8)) = multiply(inverse(sk_c8), sk_c8)),
% 0.20/0.43 inference(symmetry,[status(thm)],[132])).
% 0.20/0.43 tff(134,plain,
% 0.20/0.43 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(inverse(sk_c8), sk_c8), sk_c8) = multiply(inverse(sk_c8), multiply(sk_c8, sk_c8)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(135,plain,
% 0.20/0.43 (multiply(multiply(inverse(sk_c8), sk_c8), sk_c8) = multiply(inverse(sk_c8), multiply(sk_c8, sk_c8))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[134, 30])).
% 0.20/0.43 tff(136,plain,
% 0.20/0.43 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c8, sk_c5)),
% 0.20/0.43 inference(transitivity,[status(thm)],[131, 96, 95])).
% 0.20/0.43 tff(137,plain,
% 0.20/0.43 (multiply(multiply(inverse(sk_c8), sk_c8), sk_c8) = multiply(multiply(sk_c8, sk_c5), sk_c8)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[136])).
% 0.20/0.43 tff(138,plain,
% 0.20/0.43 (multiply(multiply(sk_c8, sk_c5), sk_c8) = multiply(multiply(inverse(sk_c8), sk_c8), sk_c8)),
% 0.20/0.43 inference(symmetry,[status(thm)],[137])).
% 0.20/0.43 tff(139,plain,
% 0.20/0.43 (sk_c8 = sk_c4),
% 0.20/0.43 inference(transitivity,[status(thm)],[65, 91, 138, 135, 133, 131, 129, 128, 125, 122, 102, 99, 94])).
% 0.20/0.43 tff(140,plain,
% 0.20/0.43 (inverse(sk_c8) = inverse(sk_c4)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[139])).
% 0.20/0.43 tff(141,plain,
% 0.20/0.43 (inverse(sk_c8) = sk_c7),
% 0.20/0.43 inference(transitivity,[status(thm)],[140, 92, 65, 91, 46, 85, 81])).
% 0.20/0.43 tff(142,assumption,(~(inverse(sk_c8) = sk_c7)), introduced(assumption)).
% 0.20/0.43 tff(143,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[142, 141])).
% 0.20/0.44 tff(144,plain,((inverse(sk_c8) = sk_c7) | (~(multiply(sk_c8, sk_c6) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(multiply(sk_c5, sk_c8) = sk_c6))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(145,plain,
% 0.20/0.44 (inverse(sk_c8) = sk_c7),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[144, 37, 80, 59, 76, 41])).
% 0.20/0.44 tff(146,plain,
% 0.20/0.44 (inverse(sk_c7) = sk_c8),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[145, 72])).
% 0.20/0.44 tff(147,plain,
% 0.20/0.44 (inverse(sk_c4) = sk_c7),
% 0.20/0.44 inference(transitivity,[status(thm)],[80, 65, 64, 46, 44, 37])).
% 0.20/0.44 tff(148,plain,
% 0.20/0.44 (multiply(inverse(sk_c5), sk_c5) = multiply(sk_c8, sk_c5)),
% 0.20/0.44 inference(symmetry,[status(thm)],[61])).
% 0.20/0.44 tff(149,plain,
% 0.20/0.44 (sk_c8 = inverse(sk_c4)),
% 0.20/0.44 inference(symmetry,[status(thm)],[80])).
% 0.20/0.44 tff(150,plain,
% 0.20/0.44 (multiply(sk_c8, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[149])).
% 0.20/0.44 tff(151,plain,
% 0.20/0.44 (multiply(sk_c8, sk_c4) = multiply(sk_c8, sk_c5)),
% 0.20/0.44 inference(transitivity,[status(thm)],[150, 114, 96, 148])).
% 0.20/0.44 tff(152,plain,
% 0.20/0.44 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(multiply(sk_c8, sk_c5), sk_c8)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[151])).
% 0.20/0.44 tff(153,plain,
% 0.20/0.44 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.20/0.44 inference(symmetry,[status(thm)],[112])).
% 0.20/0.44 tff(154,plain,
% 0.20/0.44 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7),
% 0.20/0.44 inference(transitivity,[status(thm)],[153, 152, 46, 44, 37])).
% 0.20/0.44 tff(155,plain,
% 0.20/0.44 (^[X6: $i, X4: $i, X3: $i, X1: $i] : refl(((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(156,plain,
% 0.20/0.44 (![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7))) <=> ![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[155])).
% 0.20/0.44 tff(157,plain,
% 0.20/0.44 (![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7))) <=> ![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(158,plain,
% 0.20/0.44 (^[X6: $i, X4: $i, X3: $i, X1: $i] : rewrite(((~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(159,plain,
% 0.20/0.44 (![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7))) <=> ![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[158])).
% 0.20/0.44 tff(160,plain,
% 0.20/0.44 (![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7))) <=> ![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))),
% 0.20/0.44 inference(elim_unused_vars,[status(thm)],[])).
% 0.20/0.44 tff(161,plain,
% 0.20/0.44 (![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))) <=> ![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))),
% 0.20/0.44 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.20/0.44 tff(162,plain,
% 0.20/0.44 (![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))) <=> ![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[161, 160])).
% 0.20/0.44 tff(163,plain,
% 0.20/0.44 (![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))) <=> ![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[162, 159])).
% 0.20/0.44 tff(164,plain,
% 0.20/0.44 (^[X6: $i, 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(trans(monotonicity(rewrite(((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)))), ((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(X4, sk_c7) = sk_c8)))), ((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(X4, sk_c7) = sk_c8))))), (((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))), (((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))))), ((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, X5) = sk_c7))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X5) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))), ((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, X5) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))))), (((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(X6, sk_c8) = X5))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(X6, sk_c8) = X5))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))), (((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))))), ((((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X6) = sk_c8))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X6) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))), ((((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))))), (((((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(X1) = sk_c8))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X1) = sk_c8))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X1) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))), (((((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(X1) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))))), ((((((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))), ((((((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))))), (((((((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))), (((((((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))))), ((((((((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(X3, sk_c8) = X2))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(X3, sk_c8) = X2))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))), ((((((((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))))), (((((((((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))) | (~(inverse(X3) = sk_c8))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c8))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))), (((((((((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))) | (~(inverse(X3) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(165,plain,
% 0.20/0.45 (![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((((((((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))) | (~(inverse(X3) = sk_c8))) <=> ![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X6, sk_c8) = X5)) | (~(multiply(sk_c8, X5) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[164])).
% 0.20/0.46 tff(166,plain,
% 0.20/0.46 (![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((((((((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))) | (~(inverse(X3) = sk_c8))) <=> ![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[165, 163])).
% 0.20/0.46 tff(167,axiom,(![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((((((((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, X5) = sk_c7))) | (~(multiply(X6, sk_c8) = X5))) | (~(inverse(X6) = sk_c8))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))) | (~(inverse(X3) = sk_c8)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_36')).
% 0.20/0.46 tff(168,plain,
% 0.20/0.46 (![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.20/0.46 tff(169,plain,
% 0.20/0.46 (![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[168, 157])).
% 0.20/0.46 tff(170,plain,(
% 0.20/0.46 ![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[169])).
% 0.20/0.46 tff(171,plain,
% 0.20/0.46 (![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[170, 156])).
% 0.20/0.46 tff(172,plain,
% 0.20/0.46 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c7)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c7)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(173,plain,
% 0.20/0.46 (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c7)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(174,plain,
% 0.20/0.46 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c7)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c7))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[173])).
% 0.20/0.46 tff(175,plain,
% 0.20/0.46 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c7)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c7)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[174, 172])).
% 0.20/0.46 tff(176,plain,
% 0.20/0.46 ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c7)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(177,plain,
% 0.20/0.46 ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c7))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.20/0.46 tff(178,plain,
% 0.20/0.46 ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c7))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[177, 80, 76, 171])).
% 0.20/0.46 tff(179,plain,
% 0.20/0.46 (~(inverse(sk_c7) = sk_c8)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[178, 145, 154, 147])).
% 0.20/0.46 tff(180,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[179, 146])).
% 0.20/0.46 tff(181,plain,(inverse(sk_c2) = sk_c8), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(182,plain,
% 0.20/0.46 (sk_c8 = inverse(sk_c2)),
% 0.20/0.46 inference(symmetry,[status(thm)],[181])).
% 0.20/0.46 tff(183,plain,
% 0.20/0.46 (multiply(sk_c8, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.20/0.46 inference(monotonicity,[status(thm)],[182])).
% 0.20/0.46 tff(184,plain,
% 0.20/0.46 (multiply(inverse(sk_c2), sk_c2) = multiply(sk_c8, sk_c2)),
% 0.20/0.46 inference(symmetry,[status(thm)],[183])).
% 0.20/0.46 tff(185,plain,
% 0.20/0.46 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c2), sk_c2) = identity)),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(186,plain,
% 0.20/0.46 (multiply(inverse(sk_c2), sk_c2) = identity),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[185, 53])).
% 0.20/0.46 tff(187,plain,
% 0.20/0.46 (identity = multiply(inverse(sk_c2), sk_c2)),
% 0.20/0.46 inference(symmetry,[status(thm)],[186])).
% 0.20/0.46 tff(188,plain,
% 0.20/0.46 (identity = multiply(sk_c8, sk_c2)),
% 0.20/0.46 inference(transitivity,[status(thm)],[187, 184])).
% 0.20/0.46 tff(189,plain,
% 0.20/0.46 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c2), sk_c8)),
% 0.20/0.46 inference(monotonicity,[status(thm)],[188])).
% 0.20/0.46 tff(190,plain,
% 0.20/0.46 (inverse(sk_c2) = sk_c7),
% 0.20/0.46 inference(transitivity,[status(thm)],[181, 65, 189, 32, 23, 16])).
% 0.20/0.46 tff(191,plain,
% 0.20/0.46 ((sk_c7 = inverse(sk_c2)) <=> (inverse(sk_c2) = sk_c7)),
% 0.20/0.46 inference(commutativity,[status(thm)],[])).
% 0.20/0.46 tff(192,plain,
% 0.20/0.46 (((inverse(sk_c1) = sk_c7) | (inverse(sk_c5) = sk_c8)) <=> ((inverse(sk_c1) = sk_c7) | (inverse(sk_c5) = sk_c8))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(193,axiom,((inverse(sk_c1) = sk_c7) | (inverse(sk_c5) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_20')).
% 0.20/0.46 tff(194,plain,
% 0.20/0.46 ((inverse(sk_c1) = sk_c7) | (inverse(sk_c5) = sk_c8)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.20/0.46 tff(195,plain,
% 0.20/0.46 (inverse(sk_c1) = sk_c7),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[194, 10])).
% 0.20/0.46 tff(196,plain,
% 0.20/0.46 ((inverse(sk_c1) = sk_c8) <=> (sk_c7 = inverse(sk_c2))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[195, 182])).
% 0.20/0.46 tff(197,plain,
% 0.20/0.46 ((inverse(sk_c1) = sk_c8) <=> (inverse(sk_c2) = sk_c7)),
% 0.20/0.46 inference(transitivity,[status(thm)],[196, 191])).
% 0.20/0.46 tff(198,plain,
% 0.20/0.46 ((~(inverse(sk_c1) = sk_c8)) <=> (~(inverse(sk_c2) = sk_c7))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[197])).
% 0.20/0.46 tff(199,plain,
% 0.20/0.46 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7),
% 0.20/0.46 inference(transitivity,[status(thm)],[23, 16])).
% 0.20/0.46 tff(200,plain,
% 0.20/0.46 (((inverse(sk_c5) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8)) <=> ((inverse(sk_c5) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(201,plain,
% 0.20/0.46 (((multiply(sk_c1, sk_c7) = sk_c8) | (inverse(sk_c5) = sk_c8)) <=> ((inverse(sk_c5) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(202,axiom,((multiply(sk_c1, sk_c7) = sk_c8) | (inverse(sk_c5) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_15')).
% 0.20/0.46 tff(203,plain,
% 0.20/0.46 ((inverse(sk_c5) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.20/0.46 tff(204,plain,
% 0.20/0.46 ((inverse(sk_c5) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[203, 200])).
% 0.20/0.46 tff(205,plain,
% 0.20/0.46 (multiply(sk_c1, sk_c7) = sk_c8),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[204, 10])).
% 0.20/0.46 tff(206,plain,
% 0.20/0.46 (((inverse(sk_c5) = sk_c8) | (inverse(sk_c7) = sk_c8)) <=> ((inverse(sk_c5) = sk_c8) | (inverse(sk_c7) = sk_c8))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(207,plain,
% 0.20/0.46 (((inverse(sk_c7) = sk_c8) | (inverse(sk_c5) = sk_c8)) <=> ((inverse(sk_c5) = sk_c8) | (inverse(sk_c7) = sk_c8))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(208,axiom,((inverse(sk_c7) = sk_c8) | (inverse(sk_c5) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_10')).
% 0.20/0.46 tff(209,plain,
% 0.20/0.46 ((inverse(sk_c5) = sk_c8) | (inverse(sk_c7) = sk_c8)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.20/0.46 tff(210,plain,
% 0.20/0.46 ((inverse(sk_c5) = sk_c8) | (inverse(sk_c7) = sk_c8)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[209, 206])).
% 0.20/0.46 tff(211,plain,
% 0.20/0.46 (inverse(sk_c7) = sk_c8),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[210, 10])).
% 0.20/0.46 tff(212,plain,
% 0.20/0.46 (((inverse(sk_c8) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6)) <=> ((inverse(sk_c8) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(213,axiom,((inverse(sk_c8) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_4')).
% 0.20/0.46 tff(214,plain,
% 0.20/0.46 ((inverse(sk_c8) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.20/0.46 tff(215,plain,
% 0.20/0.46 (multiply(sk_c5, sk_c8) = sk_c6),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[214, 142])).
% 0.20/0.46 tff(216,plain,
% 0.20/0.46 (((inverse(sk_c8) = sk_c7) | (multiply(sk_c4, sk_c7) = sk_c8)) <=> ((inverse(sk_c8) = sk_c7) | (multiply(sk_c4, sk_c7) = sk_c8))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(217,axiom,((inverse(sk_c8) = sk_c7) | (multiply(sk_c4, sk_c7) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_2')).
% 0.20/0.47 tff(218,plain,
% 0.20/0.47 ((inverse(sk_c8) = sk_c7) | (multiply(sk_c4, sk_c7) = sk_c8)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.20/0.47 tff(219,plain,
% 0.20/0.47 (multiply(sk_c4, sk_c7) = sk_c8),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[218, 142])).
% 0.20/0.47 tff(220,plain,
% 0.20/0.47 (((inverse(sk_c8) = sk_c7) | (inverse(sk_c5) = sk_c8)) <=> ((inverse(sk_c8) = sk_c7) | (inverse(sk_c5) = sk_c8))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(221,axiom,((inverse(sk_c8) = sk_c7) | (inverse(sk_c5) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_5')).
% 0.20/0.47 tff(222,plain,
% 0.20/0.47 ((inverse(sk_c8) = sk_c7) | (inverse(sk_c5) = sk_c8)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.20/0.47 tff(223,plain,
% 0.20/0.47 ((inverse(sk_c8) = sk_c7) | (inverse(sk_c5) = sk_c8)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[222, 220])).
% 0.20/0.47 tff(224,plain,
% 0.20/0.47 ((inverse(sk_c8) = sk_c7) | (inverse(sk_c5) = sk_c8)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[223, 220])).
% 0.20/0.47 tff(225,plain,
% 0.20/0.47 ((inverse(sk_c8) = sk_c7) | (inverse(sk_c5) = sk_c8)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[224, 220])).
% 0.20/0.47 tff(226,plain,
% 0.20/0.47 ((inverse(sk_c8) = sk_c7) | (inverse(sk_c5) = sk_c8)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[225, 220])).
% 0.20/0.47 tff(227,plain,
% 0.20/0.47 (inverse(sk_c5) = sk_c8),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[226, 142])).
% 0.20/0.47 tff(228,plain,
% 0.20/0.47 (((inverse(sk_c8) = sk_c7) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c8) = sk_c7) | (inverse(sk_c4) = sk_c8))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(229,axiom,((inverse(sk_c8) = sk_c7) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_1')).
% 0.20/0.47 tff(230,plain,
% 0.20/0.47 ((inverse(sk_c8) = sk_c7) | (inverse(sk_c4) = sk_c8)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.20/0.47 tff(231,plain,
% 0.20/0.47 ((inverse(sk_c8) = sk_c7) | (inverse(sk_c4) = sk_c8)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[230, 228])).
% 0.20/0.47 tff(232,plain,
% 0.20/0.47 ((inverse(sk_c8) = sk_c7) | (inverse(sk_c4) = sk_c8)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[231, 228])).
% 0.20/0.47 tff(233,plain,
% 0.20/0.47 ((inverse(sk_c8) = sk_c7) | (inverse(sk_c4) = sk_c8)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[232, 228])).
% 0.20/0.47 tff(234,plain,
% 0.20/0.47 ((inverse(sk_c8) = sk_c7) | (inverse(sk_c4) = sk_c8)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[233, 228])).
% 0.20/0.47 tff(235,plain,
% 0.20/0.47 (inverse(sk_c4) = sk_c8),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[234, 142])).
% 0.20/0.47 tff(236,plain,
% 0.20/0.47 (((inverse(sk_c8) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7)) <=> ((inverse(sk_c8) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(237,axiom,((inverse(sk_c8) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_3')).
% 0.20/0.47 tff(238,plain,
% 0.20/0.47 ((inverse(sk_c8) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.20/0.47 tff(239,plain,
% 0.20/0.47 (multiply(sk_c8, sk_c6) = sk_c7),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[238, 142])).
% 0.20/0.47 tff(240,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[144, 239, 142, 235, 227, 219, 215])).
% 0.20/0.47 tff(241,plain,(inverse(sk_c8) = sk_c7), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(242,plain,
% 0.20/0.47 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(243,plain,
% 0.20/0.47 (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(244,plain,
% 0.20/0.47 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(inverse(sk_c1) = sk_c7))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[243])).
% 0.20/0.47 tff(245,plain,
% 0.20/0.47 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[244, 242])).
% 0.20/0.47 tff(246,plain,
% 0.20/0.47 ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(247,plain,
% 0.20/0.47 ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(inverse(sk_c1) = sk_c7))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.20/0.47 tff(248,plain,
% 0.20/0.47 (~(inverse(sk_c1) = sk_c8)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[247, 241, 211, 205, 195, 181, 171, 199])).
% 0.20/0.47 tff(249,plain,
% 0.20/0.47 (~(inverse(sk_c2) = sk_c7)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[248, 198])).
% 0.20/0.47 tff(250,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[249, 190])).
% 0.20/0.47 tff(251,plain,(inverse(sk_c5) = sk_c8), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(252,plain,
% 0.20/0.47 (sk_c8 = inverse(sk_c5)),
% 0.20/0.47 inference(symmetry,[status(thm)],[251])).
% 0.20/0.47 tff(253,plain,
% 0.20/0.47 (multiply(sk_c8, sk_c5) = multiply(inverse(sk_c5), sk_c5)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[252])).
% 0.20/0.47 tff(254,plain,
% 0.20/0.47 (multiply(inverse(sk_c5), sk_c5) = multiply(sk_c8, sk_c5)),
% 0.20/0.47 inference(symmetry,[status(thm)],[253])).
% 0.20/0.47 tff(255,plain,
% 0.20/0.47 (identity = multiply(sk_c8, sk_c5)),
% 0.20/0.47 inference(transitivity,[status(thm)],[96, 254])).
% 0.20/0.47 tff(256,plain,
% 0.20/0.47 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c5), sk_c8)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[255])).
% 0.20/0.47 tff(257,plain,
% 0.20/0.47 (multiply(multiply(sk_c8, sk_c5), sk_c8) = multiply(identity, sk_c8)),
% 0.20/0.47 inference(symmetry,[status(thm)],[256])).
% 0.20/0.47 tff(258,assumption,(~(multiply(sk_c5, sk_c8) = sk_c6)), introduced(assumption)).
% 0.20/0.47 tff(259,plain,
% 0.20/0.47 (((multiply(sk_c5, sk_c8) = sk_c6) | (multiply(sk_c8, sk_c3) = sk_c7)) <=> ((multiply(sk_c5, sk_c8) = sk_c6) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(260,plain,
% 0.20/0.47 (((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6)) <=> ((multiply(sk_c5, sk_c8) = sk_c6) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(261,axiom,((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_24')).
% 0.20/0.47 tff(262,plain,
% 0.20/0.47 ((multiply(sk_c5, sk_c8) = sk_c6) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.20/0.47 tff(263,plain,
% 0.20/0.47 ((multiply(sk_c5, sk_c8) = sk_c6) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[262, 259])).
% 0.20/0.47 tff(264,plain,
% 0.20/0.47 (multiply(sk_c8, sk_c3) = sk_c7),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[263, 258])).
% 0.20/0.47 tff(265,plain,
% 0.20/0.47 (((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c5, sk_c8) = sk_c6)) <=> ((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c5, sk_c8) = sk_c6))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(266,axiom,((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c5, sk_c8) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_29')).
% 0.20/0.47 tff(267,plain,
% 0.20/0.47 ((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c5, sk_c8) = sk_c6)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.20/0.47 tff(268,plain,
% 0.20/0.47 (multiply(sk_c2, sk_c8) = sk_c3),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[267, 258])).
% 0.20/0.47 tff(269,plain,
% 0.20/0.47 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = multiply(sk_c8, sk_c3)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[268])).
% 0.20/0.47 tff(270,plain,
% 0.20/0.47 (inverse(sk_c2) = sk_c7),
% 0.20/0.47 inference(transitivity,[status(thm)],[181, 65, 189, 32, 269, 264])).
% 0.20/0.47 tff(271,plain,
% 0.20/0.47 (((inverse(sk_c1) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6)) <=> ((inverse(sk_c1) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(272,axiom,((inverse(sk_c1) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_19')).
% 0.20/0.47 tff(273,plain,
% 0.20/0.47 ((inverse(sk_c1) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.20/0.47 tff(274,plain,
% 0.20/0.47 (inverse(sk_c1) = sk_c7),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[273, 258])).
% 0.20/0.47 tff(275,plain,
% 0.20/0.47 ((inverse(sk_c1) = sk_c8) <=> (sk_c7 = inverse(sk_c2))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[274, 182])).
% 0.20/0.47 tff(276,plain,
% 0.20/0.47 ((inverse(sk_c1) = sk_c8) <=> (inverse(sk_c2) = sk_c7)),
% 0.20/0.47 inference(transitivity,[status(thm)],[275, 191])).
% 0.20/0.47 tff(277,plain,
% 0.20/0.47 ((~(inverse(sk_c1) = sk_c8)) <=> (~(inverse(sk_c2) = sk_c7))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[276])).
% 0.20/0.47 tff(278,plain,
% 0.20/0.47 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7),
% 0.20/0.47 inference(transitivity,[status(thm)],[269, 264])).
% 0.20/0.47 tff(279,plain,
% 0.20/0.47 (((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6)) <=> ((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(280,axiom,((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_14')).
% 0.20/0.47 tff(281,plain,
% 0.20/0.47 ((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.20/0.47 tff(282,plain,
% 0.20/0.47 (multiply(sk_c1, sk_c7) = sk_c8),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[281, 258])).
% 0.20/0.47 tff(283,plain,
% 0.20/0.47 (multiply(sk_c8, sk_c5) = identity),
% 0.20/0.47 inference(transitivity,[status(thm)],[253, 55])).
% 0.20/0.47 tff(284,plain,
% 0.20/0.47 (multiply(multiply(sk_c8, sk_c5), sk_c8) = multiply(identity, sk_c8)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[283])).
% 0.20/0.47 tff(285,assumption,(~(inverse(sk_c7) = sk_c8)), introduced(assumption)).
% 0.20/0.47 tff(286,plain,
% 0.20/0.47 (((inverse(sk_c7) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6)) <=> ((inverse(sk_c7) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(287,axiom,((inverse(sk_c7) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_9')).
% 0.20/0.47 tff(288,plain,
% 0.20/0.47 ((inverse(sk_c7) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.20/0.47 tff(289,plain,
% 0.20/0.47 (multiply(sk_c5, sk_c8) = sk_c6),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[288, 285])).
% 0.20/0.47 tff(290,plain,
% 0.20/0.47 (sk_c6 = multiply(sk_c5, sk_c8)),
% 0.20/0.47 inference(symmetry,[status(thm)],[289])).
% 0.20/0.47 tff(291,plain,
% 0.20/0.47 (multiply(sk_c8, sk_c6) = multiply(sk_c8, multiply(sk_c5, sk_c8))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[290])).
% 0.20/0.47 tff(292,assumption,(~(multiply(sk_c8, sk_c6) = sk_c7)), introduced(assumption)).
% 0.20/0.47 tff(293,plain,
% 0.20/0.47 (((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7)) <=> ((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(294,axiom,((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_23')).
% 0.20/0.47 tff(295,plain,
% 0.20/0.47 ((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[294, 293])).
% 0.20/0.47 tff(296,plain,
% 0.20/0.47 (multiply(sk_c8, sk_c3) = sk_c7),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[295, 292])).
% 0.20/0.47 tff(297,plain,
% 0.20/0.47 (((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c8, sk_c6) = sk_c7)) <=> ((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c8, sk_c6) = sk_c7))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(298,axiom,((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c8, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_28')).
% 0.20/0.47 tff(299,plain,
% 0.20/0.47 ((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c8, sk_c6) = sk_c7)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.20/0.47 tff(300,plain,
% 0.20/0.47 (multiply(sk_c2, sk_c8) = sk_c3),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[299, 292])).
% 0.20/0.47 tff(301,plain,
% 0.20/0.47 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = multiply(sk_c8, sk_c3)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[300])).
% 0.20/0.47 tff(302,plain,
% 0.20/0.47 (inverse(sk_c2) = sk_c7),
% 0.20/0.47 inference(transitivity,[status(thm)],[181, 65, 189, 32, 301, 296])).
% 0.20/0.47 tff(303,plain,
% 0.20/0.47 (((inverse(sk_c1) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7)) <=> ((inverse(sk_c1) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(304,axiom,((inverse(sk_c1) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_18')).
% 0.20/0.48 tff(305,plain,
% 0.20/0.48 ((inverse(sk_c1) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.20/0.48 tff(306,plain,
% 0.20/0.48 (inverse(sk_c1) = sk_c7),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[305, 292])).
% 0.20/0.48 tff(307,plain,
% 0.20/0.48 ((inverse(sk_c1) = sk_c8) <=> (sk_c7 = inverse(sk_c2))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[306, 182])).
% 0.20/0.48 tff(308,plain,
% 0.20/0.48 ((inverse(sk_c1) = sk_c8) <=> (inverse(sk_c2) = sk_c7)),
% 0.20/0.48 inference(transitivity,[status(thm)],[307, 191])).
% 0.20/0.48 tff(309,plain,
% 0.20/0.48 ((~(inverse(sk_c1) = sk_c8)) <=> (~(inverse(sk_c2) = sk_c7))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[308])).
% 0.20/0.48 tff(310,plain,
% 0.20/0.48 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7),
% 0.20/0.48 inference(transitivity,[status(thm)],[301, 296])).
% 0.20/0.48 tff(311,plain,
% 0.20/0.48 (((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7)) <=> ((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(312,axiom,((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_13')).
% 0.20/0.48 tff(313,plain,
% 0.20/0.48 ((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.20/0.48 tff(314,plain,
% 0.20/0.48 (multiply(sk_c1, sk_c7) = sk_c8),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[313, 292])).
% 0.20/0.48 tff(315,plain,
% 0.20/0.48 (((inverse(sk_c7) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7)) <=> ((inverse(sk_c7) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(316,axiom,((inverse(sk_c7) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_8')).
% 0.20/0.48 tff(317,plain,
% 0.20/0.48 ((inverse(sk_c7) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.20/0.48 tff(318,plain,
% 0.20/0.48 (inverse(sk_c7) = sk_c8),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[317, 292])).
% 0.20/0.48 tff(319,plain,
% 0.20/0.48 (~(inverse(sk_c1) = sk_c8)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[247, 241, 318, 314, 306, 181, 171, 310])).
% 0.20/0.48 tff(320,plain,
% 0.20/0.48 (~(inverse(sk_c2) = sk_c7)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[319, 309])).
% 0.20/0.48 tff(321,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[320, 302])).
% 0.20/0.48 tff(322,plain,(multiply(sk_c8, sk_c6) = sk_c7), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(323,plain,
% 0.20/0.48 (sk_c7 = multiply(sk_c8, sk_c6)),
% 0.20/0.48 inference(symmetry,[status(thm)],[322])).
% 0.20/0.48 tff(324,plain,
% 0.20/0.48 (sk_c7 = sk_c8),
% 0.20/0.48 inference(transitivity,[status(thm)],[323, 291, 67, 284, 9])).
% 0.20/0.48 tff(325,plain,
% 0.20/0.48 (inverse(sk_c7) = inverse(sk_c8)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[324])).
% 0.20/0.48 tff(326,plain,
% 0.20/0.48 (inverse(sk_c7) = sk_c8),
% 0.20/0.48 inference(transitivity,[status(thm)],[325, 241, 323, 291, 67, 284, 9])).
% 0.20/0.48 tff(327,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[285, 326])).
% 0.20/0.48 tff(328,plain,(inverse(sk_c7) = sk_c8), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(329,plain,
% 0.20/0.48 (~(inverse(sk_c1) = sk_c8)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[247, 241, 328, 282, 274, 181, 171, 278])).
% 0.20/0.48 tff(330,plain,
% 0.20/0.48 (~(inverse(sk_c2) = sk_c7)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[329, 277])).
% 0.20/0.48 tff(331,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[330, 270])).
% 0.20/0.48 tff(332,plain,(multiply(sk_c5, sk_c8) = sk_c6), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(333,plain,
% 0.20/0.48 (multiply(sk_c8, multiply(sk_c5, sk_c8)) = multiply(sk_c8, sk_c6)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[332])).
% 0.20/0.48 tff(334,plain,
% 0.20/0.48 (multiply(sk_c8, sk_c6) = multiply(sk_c8, multiply(sk_c5, sk_c8))),
% 0.20/0.48 inference(symmetry,[status(thm)],[333])).
% 0.20/0.48 tff(335,assumption,(~(inverse(sk_c4) = sk_c8)), introduced(assumption)).
% 0.20/0.48 tff(336,plain,
% 0.20/0.48 (((inverse(sk_c1) = sk_c7) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c1) = sk_c7) | (inverse(sk_c4) = sk_c8))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(337,axiom,((inverse(sk_c1) = sk_c7) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_16')).
% 0.20/0.48 tff(338,plain,
% 0.20/0.48 ((inverse(sk_c1) = sk_c7) | (inverse(sk_c4) = sk_c8)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.20/0.48 tff(339,plain,
% 0.20/0.48 (inverse(sk_c1) = sk_c7),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[338, 335])).
% 0.20/0.48 tff(340,plain,
% 0.20/0.48 (inverse(sk_c1) = sk_c8),
% 0.20/0.48 inference(transitivity,[status(thm)],[339, 323, 334, 67, 257, 9])).
% 0.20/0.48 tff(341,plain,
% 0.20/0.48 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c7), sk_c7) = identity)),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(342,plain,
% 0.20/0.48 (multiply(inverse(sk_c7), sk_c7) = identity),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[341, 53])).
% 0.20/0.48 tff(343,plain,
% 0.20/0.48 (sk_c8 = inverse(sk_c7)),
% 0.20/0.48 inference(symmetry,[status(thm)],[328])).
% 0.20/0.48 tff(344,plain,
% 0.20/0.48 (multiply(sk_c8, sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[343])).
% 0.20/0.48 tff(345,plain,
% 0.20/0.48 (multiply(sk_c8, sk_c7) = multiply(sk_c8, sk_c5)),
% 0.20/0.48 inference(transitivity,[status(thm)],[344, 342, 96, 254])).
% 0.20/0.48 tff(346,plain,
% 0.20/0.48 (multiply(multiply(sk_c8, sk_c7), sk_c8) = multiply(multiply(sk_c8, sk_c5), sk_c8)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[345])).
% 0.20/0.48 tff(347,plain,
% 0.20/0.48 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c7), sk_c8) = multiply(sk_c8, multiply(sk_c7, sk_c8)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(348,plain,
% 0.20/0.48 (multiply(multiply(sk_c8, sk_c7), sk_c8) = multiply(sk_c8, multiply(sk_c7, sk_c8))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[347, 30])).
% 0.20/0.48 tff(349,plain,
% 0.20/0.48 (multiply(sk_c8, multiply(sk_c7, sk_c8)) = multiply(multiply(sk_c8, sk_c7), sk_c8)),
% 0.20/0.48 inference(symmetry,[status(thm)],[348])).
% 0.20/0.48 tff(350,plain,
% 0.20/0.48 (multiply(sk_c8, multiply(sk_c7, sk_c8)) = sk_c7),
% 0.20/0.48 inference(transitivity,[status(thm)],[349, 346, 46, 333, 322])).
% 0.20/0.48 tff(351,plain,
% 0.20/0.48 (((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(352,plain,
% 0.20/0.48 (((multiply(sk_c1, sk_c7) = sk_c8) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(353,axiom,((multiply(sk_c1, sk_c7) = sk_c8) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_11')).
% 0.20/0.48 tff(354,plain,
% 0.20/0.48 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[353, 352])).
% 0.20/0.48 tff(355,plain,
% 0.20/0.48 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[354, 351])).
% 0.20/0.48 tff(356,plain,
% 0.20/0.48 (multiply(sk_c1, sk_c7) = sk_c8),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[355, 335])).
% 0.20/0.48 tff(357,plain,
% 0.20/0.48 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c7, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c7, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(358,plain,
% 0.20/0.48 (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c7, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c7, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c7, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(359,plain,
% 0.20/0.48 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c7, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c7, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c7, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[358])).
% 0.20/0.48 tff(360,plain,
% 0.20/0.48 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c7, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c7, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c7, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[359, 357])).
% 0.20/0.48 tff(361,plain,
% 0.20/0.48 ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c7, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c7, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(362,plain,
% 0.20/0.48 ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c7, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[361, 360])).
% 0.20/0.48 tff(363,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[362, 241, 328, 356, 339, 171, 350, 340])).
% 0.20/0.48 tff(364,plain,(inverse(sk_c4) = sk_c8), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(365,plain,
% 0.20/0.48 (inverse(sk_c4) = sk_c7),
% 0.20/0.48 inference(transitivity,[status(thm)],[364, 65, 256, 46, 333, 322])).
% 0.20/0.48 tff(366,plain,
% 0.20/0.48 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c7, sk_c8)) = sk_c7)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c7, sk_c8)) = sk_c7)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(367,plain,
% 0.20/0.48 (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c7, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c7, sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c7, sk_c8)) = sk_c7)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(368,plain,
% 0.20/0.48 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c7, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c7, sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c7)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c7, sk_c8)) = sk_c7))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[367])).
% 0.20/0.48 tff(369,plain,
% 0.20/0.48 (((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c7, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c7, sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c7)))) <=> ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c7, sk_c8)) = sk_c7)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[368, 366])).
% 0.20/0.48 tff(370,plain,
% 0.20/0.48 ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c7, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c7, sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c7)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(371,plain,
% 0.20/0.48 ((~![X6: $i, X4: $i, X3: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(X6) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(sk_c8, multiply(X6, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(inverse(X4) = sk_c7)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c7, sk_c8)) = sk_c7))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[370, 369])).
% 0.20/0.48 tff(372,plain,
% 0.20/0.48 (~(multiply(sk_c4, sk_c7) = sk_c8)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[371, 241, 364, 328, 171, 350, 365])).
% 0.20/0.48 tff(373,plain,
% 0.20/0.48 (((inverse(sk_c1) = sk_c7) | (multiply(sk_c4, sk_c7) = sk_c8)) <=> ((inverse(sk_c1) = sk_c7) | (multiply(sk_c4, sk_c7) = sk_c8))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(374,axiom,((inverse(sk_c1) = sk_c7) | (multiply(sk_c4, sk_c7) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_17')).
% 0.20/0.48 tff(375,plain,
% 0.20/0.48 ((inverse(sk_c1) = sk_c7) | (multiply(sk_c4, sk_c7) = sk_c8)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[374, 373])).
% 0.20/0.48 tff(376,plain,
% 0.20/0.48 (inverse(sk_c1) = sk_c7),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[375, 372])).
% 0.20/0.49 tff(377,plain,
% 0.20/0.49 (inverse(sk_c1) = sk_c8),
% 0.20/0.49 inference(transitivity,[status(thm)],[376, 323, 334, 67, 257, 9])).
% 0.20/0.49 tff(378,plain,
% 0.20/0.49 (((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c4, sk_c7) = sk_c8)) <=> ((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c4, sk_c7) = sk_c8))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(379,axiom,((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c4, sk_c7) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_12')).
% 0.20/0.49 tff(380,plain,
% 0.20/0.49 ((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c4, sk_c7) = sk_c8)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.20/0.49 tff(381,plain,
% 0.20/0.49 (multiply(sk_c1, sk_c7) = sk_c8),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[380, 372])).
% 0.20/0.49 tff(382,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[362, 241, 328, 381, 376, 171, 350, 377])).
% 0.20/0.49 % SZS output end Proof
% 0.20/0.49 % E exiting
%------------------------------------------------------------------------------