%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP240-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:07:30 AM UTC 2025
% Result : Unsatisfiable 0.62s 0.78s
% Output : Proof 0.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP240-1 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 15:49:54 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.62/0.78 % SZS status Unsatisfiable
% 0.62/0.78 % SZS output start Proof
% 0.62/0.78 tff(sk_c9_type, type, (
% 0.62/0.78 sk_c9: $i)).
% 0.62/0.78 tff(multiply_type, type, (
% 0.62/0.78 multiply: ( $i * $i ) > $i)).
% 0.62/0.78 tff(sk_c10_type, type, (
% 0.62/0.78 sk_c10: $i)).
% 0.62/0.78 tff(inverse_type, type, (
% 0.62/0.78 inverse: $i > $i)).
% 0.62/0.78 tff(sk_c8_type, type, (
% 0.62/0.78 sk_c8: $i)).
% 0.62/0.78 tff(identity_type, type, (
% 0.62/0.78 identity: $i)).
% 0.62/0.78 tff(sk_c7_type, type, (
% 0.62/0.78 sk_c7: $i)).
% 0.62/0.78 tff(sk_c4_type, type, (
% 0.62/0.78 sk_c4: $i)).
% 0.62/0.78 tff(sk_c3_type, type, (
% 0.62/0.78 sk_c3: $i)).
% 0.62/0.78 tff(sk_c2_type, type, (
% 0.62/0.78 sk_c2: $i)).
% 0.62/0.78 tff(sk_c1_type, type, (
% 0.62/0.78 sk_c1: $i)).
% 0.62/0.78 tff(1,plain,
% 0.62/0.78 (^[X: $i] : refl((multiply(inverse(X), X) = identity) <=> (multiply(inverse(X), X) = identity))),
% 0.62/0.78 inference(bind,[status(th)],[])).
% 0.62/0.78 tff(2,plain,
% 0.62/0.78 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.62/0.78 inference(quant_intro,[status(thm)],[1])).
% 0.62/0.78 tff(3,plain,
% 0.62/0.78 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(4,axiom,(![X: $i] : (multiply(inverse(X), X) = identity)), file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax','left_inverse')).
% 0.62/0.78 tff(5,plain,
% 0.62/0.78 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.62/0.78 tff(6,plain,(
% 0.62/0.78 ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.62/0.78 inference(skolemize,[status(sab)],[5])).
% 0.62/0.78 tff(7,plain,
% 0.62/0.78 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.62/0.78 tff(8,plain,
% 0.62/0.78 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c10), sk_c10) = identity)),
% 0.62/0.78 inference(quant_inst,[status(thm)],[])).
% 0.62/0.78 tff(9,plain,
% 0.62/0.78 (multiply(inverse(sk_c10), sk_c10) = identity),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.62/0.78 tff(10,plain,
% 0.62/0.78 (identity = multiply(inverse(sk_c10), sk_c10)),
% 0.62/0.78 inference(symmetry,[status(thm)],[9])).
% 0.62/0.78 tff(11,plain,
% 0.62/0.78 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c9), sk_c9) = identity)),
% 0.62/0.78 inference(quant_inst,[status(thm)],[])).
% 0.62/0.78 tff(12,plain,
% 0.62/0.78 (multiply(inverse(sk_c9), sk_c9) = identity),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[11, 7])).
% 0.62/0.78 tff(13,assumption,(~(multiply(sk_c10, sk_c8) = sk_c9)), introduced(assumption)).
% 0.62/0.78 tff(14,plain,
% 0.62/0.78 (((inverse(sk_c9) = sk_c10) | (multiply(sk_c10, sk_c8) = sk_c9)) <=> ((inverse(sk_c9) = sk_c10) | (multiply(sk_c10, sk_c8) = sk_c9))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(15,axiom,((inverse(sk_c9) = sk_c10) | (multiply(sk_c10, sk_c8) = sk_c9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_14')).
% 0.62/0.78 tff(16,plain,
% 0.62/0.78 ((inverse(sk_c9) = sk_c10) | (multiply(sk_c10, sk_c8) = sk_c9)),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.62/0.78 tff(17,plain,
% 0.62/0.78 (inverse(sk_c9) = sk_c10),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[16, 13])).
% 0.62/0.78 tff(18,plain,
% 0.62/0.78 (sk_c10 = inverse(sk_c9)),
% 0.62/0.78 inference(symmetry,[status(thm)],[17])).
% 0.62/0.78 tff(19,plain,
% 0.62/0.78 (multiply(sk_c10, sk_c9) = multiply(inverse(sk_c9), sk_c9)),
% 0.62/0.78 inference(monotonicity,[status(thm)],[18])).
% 0.62/0.78 tff(20,assumption,(~(inverse(sk_c10) = sk_c9)), introduced(assumption)).
% 0.62/0.78 tff(21,plain,
% 0.62/0.78 (((inverse(sk_c10) = sk_c9) | (multiply(sk_c7, sk_c10) = sk_c8)) <=> ((inverse(sk_c10) = sk_c9) | (multiply(sk_c7, sk_c10) = sk_c8))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(22,axiom,((inverse(sk_c10) = sk_c9) | (multiply(sk_c7, sk_c10) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_7')).
% 0.62/0.78 tff(23,plain,
% 0.62/0.78 ((inverse(sk_c10) = sk_c9) | (multiply(sk_c7, sk_c10) = sk_c8)),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.62/0.78 tff(24,plain,
% 0.62/0.78 (multiply(sk_c7, sk_c10) = sk_c8),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[23, 20])).
% 0.62/0.78 tff(25,plain,
% 0.62/0.78 (((inverse(sk_c10) = sk_c9) | (multiply(sk_c4, sk_c9) = sk_c10)) <=> ((inverse(sk_c10) = sk_c9) | (multiply(sk_c4, sk_c9) = sk_c10))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(26,axiom,((inverse(sk_c10) = sk_c9) | (multiply(sk_c4, sk_c9) = sk_c10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_2')).
% 0.62/0.78 tff(27,plain,
% 0.62/0.79 ((inverse(sk_c10) = sk_c9) | (multiply(sk_c4, sk_c9) = sk_c10)),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.62/0.79 tff(28,plain,
% 0.62/0.79 (multiply(sk_c4, sk_c9) = sk_c10),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[27, 20])).
% 0.62/0.79 tff(29,plain,
% 0.62/0.79 (((inverse(sk_c10) = sk_c9) | (inverse(sk_c7) = sk_c10)) <=> ((inverse(sk_c10) = sk_c9) | (inverse(sk_c7) = sk_c10))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(30,axiom,((inverse(sk_c10) = sk_c9) | (inverse(sk_c7) = sk_c10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_8')).
% 0.62/0.79 tff(31,plain,
% 0.62/0.79 ((inverse(sk_c10) = sk_c9) | (inverse(sk_c7) = sk_c10)),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.62/0.79 tff(32,plain,
% 0.62/0.79 (inverse(sk_c7) = sk_c10),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[31, 20])).
% 0.62/0.79 tff(33,plain,
% 0.62/0.79 (((inverse(sk_c10) = sk_c9) | (inverse(sk_c4) = sk_c10)) <=> ((inverse(sk_c10) = sk_c9) | (inverse(sk_c4) = sk_c10))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(34,axiom,((inverse(sk_c10) = sk_c9) | (inverse(sk_c4) = sk_c10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_1')).
% 0.62/0.79 tff(35,plain,
% 0.62/0.79 ((inverse(sk_c10) = sk_c9) | (inverse(sk_c4) = sk_c10)),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.62/0.79 tff(36,plain,
% 0.62/0.79 (inverse(sk_c4) = sk_c10),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[35, 20])).
% 0.62/0.79 tff(37,plain,
% 0.62/0.79 (((inverse(sk_c10) = sk_c9) | (multiply(sk_c10, sk_c8) = sk_c9)) <=> ((inverse(sk_c10) = sk_c9) | (multiply(sk_c10, sk_c8) = sk_c9))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(38,axiom,((inverse(sk_c10) = sk_c9) | (multiply(sk_c10, sk_c8) = sk_c9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_6')).
% 0.62/0.79 tff(39,plain,
% 0.62/0.79 ((inverse(sk_c10) = sk_c9) | (multiply(sk_c10, sk_c8) = sk_c9)),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.62/0.79 tff(40,plain,
% 0.62/0.79 (multiply(sk_c10, sk_c8) = sk_c9),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[39, 20])).
% 0.62/0.79 tff(41,assumption,(multiply(sk_c10, sk_c8) = sk_c9), introduced(assumption)).
% 0.62/0.79 tff(42,assumption,(multiply(sk_c7, sk_c10) = sk_c8), introduced(assumption)).
% 0.62/0.79 tff(43,plain,
% 0.62/0.79 (sk_c8 = multiply(sk_c7, sk_c10)),
% 0.62/0.79 inference(symmetry,[status(thm)],[42])).
% 0.62/0.79 tff(44,plain,
% 0.62/0.79 (multiply(sk_c10, sk_c8) = multiply(sk_c10, multiply(sk_c7, sk_c10))),
% 0.62/0.79 inference(monotonicity,[status(thm)],[43])).
% 0.62/0.79 tff(45,plain,
% 0.62/0.79 (multiply(sk_c10, multiply(sk_c7, sk_c10)) = multiply(sk_c10, sk_c8)),
% 0.62/0.79 inference(symmetry,[status(thm)],[44])).
% 0.62/0.79 tff(46,plain,
% 0.62/0.79 (^[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))))),
% 0.62/0.79 inference(bind,[status(th)],[])).
% 0.62/0.79 tff(47,plain,
% 0.62/0.79 (![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)))),
% 0.62/0.79 inference(quant_intro,[status(thm)],[46])).
% 0.62/0.79 tff(48,plain,
% 0.62/0.79 (![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)))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(49,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')).
% 0.62/0.79 tff(50,plain,
% 0.62/0.79 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.62/0.79 tff(51,plain,(
% 0.62/0.79 ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.62/0.79 inference(skolemize,[status(sab)],[50])).
% 0.62/0.79 tff(52,plain,
% 0.62/0.79 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.62/0.79 tff(53,plain,
% 0.62/0.79 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c10, sk_c7), sk_c10) = multiply(sk_c10, multiply(sk_c7, sk_c10)))),
% 0.62/0.79 inference(quant_inst,[status(thm)],[])).
% 0.62/0.79 tff(54,plain,
% 0.62/0.79 (multiply(multiply(sk_c10, sk_c7), sk_c10) = multiply(sk_c10, multiply(sk_c7, sk_c10))),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.62/0.79 tff(55,plain,
% 0.62/0.79 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c7), sk_c7) = identity)),
% 0.62/0.79 inference(quant_inst,[status(thm)],[])).
% 0.62/0.79 tff(56,plain,
% 0.62/0.79 (multiply(inverse(sk_c7), sk_c7) = identity),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[55, 7])).
% 0.62/0.79 tff(57,assumption,(inverse(sk_c7) = sk_c10), introduced(assumption)).
% 0.62/0.79 tff(58,plain,
% 0.62/0.79 (sk_c10 = inverse(sk_c7)),
% 0.62/0.79 inference(symmetry,[status(thm)],[57])).
% 0.62/0.79 tff(59,plain,
% 0.62/0.79 (multiply(sk_c10, sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.62/0.79 inference(monotonicity,[status(thm)],[58])).
% 0.62/0.79 tff(60,plain,
% 0.62/0.79 (multiply(sk_c10, sk_c7) = identity),
% 0.62/0.79 inference(transitivity,[status(thm)],[59, 56])).
% 0.62/0.79 tff(61,plain,
% 0.62/0.79 (multiply(multiply(sk_c10, sk_c7), sk_c10) = multiply(identity, sk_c10)),
% 0.62/0.79 inference(monotonicity,[status(thm)],[60])).
% 0.62/0.79 tff(62,plain,
% 0.62/0.79 (multiply(identity, sk_c10) = multiply(multiply(sk_c10, sk_c7), sk_c10)),
% 0.62/0.79 inference(symmetry,[status(thm)],[61])).
% 0.62/0.79 tff(63,plain,
% 0.62/0.79 (^[X: $i] : refl((multiply(identity, X) = X) <=> (multiply(identity, X) = X))),
% 0.62/0.79 inference(bind,[status(th)],[])).
% 0.62/0.79 tff(64,plain,
% 0.62/0.79 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.62/0.79 inference(quant_intro,[status(thm)],[63])).
% 0.62/0.79 tff(65,plain,
% 0.62/0.79 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(66,axiom,(![X: $i] : (multiply(identity, X) = X)), file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax','left_identity')).
% 0.62/0.79 tff(67,plain,
% 0.62/0.79 (![X: $i] : (multiply(identity, X) = X)),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.62/0.79 tff(68,plain,(
% 0.62/0.79 ![X: $i] : (multiply(identity, X) = X)),
% 0.62/0.79 inference(skolemize,[status(sab)],[67])).
% 0.62/0.79 tff(69,plain,
% 0.62/0.79 (![X: $i] : (multiply(identity, X) = X)),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.62/0.79 tff(70,plain,
% 0.62/0.79 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c10) = sk_c10)),
% 0.62/0.79 inference(quant_inst,[status(thm)],[])).
% 0.62/0.79 tff(71,plain,
% 0.62/0.79 (multiply(identity, sk_c10) = sk_c10),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.62/0.79 tff(72,plain,
% 0.62/0.79 (sk_c10 = multiply(identity, sk_c10)),
% 0.62/0.79 inference(symmetry,[status(thm)],[71])).
% 0.62/0.79 tff(73,assumption,(inverse(sk_c4) = sk_c10), introduced(assumption)).
% 0.62/0.79 tff(74,plain,
% 0.62/0.79 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c4) = sk_c4)),
% 0.62/0.79 inference(quant_inst,[status(thm)],[])).
% 0.62/0.79 tff(75,plain,
% 0.62/0.79 (multiply(identity, sk_c4) = sk_c4),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[74, 69])).
% 0.62/0.79 tff(76,plain,
% 0.62/0.79 (multiply(inverse(sk_c7), sk_c7) = multiply(sk_c10, sk_c7)),
% 0.62/0.79 inference(symmetry,[status(thm)],[59])).
% 0.62/0.79 tff(77,plain,
% 0.62/0.79 (identity = multiply(inverse(sk_c7), sk_c7)),
% 0.62/0.79 inference(symmetry,[status(thm)],[56])).
% 0.62/0.79 tff(78,plain,
% 0.62/0.79 (identity = multiply(sk_c10, sk_c7)),
% 0.62/0.79 inference(transitivity,[status(thm)],[77, 76])).
% 0.62/0.79 tff(79,plain,
% 0.62/0.79 (multiply(identity, sk_c4) = multiply(multiply(sk_c10, sk_c7), sk_c4)),
% 0.62/0.79 inference(monotonicity,[status(thm)],[78])).
% 0.62/0.79 tff(80,plain,
% 0.62/0.79 (multiply(multiply(sk_c10, sk_c7), sk_c4) = multiply(identity, sk_c4)),
% 0.62/0.79 inference(symmetry,[status(thm)],[79])).
% 0.62/0.79 tff(81,plain,
% 0.62/0.79 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c10, sk_c7), sk_c4) = multiply(sk_c10, multiply(sk_c7, sk_c4)))),
% 0.62/0.79 inference(quant_inst,[status(thm)],[])).
% 0.62/0.79 tff(82,plain,
% 0.62/0.79 (multiply(multiply(sk_c10, sk_c7), sk_c4) = multiply(sk_c10, multiply(sk_c7, sk_c4))),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[81, 52])).
% 0.62/0.79 tff(83,plain,
% 0.62/0.79 (multiply(sk_c10, multiply(sk_c7, sk_c4)) = multiply(multiply(sk_c10, sk_c7), sk_c4)),
% 0.62/0.79 inference(symmetry,[status(thm)],[82])).
% 0.62/0.79 tff(84,plain,
% 0.62/0.79 (sk_c10 = inverse(sk_c4)),
% 0.62/0.79 inference(symmetry,[status(thm)],[73])).
% 0.62/0.79 tff(85,plain,
% 0.62/0.79 (multiply(sk_c10, sk_c10) = multiply(inverse(sk_c4), sk_c10)),
% 0.62/0.79 inference(monotonicity,[status(thm)],[84])).
% 0.62/0.79 tff(86,plain,
% 0.62/0.79 (multiply(inverse(sk_c4), sk_c10) = multiply(sk_c10, sk_c10)),
% 0.62/0.79 inference(symmetry,[status(thm)],[85])).
% 0.62/0.79 tff(87,plain,
% 0.62/0.79 (sk_c10 = sk_c9),
% 0.62/0.79 inference(transitivity,[status(thm)],[72, 62, 54, 45, 41])).
% 0.62/0.79 tff(88,plain,
% 0.62/0.79 (multiply(sk_c4, sk_c10) = multiply(sk_c4, sk_c9)),
% 0.62/0.79 inference(monotonicity,[status(thm)],[87])).
% 0.62/0.79 tff(89,plain,
% 0.62/0.79 (multiply(sk_c4, sk_c9) = multiply(sk_c4, sk_c10)),
% 0.62/0.79 inference(symmetry,[status(thm)],[88])).
% 0.62/0.79 tff(90,assumption,(multiply(sk_c4, sk_c9) = sk_c10), introduced(assumption)).
% 0.62/0.79 tff(91,plain,
% 0.62/0.79 (sk_c10 = multiply(sk_c4, sk_c9)),
% 0.62/0.79 inference(symmetry,[status(thm)],[90])).
% 0.62/0.79 tff(92,plain,
% 0.62/0.79 (sk_c10 = multiply(sk_c4, sk_c10)),
% 0.62/0.79 inference(transitivity,[status(thm)],[91, 89])).
% 0.62/0.79 tff(93,plain,
% 0.62/0.79 (multiply(inverse(sk_c4), sk_c10) = multiply(sk_c10, multiply(sk_c4, sk_c10))),
% 0.62/0.79 inference(monotonicity,[status(thm)],[73, 92])).
% 0.62/0.79 tff(94,plain,
% 0.62/0.79 (multiply(sk_c10, multiply(sk_c4, sk_c10)) = multiply(inverse(sk_c4), sk_c10)),
% 0.62/0.79 inference(symmetry,[status(thm)],[93])).
% 0.62/0.79 tff(95,plain,
% 0.62/0.79 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c10, sk_c4), sk_c10) = multiply(sk_c10, multiply(sk_c4, sk_c10)))),
% 0.62/0.79 inference(quant_inst,[status(thm)],[])).
% 0.62/0.79 tff(96,plain,
% 0.62/0.79 (multiply(multiply(sk_c10, sk_c4), sk_c10) = multiply(sk_c10, multiply(sk_c4, sk_c10))),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[95, 52])).
% 0.62/0.79 tff(97,plain,
% 0.62/0.79 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c4), sk_c4) = identity)),
% 0.62/0.79 inference(quant_inst,[status(thm)],[])).
% 0.62/0.79 tff(98,plain,
% 0.62/0.79 (multiply(inverse(sk_c4), sk_c4) = identity),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[97, 7])).
% 0.62/0.79 tff(99,plain,
% 0.62/0.79 (multiply(sk_c10, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.62/0.79 inference(monotonicity,[status(thm)],[84])).
% 0.62/0.79 tff(100,plain,
% 0.62/0.79 (multiply(sk_c10, sk_c4) = multiply(sk_c10, sk_c7)),
% 0.62/0.79 inference(transitivity,[status(thm)],[99, 98, 77, 76])).
% 0.62/0.79 tff(101,plain,
% 0.62/0.79 (multiply(multiply(sk_c10, sk_c4), sk_c10) = multiply(multiply(sk_c10, sk_c7), sk_c10)),
% 0.62/0.79 inference(monotonicity,[status(thm)],[100])).
% 0.62/0.79 tff(102,plain,
% 0.62/0.79 (multiply(multiply(sk_c10, sk_c7), sk_c10) = multiply(multiply(sk_c10, sk_c4), sk_c10)),
% 0.62/0.79 inference(symmetry,[status(thm)],[101])).
% 0.62/0.79 tff(103,plain,
% 0.62/0.79 (sk_c10 = multiply(sk_c10, sk_c10)),
% 0.62/0.79 inference(transitivity,[status(thm)],[72, 62, 102, 96, 94, 86])).
% 0.62/0.79 tff(104,plain,
% 0.62/0.79 (multiply(sk_c10, multiply(sk_c7, sk_c4)) = multiply(multiply(sk_c10, sk_c10), multiply(sk_c7, sk_c4))),
% 0.62/0.79 inference(monotonicity,[status(thm)],[103])).
% 0.62/0.79 tff(105,plain,
% 0.62/0.79 (multiply(multiply(sk_c10, sk_c10), multiply(sk_c7, sk_c4)) = multiply(sk_c10, multiply(sk_c7, sk_c4))),
% 0.62/0.79 inference(symmetry,[status(thm)],[104])).
% 0.62/0.79 tff(106,plain,
% 0.62/0.79 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c10, sk_c10), multiply(sk_c7, sk_c4)) = multiply(sk_c10, multiply(sk_c10, multiply(sk_c7, sk_c4))))),
% 0.62/0.79 inference(quant_inst,[status(thm)],[])).
% 0.62/0.79 tff(107,plain,
% 0.62/0.79 (multiply(multiply(sk_c10, sk_c10), multiply(sk_c7, sk_c4)) = multiply(sk_c10, multiply(sk_c10, multiply(sk_c7, sk_c4)))),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[106, 52])).
% 0.62/0.79 tff(108,plain,
% 0.62/0.79 (multiply(sk_c10, multiply(sk_c10, multiply(sk_c7, sk_c4))) = multiply(multiply(sk_c10, sk_c10), multiply(sk_c7, sk_c4))),
% 0.62/0.79 inference(symmetry,[status(thm)],[107])).
% 0.62/0.79 tff(109,plain,
% 0.62/0.79 (multiply(sk_c10, multiply(sk_c7, sk_c4)) = sk_c4),
% 0.62/0.79 inference(transitivity,[status(thm)],[83, 80, 75])).
% 0.62/0.79 tff(110,plain,
% 0.62/0.79 (multiply(sk_c10, multiply(sk_c10, multiply(sk_c7, sk_c4))) = multiply(inverse(sk_c4), sk_c4)),
% 0.62/0.79 inference(monotonicity,[status(thm)],[84, 109])).
% 0.62/0.79 tff(111,plain,
% 0.62/0.79 (multiply(inverse(sk_c4), sk_c4) = multiply(sk_c10, multiply(sk_c10, multiply(sk_c7, sk_c4)))),
% 0.62/0.79 inference(symmetry,[status(thm)],[110])).
% 0.62/0.79 tff(112,plain,
% 0.62/0.79 (identity = multiply(inverse(sk_c4), sk_c4)),
% 0.62/0.79 inference(symmetry,[status(thm)],[98])).
% 0.62/0.79 tff(113,plain,
% 0.62/0.79 (multiply(inverse(sk_c10), sk_c10) = multiply(inverse(sk_c10), multiply(sk_c10, sk_c10))),
% 0.62/0.79 inference(monotonicity,[status(thm)],[103])).
% 0.62/0.79 tff(114,plain,
% 0.62/0.79 (multiply(inverse(sk_c10), multiply(sk_c10, sk_c10)) = multiply(inverse(sk_c10), sk_c10)),
% 0.62/0.79 inference(symmetry,[status(thm)],[113])).
% 0.62/0.79 tff(115,plain,
% 0.62/0.79 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(inverse(sk_c10), sk_c10), sk_c10) = multiply(inverse(sk_c10), multiply(sk_c10, sk_c10)))),
% 0.62/0.79 inference(quant_inst,[status(thm)],[])).
% 0.62/0.79 tff(116,plain,
% 0.62/0.79 (multiply(multiply(inverse(sk_c10), sk_c10), sk_c10) = multiply(inverse(sk_c10), multiply(sk_c10, sk_c10))),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[115, 52])).
% 0.62/0.79 tff(117,plain,
% 0.62/0.79 (multiply(inverse(sk_c10), sk_c10) = multiply(sk_c10, sk_c7)),
% 0.62/0.79 inference(transitivity,[status(thm)],[9, 77, 76])).
% 0.62/0.79 tff(118,plain,
% 0.62/0.79 (multiply(multiply(inverse(sk_c10), sk_c10), sk_c10) = multiply(multiply(sk_c10, sk_c7), sk_c10)),
% 0.62/0.79 inference(monotonicity,[status(thm)],[117])).
% 0.62/0.79 tff(119,plain,
% 0.62/0.79 (multiply(multiply(sk_c10, sk_c7), sk_c10) = multiply(multiply(inverse(sk_c10), sk_c10), sk_c10)),
% 0.62/0.79 inference(symmetry,[status(thm)],[118])).
% 0.62/0.79 tff(120,plain,
% 0.62/0.79 (sk_c10 = sk_c4),
% 0.62/0.79 inference(transitivity,[status(thm)],[72, 62, 119, 116, 114, 9, 112, 111, 108, 105, 83, 80, 75])).
% 0.62/0.79 tff(121,plain,
% 0.62/0.79 (inverse(sk_c10) = inverse(sk_c4)),
% 0.62/0.79 inference(monotonicity,[status(thm)],[120])).
% 0.62/0.79 tff(122,plain,
% 0.62/0.79 (inverse(sk_c10) = sk_c9),
% 0.62/0.79 inference(transitivity,[status(thm)],[121, 73, 72, 62, 54, 45, 41])).
% 0.62/0.79 tff(123,plain,
% 0.62/0.79 ($false),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[20, 122])).
% 0.62/0.79 tff(124,plain,((inverse(sk_c10) = sk_c9) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c4) = sk_c10)) | (~(inverse(sk_c7) = sk_c10)) | (~(multiply(sk_c4, sk_c9) = sk_c10)) | (~(multiply(sk_c7, sk_c10) = sk_c8))), inference(lemma,lemma(discharge,[]))).
% 0.62/0.79 tff(125,plain,
% 0.62/0.79 ($false),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[124, 40, 20, 36, 32, 28, 24])).
% 0.62/0.79 tff(126,plain,(inverse(sk_c10) = sk_c9), inference(lemma,lemma(discharge,[]))).
% 0.62/0.79 tff(127,plain,
% 0.62/0.79 (multiply(sk_c10, inverse(sk_c10)) = multiply(sk_c10, sk_c9)),
% 0.62/0.79 inference(monotonicity,[status(thm)],[126])).
% 0.62/0.79 tff(128,plain,
% 0.62/0.79 (multiply(sk_c10, inverse(sk_c10)) = multiply(inverse(sk_c10), sk_c10)),
% 0.62/0.79 inference(transitivity,[status(thm)],[127, 19, 12, 10])).
% 0.62/0.79 tff(129,plain,
% 0.62/0.79 ((multiply(sk_c10, inverse(sk_c10)) = sk_c9) <=> (multiply(inverse(sk_c10), sk_c10) = sk_c9)),
% 0.62/0.79 inference(monotonicity,[status(thm)],[128])).
% 0.62/0.79 tff(130,plain,
% 0.62/0.79 ((~(multiply(sk_c10, inverse(sk_c10)) = sk_c9)) <=> (~(multiply(inverse(sk_c10), sk_c10) = sk_c9))),
% 0.62/0.79 inference(monotonicity,[status(thm)],[129])).
% 0.62/0.79 tff(131,plain,
% 0.62/0.79 (((multiply(sk_c10, sk_c3) = sk_c9) | (multiply(sk_c10, sk_c8) = sk_c9)) <=> ((multiply(sk_c10, sk_c3) = sk_c9) | (multiply(sk_c10, sk_c8) = sk_c9))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(132,axiom,((multiply(sk_c10, sk_c3) = sk_c9) | (multiply(sk_c10, sk_c8) = sk_c9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_38')).
% 0.62/0.79 tff(133,plain,
% 0.62/0.79 ((multiply(sk_c10, sk_c3) = sk_c9) | (multiply(sk_c10, sk_c8) = sk_c9)),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.62/0.79 tff(134,plain,
% 0.62/0.79 (multiply(sk_c10, sk_c3) = sk_c9),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[133, 13])).
% 0.62/0.79 tff(135,plain,
% 0.62/0.79 (((multiply(sk_c10, sk_c8) = sk_c9) | (multiply(sk_c2, sk_c10) = sk_c3)) <=> ((multiply(sk_c10, sk_c8) = sk_c9) | (multiply(sk_c2, sk_c10) = sk_c3))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(136,plain,
% 0.62/0.79 (((multiply(sk_c2, sk_c10) = sk_c3) | (multiply(sk_c10, sk_c8) = sk_c9)) <=> ((multiply(sk_c10, sk_c8) = sk_c9) | (multiply(sk_c2, sk_c10) = sk_c3))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(137,axiom,((multiply(sk_c2, sk_c10) = sk_c3) | (multiply(sk_c10, sk_c8) = sk_c9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_46')).
% 0.62/0.79 tff(138,plain,
% 0.62/0.79 ((multiply(sk_c10, sk_c8) = sk_c9) | (multiply(sk_c2, sk_c10) = sk_c3)),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.62/0.79 tff(139,plain,
% 0.62/0.79 ((multiply(sk_c10, sk_c8) = sk_c9) | (multiply(sk_c2, sk_c10) = sk_c3)),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[138, 135])).
% 0.62/0.79 tff(140,plain,
% 0.62/0.79 (multiply(sk_c2, sk_c10) = sk_c3),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[139, 13])).
% 0.62/0.79 tff(141,plain,
% 0.62/0.79 (multiply(sk_c10, multiply(sk_c2, sk_c10)) = multiply(sk_c10, sk_c3)),
% 0.62/0.79 inference(monotonicity,[status(thm)],[140])).
% 0.62/0.79 tff(142,plain,
% 0.62/0.79 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c10, sk_c2), sk_c10) = multiply(sk_c10, multiply(sk_c2, sk_c10)))),
% 0.62/0.79 inference(quant_inst,[status(thm)],[])).
% 0.62/0.79 tff(143,plain,
% 0.62/0.79 (multiply(multiply(sk_c10, sk_c2), sk_c10) = multiply(sk_c10, multiply(sk_c2, sk_c10))),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[142, 52])).
% 0.62/0.79 tff(144,assumption,(~(inverse(sk_c2) = sk_c10)), introduced(assumption)).
% 0.62/0.79 tff(145,plain,
% 0.62/0.79 (((inverse(sk_c2) = sk_c10) | (multiply(sk_c10, sk_c8) = sk_c9)) <=> ((inverse(sk_c2) = sk_c10) | (multiply(sk_c10, sk_c8) = sk_c9))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(146,axiom,((inverse(sk_c2) = sk_c10) | (multiply(sk_c10, sk_c8) = sk_c9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_54')).
% 0.62/0.79 tff(147,plain,
% 0.62/0.79 ((inverse(sk_c2) = sk_c10) | (multiply(sk_c10, sk_c8) = sk_c9)),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.62/0.79 tff(148,plain,
% 0.62/0.79 (multiply(sk_c10, sk_c8) = sk_c9),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[147, 144])).
% 0.62/0.79 tff(149,plain,
% 0.62/0.79 (((inverse(sk_c2) = sk_c10) | (multiply(sk_c7, sk_c10) = sk_c8)) <=> ((inverse(sk_c2) = sk_c10) | (multiply(sk_c7, sk_c10) = sk_c8))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(150,axiom,((inverse(sk_c2) = sk_c10) | (multiply(sk_c7, sk_c10) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_55')).
% 0.62/0.79 tff(151,plain,
% 0.62/0.79 ((inverse(sk_c2) = sk_c10) | (multiply(sk_c7, sk_c10) = sk_c8)),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.62/0.79 tff(152,plain,
% 0.62/0.79 (multiply(sk_c7, sk_c10) = sk_c8),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[151, 144])).
% 0.62/0.79 tff(153,plain,
% 0.62/0.79 (sk_c8 = multiply(sk_c7, sk_c10)),
% 0.62/0.79 inference(symmetry,[status(thm)],[152])).
% 0.62/0.79 tff(154,plain,
% 0.62/0.79 (multiply(sk_c10, sk_c8) = multiply(sk_c10, multiply(sk_c7, sk_c10))),
% 0.62/0.79 inference(monotonicity,[status(thm)],[153])).
% 0.62/0.79 tff(155,plain,
% 0.62/0.79 (multiply(sk_c10, multiply(sk_c7, sk_c10)) = multiply(sk_c10, sk_c8)),
% 0.62/0.79 inference(symmetry,[status(thm)],[154])).
% 0.62/0.79 tff(156,plain,
% 0.62/0.79 (((inverse(sk_c2) = sk_c10) | (inverse(sk_c7) = sk_c10)) <=> ((inverse(sk_c2) = sk_c10) | (inverse(sk_c7) = sk_c10))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(157,axiom,((inverse(sk_c2) = sk_c10) | (inverse(sk_c7) = sk_c10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_56')).
% 0.62/0.79 tff(158,plain,
% 0.62/0.79 ((inverse(sk_c2) = sk_c10) | (inverse(sk_c7) = sk_c10)),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.62/0.79 tff(159,plain,
% 0.62/0.79 (inverse(sk_c7) = sk_c10),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[158, 144])).
% 0.62/0.79 tff(160,plain,
% 0.62/0.79 (sk_c10 = inverse(sk_c7)),
% 0.62/0.79 inference(symmetry,[status(thm)],[159])).
% 0.62/0.79 tff(161,plain,
% 0.62/0.79 (multiply(sk_c10, sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.62/0.79 inference(monotonicity,[status(thm)],[160])).
% 0.62/0.79 tff(162,plain,
% 0.62/0.79 (multiply(sk_c10, sk_c7) = identity),
% 0.62/0.79 inference(transitivity,[status(thm)],[161, 56])).
% 0.62/0.79 tff(163,plain,
% 0.62/0.79 (multiply(multiply(sk_c10, sk_c7), sk_c10) = multiply(identity, sk_c10)),
% 0.62/0.79 inference(monotonicity,[status(thm)],[162])).
% 0.62/0.79 tff(164,plain,
% 0.62/0.79 (multiply(identity, sk_c10) = multiply(multiply(sk_c10, sk_c7), sk_c10)),
% 0.62/0.79 inference(symmetry,[status(thm)],[163])).
% 0.62/0.79 tff(165,plain,
% 0.62/0.79 (sk_c10 = sk_c9),
% 0.62/0.79 inference(transitivity,[status(thm)],[72, 164, 54, 155, 148])).
% 0.62/0.79 tff(166,plain,
% 0.62/0.79 (multiply(sk_c10, multiply(sk_c7, sk_c10)) = multiply(multiply(sk_c10, sk_c7), sk_c10)),
% 0.62/0.79 inference(symmetry,[status(thm)],[54])).
% 0.62/0.79 tff(167,plain,
% 0.62/0.79 (sk_c9 = multiply(sk_c10, sk_c8)),
% 0.62/0.79 inference(symmetry,[status(thm)],[148])).
% 0.62/0.79 tff(168,plain,
% 0.62/0.79 (sk_c9 = sk_c10),
% 0.62/0.79 inference(transitivity,[status(thm)],[167, 154, 166, 163, 71])).
% 0.62/0.79 tff(169,plain,
% 0.62/0.79 (inverse(sk_c9) = inverse(sk_c10)),
% 0.62/0.79 inference(monotonicity,[status(thm)],[168])).
% 0.62/0.79 tff(170,plain,
% 0.62/0.79 ((inverse(sk_c9) = sk_c10) <=> (inverse(sk_c10) = sk_c9)),
% 0.62/0.79 inference(monotonicity,[status(thm)],[169, 165])).
% 0.62/0.79 tff(171,plain,
% 0.62/0.79 ((inverse(sk_c10) = sk_c9) <=> (inverse(sk_c9) = sk_c10)),
% 0.62/0.79 inference(symmetry,[status(thm)],[170])).
% 0.62/0.79 tff(172,plain,
% 0.62/0.79 (((inverse(sk_c2) = sk_c10) | (multiply(sk_c4, sk_c9) = sk_c10)) <=> ((inverse(sk_c2) = sk_c10) | (multiply(sk_c4, sk_c9) = sk_c10))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(173,axiom,((inverse(sk_c2) = sk_c10) | (multiply(sk_c4, sk_c9) = sk_c10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_50')).
% 0.62/0.79 tff(174,plain,
% 0.62/0.79 ((inverse(sk_c2) = sk_c10) | (multiply(sk_c4, sk_c9) = sk_c10)),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.62/0.79 tff(175,plain,
% 0.62/0.79 (multiply(sk_c4, sk_c9) = sk_c10),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[174, 144])).
% 0.62/0.79 tff(176,plain,
% 0.62/0.79 (((inverse(sk_c2) = sk_c10) | (inverse(sk_c4) = sk_c10)) <=> ((inverse(sk_c2) = sk_c10) | (inverse(sk_c4) = sk_c10))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(177,axiom,((inverse(sk_c2) = sk_c10) | (inverse(sk_c4) = sk_c10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_49')).
% 0.62/0.79 tff(178,plain,
% 0.62/0.79 ((inverse(sk_c2) = sk_c10) | (inverse(sk_c4) = sk_c10)),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.62/0.79 tff(179,plain,
% 0.62/0.79 (inverse(sk_c4) = sk_c10),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[178, 144])).
% 0.62/0.79 tff(180,plain,
% 0.62/0.79 (inverse(sk_c10) = sk_c9),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[124, 148, 179, 159, 175, 152])).
% 0.62/0.79 tff(181,plain,
% 0.62/0.79 (inverse(sk_c9) = sk_c10),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[180, 171])).
% 0.62/0.79 tff(182,plain,
% 0.62/0.79 (inverse(sk_c4) = sk_c9),
% 0.62/0.79 inference(transitivity,[status(thm)],[179, 72, 164, 54, 155, 148])).
% 0.62/0.79 tff(183,plain,
% 0.62/0.79 (multiply(sk_c4, sk_c10) = multiply(sk_c4, sk_c9)),
% 0.62/0.79 inference(monotonicity,[status(thm)],[165])).
% 0.62/0.79 tff(184,plain,
% 0.62/0.79 (multiply(sk_c4, inverse(sk_c4)) = multiply(sk_c4, sk_c10)),
% 0.62/0.79 inference(monotonicity,[status(thm)],[179])).
% 0.62/0.79 tff(185,plain,
% 0.62/0.79 (multiply(sk_c4, inverse(sk_c4)) = sk_c9),
% 0.62/0.79 inference(transitivity,[status(thm)],[184, 183, 175, 72, 164, 54, 155, 148])).
% 0.62/0.79 tff(186,plain,
% 0.62/0.79 (multiply(inverse(sk_c7), sk_c7) = multiply(sk_c10, sk_c7)),
% 0.62/0.79 inference(symmetry,[status(thm)],[161])).
% 0.62/0.79 tff(187,plain,
% 0.62/0.79 (sk_c10 = inverse(sk_c4)),
% 0.62/0.79 inference(symmetry,[status(thm)],[179])).
% 0.62/0.79 tff(188,plain,
% 0.62/0.79 (multiply(sk_c10, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.62/0.79 inference(monotonicity,[status(thm)],[187])).
% 0.62/0.79 tff(189,plain,
% 0.62/0.79 (multiply(sk_c10, sk_c4) = multiply(sk_c10, sk_c7)),
% 0.62/0.79 inference(transitivity,[status(thm)],[188, 98, 77, 186])).
% 0.62/0.79 tff(190,plain,
% 0.62/0.79 (multiply(multiply(sk_c10, sk_c4), sk_c10) = multiply(multiply(sk_c10, sk_c7), sk_c10)),
% 0.62/0.79 inference(monotonicity,[status(thm)],[189])).
% 0.62/0.79 tff(191,plain,
% 0.62/0.79 (multiply(sk_c10, multiply(sk_c4, sk_c10)) = multiply(multiply(sk_c10, sk_c4), sk_c10)),
% 0.62/0.79 inference(symmetry,[status(thm)],[96])).
% 0.62/0.79 tff(192,plain,
% 0.62/0.79 (multiply(sk_c4, sk_c9) = multiply(sk_c4, sk_c10)),
% 0.62/0.79 inference(symmetry,[status(thm)],[183])).
% 0.62/0.79 tff(193,plain,
% 0.62/0.79 (sk_c10 = multiply(sk_c4, sk_c9)),
% 0.62/0.79 inference(symmetry,[status(thm)],[175])).
% 0.62/0.79 tff(194,plain,
% 0.62/0.79 (sk_c10 = multiply(sk_c4, sk_c10)),
% 0.62/0.79 inference(transitivity,[status(thm)],[193, 192])).
% 0.62/0.79 tff(195,plain,
% 0.62/0.79 (multiply(inverse(sk_c4), sk_c10) = multiply(sk_c10, multiply(sk_c4, sk_c10))),
% 0.62/0.79 inference(monotonicity,[status(thm)],[179, 194])).
% 0.62/0.79 tff(196,plain,
% 0.62/0.79 (multiply(inverse(sk_c4), sk_c10) = sk_c9),
% 0.62/0.79 inference(transitivity,[status(thm)],[195, 191, 190, 54, 155, 148])).
% 0.62/0.79 tff(197,plain,
% 0.62/0.79 (multiply(sk_c10, multiply(sk_c4, sk_c10)) = sk_c9),
% 0.62/0.79 inference(transitivity,[status(thm)],[191, 190, 54, 155, 148])).
% 0.62/0.79 tff(198,plain,
% 0.62/0.79 (^[X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : refl(((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9))))),
% 0.62/0.80 inference(bind,[status(th)],[])).
% 0.62/0.80 tff(199,plain,
% 0.62/0.80 (![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9))) <=> ![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))),
% 0.62/0.80 inference(quant_intro,[status(thm)],[198])).
% 0.62/0.80 tff(200,plain,
% 0.62/0.80 (![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9))) <=> ![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(201,plain,
% 0.62/0.80 (^[X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : rewrite(((~(multiply(X4, sk_c9) = sk_c10)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9))))),
% 0.62/0.80 inference(bind,[status(th)],[])).
% 0.62/0.80 tff(202,plain,
% 0.62/0.80 (![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(multiply(X4, sk_c9) = sk_c10)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9))) <=> ![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))),
% 0.62/0.80 inference(quant_intro,[status(thm)],[201])).
% 0.62/0.80 tff(203,plain,
% 0.62/0.80 (![X6: $i, X4: $i, X3: $i, X2: $i, X7: $i, X5: $i, X8: $i, X1: $i] : ((~(multiply(X4, sk_c9) = sk_c10)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9))) <=> ![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(multiply(X4, sk_c9) = sk_c10)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))),
% 0.62/0.80 inference(elim_unused_vars,[status(thm)],[])).
% 0.62/0.80 tff(204,plain,
% 0.62/0.80 (![X6: $i, X4: $i, X3: $i, X2: $i, X7: $i, X5: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X8, sk_c10) = X7)) | (~(multiply(sk_c10, X7) = sk_c9)) | (~(multiply(X2, sk_c10) = sk_c9)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))) <=> ![X6: $i, X4: $i, X3: $i, X2: $i, X7: $i, X5: $i, X8: $i, X1: $i] : ((~(multiply(X4, sk_c9) = sk_c10)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))),
% 0.62/0.80 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.62/0.80 tff(205,plain,
% 0.62/0.80 (![X6: $i, X4: $i, X3: $i, X2: $i, X7: $i, X5: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X8, sk_c10) = X7)) | (~(multiply(sk_c10, X7) = sk_c9)) | (~(multiply(X2, sk_c10) = sk_c9)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))) <=> ![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(multiply(X4, sk_c9) = sk_c10)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))),
% 0.62/0.80 inference(transitivity,[status(thm)],[204, 203])).
% 0.62/0.80 tff(206,plain,
% 0.62/0.80 (![X6: $i, X4: $i, X3: $i, X2: $i, X7: $i, X5: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X8, sk_c10) = X7)) | (~(multiply(sk_c10, X7) = sk_c9)) | (~(multiply(X2, sk_c10) = sk_c9)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))) <=> ![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))),
% 0.62/0.80 inference(transitivity,[status(thm)],[205, 202])).
% 0.62/0.80 tff(207,plain,
% 0.62/0.80 (^[X6: $i, X4: $i, X3: $i, X2: $i, X7: $i, X5: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(X4, sk_c9) = sk_c10))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(X4, sk_c9) = sk_c10)))), (((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X4) = sk_c9))) <=> (((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X4) = sk_c9))))), rewrite((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X4) = sk_c9))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)))), (((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X4) = sk_c9))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))))), ((((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X4) = sk_c9))) | (~(multiply(sk_c10, X5) = sk_c9))) <=> (((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(multiply(sk_c10, X5) = sk_c9))))), rewrite((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(multiply(sk_c10, X5) = sk_c9))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)))), ((((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X4) = sk_c9))) | (~(multiply(sk_c10, X5) = sk_c9))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))))), (((((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X4) = sk_c9))) | (~(multiply(sk_c10, X5) = sk_c9))) | (~(multiply(X6, sk_c10) = X5))) <=> (((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(multiply(X6, sk_c10) = X5))))), rewrite((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(multiply(X6, sk_c10) = X5))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)))), (((((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X4) = sk_c9))) | (~(multiply(sk_c10, X5) = sk_c9))) | (~(multiply(X6, sk_c10) = X5))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))))), ((((((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X4) = sk_c9))) | (~(multiply(sk_c10, X5) = sk_c9))) | (~(multiply(X6, sk_c10) = X5))) | (~(inverse(X6) = sk_c10))) <=> (((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X6) = sk_c10))))), rewrite((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X6) = sk_c10))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)))), ((((((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X4) = sk_c9))) | (~(multiply(sk_c10, X5) = sk_c9))) | (~(multiply(X6, sk_c10) = X5))) | (~(inverse(X6) = sk_c10))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))))), (((((((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X4) = sk_c9))) | (~(multiply(sk_c10, X5) = sk_c9))) | (~(multiply(X6, sk_c10) = X5))) | (~(inverse(X6) = sk_c10))) | (~(inverse(X1) = sk_c10))) <=> (((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X1) = sk_c10))))), rewrite((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X1) = sk_c10))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)))), (((((((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X4) = sk_c9))) | (~(multiply(sk_c10, X5) = sk_c9))) | (~(multiply(X6, sk_c10) = X5))) | (~(inverse(X6) = sk_c10))) | (~(inverse(X1) = sk_c10))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))))), ((((((((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X4) = sk_c9))) | (~(multiply(sk_c10, X5) = sk_c9))) | (~(multiply(X6, sk_c10) = X5))) | (~(inverse(X6) = sk_c10))) | (~(inverse(X1) = sk_c10))) | (~(multiply(X1, sk_c9) = sk_c10))) <=> (((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(multiply(X1, sk_c9) = sk_c10))))), rewrite((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(multiply(X1, sk_c9) = sk_c10))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)))), ((((((((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X4) = sk_c9))) | (~(multiply(sk_c10, X5) = sk_c9))) | (~(multiply(X6, sk_c10) = X5))) | (~(inverse(X6) = sk_c10))) | (~(inverse(X1) = sk_c10))) | (~(multiply(X1, sk_c9) = sk_c10))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))))), (((((((((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X4) = sk_c9))) | (~(multiply(sk_c10, X5) = sk_c9))) | (~(multiply(X6, sk_c10) = X5))) | (~(inverse(X6) = sk_c10))) | (~(inverse(X1) = sk_c10))) | (~(multiply(X1, sk_c9) = sk_c10))) | (~(multiply(X3, X2) = sk_c9))) <=> (((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(multiply(X3, X2) = sk_c9))))), rewrite((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(multiply(X3, X2) = sk_c9))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(X3, X2) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)))), (((((((((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X4) = sk_c9))) | (~(multiply(sk_c10, X5) = sk_c9))) | (~(multiply(X6, sk_c10) = X5))) | (~(inverse(X6) = sk_c10))) | (~(inverse(X1) = sk_c10))) | (~(multiply(X1, sk_c9) = sk_c10))) | (~(multiply(X3, X2) = sk_c9))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(X3, X2) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))))), ((((((((((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X4) = sk_c9))) | (~(multiply(sk_c10, X5) = sk_c9))) | (~(multiply(X6, sk_c10) = X5))) | (~(inverse(X6) = sk_c10))) | (~(inverse(X1) = sk_c10))) | (~(multiply(X1, sk_c9) = sk_c10))) | (~(multiply(X3, X2) = sk_c9))) | (~(inverse(X3) = X2))) <=> (((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(X3, X2) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X3) = X2))))), rewrite((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(X3, X2) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X3) = X2))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)))), ((((((((((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X4) = sk_c9))) | (~(multiply(sk_c10, X5) = sk_c9))) | (~(multiply(X6, sk_c10) = X5))) | (~(inverse(X6) = sk_c10))) | (~(inverse(X1) = sk_c10))) | (~(multiply(X1, sk_c9) = sk_c10))) | (~(multiply(X3, X2) = sk_c9))) | (~(inverse(X3) = X2))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))))), (((((((((((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X4) = sk_c9))) | (~(multiply(sk_c10, X5) = sk_c9))) | (~(multiply(X6, sk_c10) = X5))) | (~(inverse(X6) = sk_c10))) | (~(inverse(X1) = sk_c10))) | (~(multiply(X1, sk_c9) = sk_c10))) | (~(multiply(X3, X2) = sk_c9))) | (~(inverse(X3) = X2))) | (~(multiply(X2, sk_c10) = sk_c9))) <=> (((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(multiply(X2, sk_c10) = sk_c9))))), rewrite((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(multiply(X2, sk_c10) = sk_c9))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(X2, sk_c10) = sk_c9)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)))), (((((((((((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X4) = sk_c9))) | (~(multiply(sk_c10, X5) = sk_c9))) | (~(multiply(X6, sk_c10) = X5))) | (~(inverse(X6) = sk_c10))) | (~(inverse(X1) = sk_c10))) | (~(multiply(X1, sk_c9) = sk_c10))) | (~(multiply(X3, X2) = sk_c9))) | (~(inverse(X3) = X2))) | (~(multiply(X2, sk_c10) = sk_c9))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(X2, sk_c10) = sk_c9)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))))), ((((((((((((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X4) = sk_c9))) | (~(multiply(sk_c10, X5) = sk_c9))) | (~(multiply(X6, sk_c10) = X5))) | (~(inverse(X6) = sk_c10))) | (~(inverse(X1) = sk_c10))) | (~(multiply(X1, sk_c9) = sk_c10))) | (~(multiply(X3, X2) = sk_c9))) | (~(inverse(X3) = X2))) | (~(multiply(X2, sk_c10) = sk_c9))) | (~(multiply(sk_c10, X7) = sk_c9))) <=> (((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(X2, sk_c10) = sk_c9)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(multiply(sk_c10, X7) = sk_c9))))), rewrite((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(X2, sk_c10) = sk_c9)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(multiply(sk_c10, X7) = sk_c9))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, X7) = sk_c9)) | (~(multiply(X2, sk_c10) = sk_c9)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)))), ((((((((((((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X4) = sk_c9))) | (~(multiply(sk_c10, X5) = sk_c9))) | (~(multiply(X6, sk_c10) = X5))) | (~(inverse(X6) = sk_c10))) | (~(inverse(X1) = sk_c10))) | (~(multiply(X1, sk_c9) = sk_c10))) | (~(multiply(X3, X2) = sk_c9))) | (~(inverse(X3) = X2))) | (~(multiply(X2, sk_c10) = sk_c9))) | (~(multiply(sk_c10, X7) = sk_c9))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, X7) = sk_c9)) | (~(multiply(X2, sk_c10) = sk_c9)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))))), (((((((((((((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X4) = sk_c9))) | (~(multiply(sk_c10, X5) = sk_c9))) | (~(multiply(X6, sk_c10) = X5))) | (~(inverse(X6) = sk_c10))) | (~(inverse(X1) = sk_c10))) | (~(multiply(X1, sk_c9) = sk_c10))) | (~(multiply(X3, X2) = sk_c9))) | (~(inverse(X3) = X2))) | (~(multiply(X2, sk_c10) = sk_c9))) | (~(multiply(sk_c10, X7) = sk_c9))) | (~(multiply(X8, sk_c10) = X7))) <=> (((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, X7) = sk_c9)) | (~(multiply(X2, sk_c10) = sk_c9)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(multiply(X8, sk_c10) = X7))))), rewrite((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, X7) = sk_c9)) | (~(multiply(X2, sk_c10) = sk_c9)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(multiply(X8, sk_c10) = X7))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(X8, sk_c10) = X7)) | (~(multiply(sk_c10, X7) = sk_c9)) | (~(multiply(X2, sk_c10) = sk_c9)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)))), (((((((((((((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X4) = sk_c9))) | (~(multiply(sk_c10, X5) = sk_c9))) | (~(multiply(X6, sk_c10) = X5))) | (~(inverse(X6) = sk_c10))) | (~(inverse(X1) = sk_c10))) | (~(multiply(X1, sk_c9) = sk_c10))) | (~(multiply(X3, X2) = sk_c9))) | (~(inverse(X3) = X2))) | (~(multiply(X2, sk_c10) = sk_c9))) | (~(multiply(sk_c10, X7) = sk_c9))) | (~(multiply(X8, sk_c10) = X7))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(X8, sk_c10) = X7)) | (~(multiply(sk_c10, X7) = sk_c9)) | (~(multiply(X2, sk_c10) = sk_c9)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))))), ((((((((((((((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X4) = sk_c9))) | (~(multiply(sk_c10, X5) = sk_c9))) | (~(multiply(X6, sk_c10) = X5))) | (~(inverse(X6) = sk_c10))) | (~(inverse(X1) = sk_c10))) | (~(multiply(X1, sk_c9) = sk_c10))) | (~(multiply(X3, X2) = sk_c9))) | (~(inverse(X3) = X2))) | (~(multiply(X2, sk_c10) = sk_c9))) | (~(multiply(sk_c10, X7) = sk_c9))) | (~(multiply(X8, sk_c10) = X7))) | (~(inverse(X8) = sk_c10))) <=> (((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(X8, sk_c10) = X7)) | (~(multiply(sk_c10, X7) = sk_c9)) | (~(multiply(X2, sk_c10) = sk_c9)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X8) = sk_c10))))), rewrite((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(X8, sk_c10) = X7)) | (~(multiply(sk_c10, X7) = sk_c9)) | (~(multiply(X2, sk_c10) = sk_c9)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X8) = sk_c10))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X8, sk_c10) = X7)) | (~(multiply(sk_c10, X7) = sk_c9)) | (~(multiply(X2, sk_c10) = sk_c9)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)))), ((((((((((((((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X4) = sk_c9))) | (~(multiply(sk_c10, X5) = sk_c9))) | (~(multiply(X6, sk_c10) = X5))) | (~(inverse(X6) = sk_c10))) | (~(inverse(X1) = sk_c10))) | (~(multiply(X1, sk_c9) = sk_c10))) | (~(multiply(X3, X2) = sk_c9))) | (~(inverse(X3) = X2))) | (~(multiply(X2, sk_c10) = sk_c9))) | (~(multiply(sk_c10, X7) = sk_c9))) | (~(multiply(X8, sk_c10) = X7))) | (~(inverse(X8) = sk_c10))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X8, sk_c10) = X7)) | (~(multiply(sk_c10, X7) = sk_c9)) | (~(multiply(X2, sk_c10) = sk_c9)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)))))),
% 0.62/0.81 inference(bind,[status(th)],[])).
% 0.62/0.81 tff(208,plain,
% 0.62/0.81 (![X6: $i, X4: $i, X3: $i, X2: $i, X7: $i, X5: $i, X8: $i, X1: $i] : (((((((((((((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X4) = sk_c9))) | (~(multiply(sk_c10, X5) = sk_c9))) | (~(multiply(X6, sk_c10) = X5))) | (~(inverse(X6) = sk_c10))) | (~(inverse(X1) = sk_c10))) | (~(multiply(X1, sk_c9) = sk_c10))) | (~(multiply(X3, X2) = sk_c9))) | (~(inverse(X3) = X2))) | (~(multiply(X2, sk_c10) = sk_c9))) | (~(multiply(sk_c10, X7) = sk_c9))) | (~(multiply(X8, sk_c10) = X7))) | (~(inverse(X8) = sk_c10))) <=> ![X6: $i, X4: $i, X3: $i, X2: $i, X7: $i, X5: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X8, sk_c10) = X7)) | (~(multiply(sk_c10, X7) = sk_c9)) | (~(multiply(X2, sk_c10) = sk_c9)) | (~(inverse(X3) = X2)) | (~(multiply(X3, X2) = sk_c9)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(inverse(X6) = sk_c10)) | (~(multiply(X6, sk_c10) = X5)) | (~(multiply(sk_c10, X5) = sk_c9)) | (~(inverse(X4) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)))),
% 0.62/0.81 inference(quant_intro,[status(thm)],[207])).
% 0.62/0.81 tff(209,plain,
% 0.62/0.81 (![X6: $i, X4: $i, X3: $i, X2: $i, X7: $i, X5: $i, X8: $i, X1: $i] : (((((((((((((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X4) = sk_c9))) | (~(multiply(sk_c10, X5) = sk_c9))) | (~(multiply(X6, sk_c10) = X5))) | (~(inverse(X6) = sk_c10))) | (~(inverse(X1) = sk_c10))) | (~(multiply(X1, sk_c9) = sk_c10))) | (~(multiply(X3, X2) = sk_c9))) | (~(inverse(X3) = X2))) | (~(multiply(X2, sk_c10) = sk_c9))) | (~(multiply(sk_c10, X7) = sk_c9))) | (~(multiply(X8, sk_c10) = X7))) | (~(inverse(X8) = sk_c10))) <=> ![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))),
% 0.62/0.81 inference(transitivity,[status(thm)],[208, 206])).
% 0.62/0.81 tff(210,axiom,(![X6: $i, X4: $i, X3: $i, X2: $i, X7: $i, X5: $i, X8: $i, X1: $i] : (((((((((((((((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(X4, sk_c9) = sk_c10))) | (~(inverse(X4) = sk_c9))) | (~(multiply(sk_c10, X5) = sk_c9))) | (~(multiply(X6, sk_c10) = X5))) | (~(inverse(X6) = sk_c10))) | (~(inverse(X1) = sk_c10))) | (~(multiply(X1, sk_c9) = sk_c10))) | (~(multiply(X3, X2) = sk_c9))) | (~(inverse(X3) = X2))) | (~(multiply(X2, sk_c10) = sk_c9))) | (~(multiply(sk_c10, X7) = sk_c9))) | (~(multiply(X8, sk_c10) = X7))) | (~(inverse(X8) = sk_c10)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_57')).
% 0.62/0.81 tff(211,plain,
% 0.62/0.81 (![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.62/0.81 tff(212,plain,
% 0.62/0.81 (![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[211, 200])).
% 0.62/0.81 tff(213,plain,(
% 0.62/0.81 ![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))),
% 0.62/0.81 inference(skolemize,[status(sab)],[212])).
% 0.62/0.81 tff(214,plain,
% 0.62/0.81 (![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[213, 199])).
% 0.62/0.81 tff(215,plain,
% 0.62/0.81 (((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c4) = sk_c10)) | (~(multiply(sk_c4, sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c4, sk_c10)) = sk_c9)) | (~(multiply(inverse(sk_c4), sk_c10) = sk_c9)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c9)) | (~(inverse(sk_c4) = sk_c9)))) <=> ((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c4) = sk_c10)) | (~(multiply(sk_c4, sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c4, sk_c10)) = sk_c9)) | (~(multiply(inverse(sk_c4), sk_c10) = sk_c9)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c9)) | (~(inverse(sk_c4) = sk_c9)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(216,plain,
% 0.62/0.81 (((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c4) = sk_c10)) | (~(multiply(sk_c4, sk_c9) = sk_c10)) | (~(inverse(sk_c4) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c4, sk_c10)) = sk_c9)) | (~(multiply(sk_c4, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c4), sk_c10) = sk_c9)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c9)) | (~(inverse(sk_c4) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c4, sk_c10)) = sk_c9)) | (~(inverse(sk_c4) = sk_c9))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c4) = sk_c10)) | (~(multiply(sk_c4, sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c4, sk_c10)) = sk_c9)) | (~(multiply(inverse(sk_c4), sk_c10) = sk_c9)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c9)) | (~(inverse(sk_c4) = sk_c9)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(217,plain,
% 0.62/0.81 (((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c4) = sk_c10)) | (~(multiply(sk_c4, sk_c9) = sk_c10)) | (~(inverse(sk_c4) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c4, sk_c10)) = sk_c9)) | (~(multiply(sk_c4, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c4), sk_c10) = sk_c9)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c9)) | (~(inverse(sk_c4) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c4, sk_c10)) = sk_c9)) | (~(inverse(sk_c4) = sk_c9)))) <=> ((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c4) = sk_c10)) | (~(multiply(sk_c4, sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c4, sk_c10)) = sk_c9)) | (~(multiply(inverse(sk_c4), sk_c10) = sk_c9)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c9)) | (~(inverse(sk_c4) = sk_c9))))),
% 0.62/0.82 inference(monotonicity,[status(thm)],[216])).
% 0.62/0.82 tff(218,plain,
% 0.62/0.82 (((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c4) = sk_c10)) | (~(multiply(sk_c4, sk_c9) = sk_c10)) | (~(inverse(sk_c4) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c4, sk_c10)) = sk_c9)) | (~(multiply(sk_c4, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c4), sk_c10) = sk_c9)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c9)) | (~(inverse(sk_c4) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c4, sk_c10)) = sk_c9)) | (~(inverse(sk_c4) = sk_c9)))) <=> ((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c4) = sk_c10)) | (~(multiply(sk_c4, sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c4, sk_c10)) = sk_c9)) | (~(multiply(inverse(sk_c4), sk_c10) = sk_c9)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c9)) | (~(inverse(sk_c4) = sk_c9)))),
% 0.62/0.82 inference(transitivity,[status(thm)],[217, 215])).
% 0.62/0.82 tff(219,plain,
% 0.62/0.82 ((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c4) = sk_c10)) | (~(multiply(sk_c4, sk_c9) = sk_c10)) | (~(inverse(sk_c4) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c4, sk_c10)) = sk_c9)) | (~(multiply(sk_c4, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c4), sk_c10) = sk_c9)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c9)) | (~(inverse(sk_c4) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c4, sk_c10)) = sk_c9)) | (~(inverse(sk_c4) = sk_c9)))),
% 0.62/0.82 inference(quant_inst,[status(thm)],[])).
% 0.62/0.82 tff(220,plain,
% 0.62/0.82 ((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c4) = sk_c10)) | (~(multiply(sk_c4, sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c4, sk_c10)) = sk_c9)) | (~(multiply(inverse(sk_c4), sk_c10) = sk_c9)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c9)) | (~(inverse(sk_c4) = sk_c9))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.62/0.82 tff(221,plain,
% 0.62/0.82 ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c4, sk_c10)) = sk_c9)) | (~(multiply(inverse(sk_c4), sk_c10) = sk_c9)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c9)) | (~(inverse(sk_c4) = sk_c9))),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[220, 179, 175, 214])).
% 0.62/0.82 tff(222,plain,
% 0.62/0.82 (~(inverse(sk_c9) = sk_c10)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[221, 180, 197, 196, 185, 182])).
% 0.62/0.82 tff(223,plain,
% 0.62/0.82 ($false),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[222, 181])).
% 0.62/0.82 tff(224,plain,(inverse(sk_c2) = sk_c10), inference(lemma,lemma(discharge,[]))).
% 0.62/0.82 tff(225,plain,
% 0.62/0.82 (sk_c10 = inverse(sk_c2)),
% 0.62/0.82 inference(symmetry,[status(thm)],[224])).
% 0.62/0.82 tff(226,plain,
% 0.62/0.82 (multiply(sk_c10, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.62/0.82 inference(monotonicity,[status(thm)],[225])).
% 0.62/0.82 tff(227,plain,
% 0.62/0.82 (multiply(inverse(sk_c2), sk_c2) = multiply(sk_c10, sk_c2)),
% 0.62/0.82 inference(symmetry,[status(thm)],[226])).
% 0.62/0.82 tff(228,plain,
% 0.62/0.82 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c2), sk_c2) = identity)),
% 0.62/0.82 inference(quant_inst,[status(thm)],[])).
% 0.62/0.82 tff(229,plain,
% 0.62/0.82 (multiply(inverse(sk_c2), sk_c2) = identity),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[228, 7])).
% 0.62/0.82 tff(230,plain,
% 0.62/0.82 (identity = multiply(inverse(sk_c2), sk_c2)),
% 0.62/0.82 inference(symmetry,[status(thm)],[229])).
% 0.62/0.82 tff(231,plain,
% 0.62/0.82 (multiply(sk_c10, sk_c9) = multiply(sk_c10, sk_c2)),
% 0.62/0.82 inference(transitivity,[status(thm)],[19, 12, 230, 227])).
% 0.62/0.82 tff(232,plain,
% 0.62/0.82 (multiply(multiply(sk_c10, sk_c9), sk_c10) = multiply(multiply(sk_c10, sk_c2), sk_c10)),
% 0.62/0.82 inference(monotonicity,[status(thm)],[231])).
% 0.62/0.82 tff(233,plain,
% 0.62/0.82 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c10, sk_c9), sk_c10) = multiply(sk_c10, multiply(sk_c9, sk_c10)))),
% 0.62/0.82 inference(quant_inst,[status(thm)],[])).
% 0.62/0.82 tff(234,plain,
% 0.62/0.82 (multiply(multiply(sk_c10, sk_c9), sk_c10) = multiply(sk_c10, multiply(sk_c9, sk_c10))),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[233, 52])).
% 0.62/0.82 tff(235,plain,
% 0.62/0.82 (multiply(sk_c10, multiply(sk_c9, sk_c10)) = multiply(multiply(sk_c10, sk_c9), sk_c10)),
% 0.62/0.82 inference(symmetry,[status(thm)],[234])).
% 0.62/0.82 tff(236,plain,
% 0.62/0.82 (multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9),
% 0.62/0.82 inference(transitivity,[status(thm)],[235, 232, 143, 141, 134])).
% 0.62/0.82 tff(237,plain,
% 0.62/0.82 (identity = multiply(sk_c10, sk_c2)),
% 0.62/0.82 inference(transitivity,[status(thm)],[230, 227])).
% 0.62/0.82 tff(238,plain,
% 0.62/0.82 (multiply(identity, sk_c10) = multiply(multiply(sk_c10, sk_c2), sk_c10)),
% 0.62/0.82 inference(monotonicity,[status(thm)],[237])).
% 0.62/0.82 tff(239,plain,
% 0.62/0.82 (sk_c10 = sk_c9),
% 0.62/0.82 inference(transitivity,[status(thm)],[72, 238, 143, 141, 134])).
% 0.62/0.82 tff(240,plain,
% 0.62/0.82 (inverse(sk_c2) = sk_c9),
% 0.62/0.82 inference(transitivity,[status(thm)],[224, 72, 238, 143, 141, 134])).
% 0.62/0.82 tff(241,plain,
% 0.62/0.82 (multiply(inverse(sk_c2), sk_c10) = multiply(sk_c9, sk_c9)),
% 0.62/0.82 inference(monotonicity,[status(thm)],[240, 239])).
% 0.62/0.82 tff(242,plain,
% 0.62/0.82 (multiply(sk_c9, sk_c9) = multiply(inverse(sk_c2), sk_c10)),
% 0.62/0.82 inference(symmetry,[status(thm)],[241])).
% 0.62/0.82 tff(243,plain,
% 0.62/0.82 ((multiply(sk_c9, sk_c9) = sk_c10) <=> (multiply(inverse(sk_c2), sk_c10) = sk_c9)),
% 0.62/0.82 inference(monotonicity,[status(thm)],[242, 239])).
% 0.62/0.82 tff(244,plain,
% 0.62/0.82 ((multiply(inverse(sk_c2), sk_c10) = sk_c9) <=> (multiply(sk_c9, sk_c9) = sk_c10)),
% 0.62/0.82 inference(symmetry,[status(thm)],[243])).
% 0.62/0.82 tff(245,plain,
% 0.62/0.82 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c9) = sk_c9)),
% 0.62/0.82 inference(quant_inst,[status(thm)],[])).
% 0.62/0.82 tff(246,plain,
% 0.62/0.82 (multiply(identity, sk_c9) = sk_c9),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[245, 69])).
% 0.62/0.82 tff(247,plain,
% 0.62/0.82 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c1), sk_c1) = identity)),
% 0.62/0.82 inference(quant_inst,[status(thm)],[])).
% 0.62/0.82 tff(248,plain,
% 0.62/0.82 (multiply(inverse(sk_c1), sk_c1) = identity),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[247, 7])).
% 0.62/0.82 tff(249,plain,
% 0.62/0.82 (((inverse(sk_c1) = sk_c9) | (multiply(sk_c10, sk_c8) = sk_c9)) <=> ((inverse(sk_c1) = sk_c9) | (multiply(sk_c10, sk_c8) = sk_c9))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(250,axiom,((inverse(sk_c1) = sk_c9) | (multiply(sk_c10, sk_c8) = sk_c9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_30')).
% 0.62/0.82 tff(251,plain,
% 0.62/0.82 ((inverse(sk_c1) = sk_c9) | (multiply(sk_c10, sk_c8) = sk_c9)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.62/0.82 tff(252,plain,
% 0.62/0.82 (inverse(sk_c1) = sk_c9),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[251, 13])).
% 0.62/0.82 tff(253,plain,
% 0.62/0.82 (sk_c9 = inverse(sk_c1)),
% 0.62/0.82 inference(symmetry,[status(thm)],[252])).
% 0.62/0.82 tff(254,plain,
% 0.62/0.82 (multiply(sk_c9, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.62/0.82 inference(monotonicity,[status(thm)],[253])).
% 0.62/0.82 tff(255,plain,
% 0.62/0.82 (multiply(sk_c9, sk_c1) = identity),
% 0.62/0.82 inference(transitivity,[status(thm)],[254, 248])).
% 0.62/0.82 tff(256,plain,
% 0.62/0.82 (multiply(multiply(sk_c9, sk_c1), sk_c9) = multiply(identity, sk_c9)),
% 0.62/0.82 inference(monotonicity,[status(thm)],[255])).
% 0.62/0.82 tff(257,plain,
% 0.62/0.82 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c9, sk_c1), sk_c9) = multiply(sk_c9, multiply(sk_c1, sk_c9)))),
% 0.62/0.82 inference(quant_inst,[status(thm)],[])).
% 0.62/0.82 tff(258,plain,
% 0.62/0.82 (multiply(multiply(sk_c9, sk_c1), sk_c9) = multiply(sk_c9, multiply(sk_c1, sk_c9))),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[257, 52])).
% 0.62/0.82 tff(259,plain,
% 0.62/0.82 (multiply(sk_c9, multiply(sk_c1, sk_c9)) = multiply(multiply(sk_c9, sk_c1), sk_c9)),
% 0.62/0.82 inference(symmetry,[status(thm)],[258])).
% 0.62/0.82 tff(260,plain,
% 0.62/0.82 (((multiply(sk_c1, sk_c9) = sk_c10) | (multiply(sk_c10, sk_c8) = sk_c9)) <=> ((multiply(sk_c1, sk_c9) = sk_c10) | (multiply(sk_c10, sk_c8) = sk_c9))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(261,axiom,((multiply(sk_c1, sk_c9) = sk_c10) | (multiply(sk_c10, sk_c8) = sk_c9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_22')).
% 0.62/0.82 tff(262,plain,
% 0.62/0.82 ((multiply(sk_c1, sk_c9) = sk_c10) | (multiply(sk_c10, sk_c8) = sk_c9)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.62/0.82 tff(263,plain,
% 0.62/0.82 (multiply(sk_c1, sk_c9) = sk_c10),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[262, 13])).
% 0.62/0.82 tff(264,plain,
% 0.62/0.82 (sk_c10 = multiply(sk_c1, sk_c9)),
% 0.62/0.82 inference(symmetry,[status(thm)],[263])).
% 0.62/0.82 tff(265,plain,
% 0.62/0.82 (multiply(inverse(sk_c10), sk_c10) = multiply(sk_c9, multiply(sk_c1, sk_c9))),
% 0.62/0.82 inference(monotonicity,[status(thm)],[126, 264])).
% 0.62/0.82 tff(266,plain,
% 0.62/0.82 (multiply(multiply(sk_c10, sk_c2), sk_c10) = multiply(identity, sk_c10)),
% 0.62/0.82 inference(symmetry,[status(thm)],[238])).
% 0.62/0.82 tff(267,plain,
% 0.62/0.82 (multiply(sk_c10, multiply(sk_c2, sk_c10)) = multiply(multiply(sk_c10, sk_c2), sk_c10)),
% 0.62/0.82 inference(symmetry,[status(thm)],[143])).
% 0.62/0.82 tff(268,plain,
% 0.62/0.82 (multiply(sk_c10, sk_c3) = multiply(sk_c10, multiply(sk_c2, sk_c10))),
% 0.62/0.82 inference(symmetry,[status(thm)],[141])).
% 0.62/0.82 tff(269,plain,
% 0.62/0.82 (sk_c9 = multiply(sk_c10, sk_c3)),
% 0.62/0.82 inference(symmetry,[status(thm)],[134])).
% 0.62/0.82 tff(270,plain,
% 0.62/0.82 (sk_c9 = sk_c10),
% 0.62/0.82 inference(transitivity,[status(thm)],[269, 268, 267, 266, 71])).
% 0.62/0.82 tff(271,plain,
% 0.62/0.82 (multiply(sk_c9, sk_c9) = multiply(sk_c10, sk_c9)),
% 0.62/0.82 inference(monotonicity,[status(thm)],[270])).
% 0.62/0.82 tff(272,plain,
% 0.62/0.82 (multiply(inverse(sk_c2), sk_c10) = sk_c9),
% 0.62/0.82 inference(transitivity,[status(thm)],[241, 271, 19, 12, 10, 265, 259, 256, 246])).
% 0.62/0.82 tff(273,plain,
% 0.62/0.82 (multiply(sk_c9, sk_c9) = sk_c10),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[272, 244])).
% 0.62/0.82 tff(274,plain,
% 0.62/0.82 (multiply(inverse(sk_c10), sk_c10) = sk_c9),
% 0.62/0.82 inference(transitivity,[status(thm)],[265, 259, 256, 246])).
% 0.62/0.82 tff(275,plain,
% 0.62/0.82 (((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c10) = sk_c9)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c9)) | (~(multiply(sk_c9, sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(sk_c1, sk_c9) = sk_c10)) | (~(inverse(sk_c1) = sk_c9)))) <=> ((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c10) = sk_c9)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c9)) | (~(multiply(sk_c9, sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(sk_c1, sk_c9) = sk_c10)) | (~(inverse(sk_c1) = sk_c9)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(276,plain,
% 0.62/0.82 (((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c9, sk_c9) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(sk_c1, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c10) = sk_c9)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(inverse(sk_c1) = sk_c9))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c10) = sk_c9)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c9)) | (~(multiply(sk_c9, sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(sk_c1, sk_c9) = sk_c10)) | (~(inverse(sk_c1) = sk_c9)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(277,plain,
% 0.62/0.82 (((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c9, sk_c9) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(sk_c1, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c10) = sk_c9)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)))) <=> ((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c10) = sk_c9)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c9)) | (~(multiply(sk_c9, sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(sk_c1, sk_c9) = sk_c10)) | (~(inverse(sk_c1) = sk_c9))))),
% 0.62/0.82 inference(monotonicity,[status(thm)],[276])).
% 0.62/0.82 tff(278,plain,
% 0.62/0.82 (((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c9, sk_c9) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(sk_c1, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c10) = sk_c9)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)))) <=> ((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c10) = sk_c9)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c9)) | (~(multiply(sk_c9, sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(sk_c1, sk_c9) = sk_c10)) | (~(inverse(sk_c1) = sk_c9)))),
% 0.62/0.82 inference(transitivity,[status(thm)],[277, 275])).
% 0.62/0.82 tff(279,plain,
% 0.62/0.82 ((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c9, sk_c9) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(sk_c1, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c10) = sk_c9)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)))),
% 0.62/0.82 inference(quant_inst,[status(thm)],[])).
% 0.62/0.82 tff(280,plain,
% 0.62/0.82 ((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c10) = sk_c9)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c9)) | (~(multiply(sk_c9, sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(sk_c1, sk_c9) = sk_c10)) | (~(inverse(sk_c1) = sk_c9))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.62/0.82 tff(281,plain,
% 0.62/0.82 ((~(multiply(inverse(sk_c10), sk_c10) = sk_c9)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c9)) | (~(multiply(sk_c9, sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9))),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[280, 126, 17, 263, 252, 214])).
% 0.62/0.82 tff(282,plain,
% 0.62/0.82 (~(multiply(sk_c10, inverse(sk_c10)) = sk_c9)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[281, 274, 273, 236])).
% 0.62/0.82 tff(283,plain,
% 0.62/0.82 (~(multiply(inverse(sk_c10), sk_c10) = sk_c9)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[282, 130])).
% 0.62/0.82 tff(284,plain,
% 0.62/0.82 ($false),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[274, 283])).
% 0.62/0.82 tff(285,plain,(multiply(sk_c10, sk_c8) = sk_c9), inference(lemma,lemma(discharge,[]))).
% 0.62/0.82 tff(286,assumption,(~(multiply(sk_c7, sk_c10) = sk_c8)), introduced(assumption)).
% 0.62/0.82 tff(287,plain,
% 0.62/0.82 (((multiply(sk_c10, sk_c3) = sk_c9) | (multiply(sk_c7, sk_c10) = sk_c8)) <=> ((multiply(sk_c10, sk_c3) = sk_c9) | (multiply(sk_c7, sk_c10) = sk_c8))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(288,axiom,((multiply(sk_c10, sk_c3) = sk_c9) | (multiply(sk_c7, sk_c10) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_39')).
% 0.62/0.83 tff(289,plain,
% 0.62/0.83 ((multiply(sk_c10, sk_c3) = sk_c9) | (multiply(sk_c7, sk_c10) = sk_c8)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[288, 287])).
% 0.62/0.83 tff(290,plain,
% 0.62/0.83 (multiply(sk_c10, sk_c3) = sk_c9),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[289, 286])).
% 0.62/0.83 tff(291,plain,
% 0.62/0.83 (((multiply(sk_c2, sk_c10) = sk_c3) | (multiply(sk_c7, sk_c10) = sk_c8)) <=> ((multiply(sk_c2, sk_c10) = sk_c3) | (multiply(sk_c7, sk_c10) = sk_c8))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(292,axiom,((multiply(sk_c2, sk_c10) = sk_c3) | (multiply(sk_c7, sk_c10) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_47')).
% 0.62/0.83 tff(293,plain,
% 0.62/0.83 ((multiply(sk_c2, sk_c10) = sk_c3) | (multiply(sk_c7, sk_c10) = sk_c8)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.62/0.83 tff(294,plain,
% 0.62/0.83 (multiply(sk_c2, sk_c10) = sk_c3),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[293, 286])).
% 0.62/0.83 tff(295,plain,
% 0.62/0.83 (sk_c3 = multiply(sk_c2, sk_c10)),
% 0.62/0.83 inference(symmetry,[status(thm)],[294])).
% 0.62/0.83 tff(296,plain,
% 0.62/0.83 (multiply(sk_c10, sk_c3) = multiply(sk_c10, multiply(sk_c2, sk_c10))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[295])).
% 0.62/0.83 tff(297,plain,
% 0.62/0.83 (multiply(sk_c10, multiply(sk_c2, sk_c10)) = multiply(sk_c10, sk_c3)),
% 0.62/0.83 inference(symmetry,[status(thm)],[296])).
% 0.62/0.83 tff(298,assumption,(~(inverse(sk_c7) = sk_c10)), introduced(assumption)).
% 0.62/0.83 tff(299,plain,
% 0.62/0.83 (((inverse(sk_c7) = sk_c10) | (inverse(sk_c9) = sk_c10)) <=> ((inverse(sk_c7) = sk_c10) | (inverse(sk_c9) = sk_c10))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(300,plain,
% 0.62/0.83 (((inverse(sk_c9) = sk_c10) | (inverse(sk_c7) = sk_c10)) <=> ((inverse(sk_c7) = sk_c10) | (inverse(sk_c9) = sk_c10))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(301,axiom,((inverse(sk_c9) = sk_c10) | (inverse(sk_c7) = sk_c10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_16')).
% 0.62/0.83 tff(302,plain,
% 0.62/0.83 ((inverse(sk_c7) = sk_c10) | (inverse(sk_c9) = sk_c10)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.62/0.83 tff(303,plain,
% 0.62/0.83 ((inverse(sk_c7) = sk_c10) | (inverse(sk_c9) = sk_c10)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[302, 299])).
% 0.62/0.83 tff(304,plain,
% 0.62/0.83 (inverse(sk_c9) = sk_c10),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[303, 298])).
% 0.62/0.83 tff(305,plain,
% 0.62/0.83 (sk_c10 = inverse(sk_c9)),
% 0.62/0.83 inference(symmetry,[status(thm)],[304])).
% 0.62/0.83 tff(306,plain,
% 0.62/0.83 (multiply(sk_c10, sk_c9) = multiply(inverse(sk_c9), sk_c9)),
% 0.62/0.83 inference(monotonicity,[status(thm)],[305])).
% 0.62/0.83 tff(307,plain,
% 0.62/0.83 (multiply(sk_c10, inverse(sk_c10)) = multiply(inverse(sk_c10), sk_c10)),
% 0.62/0.83 inference(transitivity,[status(thm)],[127, 306, 12, 10])).
% 0.62/0.83 tff(308,plain,
% 0.62/0.83 ((multiply(sk_c10, inverse(sk_c10)) = sk_c9) <=> (multiply(inverse(sk_c10), sk_c10) = sk_c9)),
% 0.62/0.83 inference(monotonicity,[status(thm)],[307])).
% 0.62/0.83 tff(309,plain,
% 0.62/0.83 ((~(multiply(sk_c10, inverse(sk_c10)) = sk_c9)) <=> (~(multiply(inverse(sk_c10), sk_c10) = sk_c9))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[308])).
% 0.62/0.83 tff(310,plain,
% 0.62/0.83 (((inverse(sk_c7) = sk_c10) | (multiply(sk_c10, sk_c3) = sk_c9)) <=> ((inverse(sk_c7) = sk_c10) | (multiply(sk_c10, sk_c3) = sk_c9))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(311,plain,
% 0.62/0.83 (((multiply(sk_c10, sk_c3) = sk_c9) | (inverse(sk_c7) = sk_c10)) <=> ((inverse(sk_c7) = sk_c10) | (multiply(sk_c10, sk_c3) = sk_c9))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(312,axiom,((multiply(sk_c10, sk_c3) = sk_c9) | (inverse(sk_c7) = sk_c10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_40')).
% 0.62/0.83 tff(313,plain,
% 0.62/0.83 ((inverse(sk_c7) = sk_c10) | (multiply(sk_c10, sk_c3) = sk_c9)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.62/0.83 tff(314,plain,
% 0.62/0.83 ((inverse(sk_c7) = sk_c10) | (multiply(sk_c10, sk_c3) = sk_c9)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[313, 310])).
% 0.62/0.83 tff(315,plain,
% 0.62/0.83 (multiply(sk_c10, sk_c3) = sk_c9),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[314, 298])).
% 0.62/0.83 tff(316,plain,
% 0.62/0.83 (((inverse(sk_c7) = sk_c10) | (multiply(sk_c2, sk_c10) = sk_c3)) <=> ((inverse(sk_c7) = sk_c10) | (multiply(sk_c2, sk_c10) = sk_c3))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(317,plain,
% 0.62/0.83 (((multiply(sk_c2, sk_c10) = sk_c3) | (inverse(sk_c7) = sk_c10)) <=> ((inverse(sk_c7) = sk_c10) | (multiply(sk_c2, sk_c10) = sk_c3))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(318,axiom,((multiply(sk_c2, sk_c10) = sk_c3) | (inverse(sk_c7) = sk_c10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_48')).
% 0.62/0.83 tff(319,plain,
% 0.62/0.83 ((inverse(sk_c7) = sk_c10) | (multiply(sk_c2, sk_c10) = sk_c3)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.62/0.83 tff(320,plain,
% 0.62/0.83 ((inverse(sk_c7) = sk_c10) | (multiply(sk_c2, sk_c10) = sk_c3)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[319, 316])).
% 0.62/0.83 tff(321,plain,
% 0.62/0.83 (multiply(sk_c2, sk_c10) = sk_c3),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[320, 298])).
% 0.62/0.83 tff(322,plain,
% 0.62/0.83 (multiply(sk_c10, multiply(sk_c2, sk_c10)) = multiply(sk_c10, sk_c3)),
% 0.62/0.83 inference(monotonicity,[status(thm)],[321])).
% 0.62/0.83 tff(323,plain,
% 0.62/0.83 (multiply(sk_c10, sk_c9) = multiply(sk_c10, sk_c2)),
% 0.62/0.83 inference(transitivity,[status(thm)],[306, 12, 230, 227])).
% 0.62/0.83 tff(324,plain,
% 0.62/0.83 (multiply(multiply(sk_c10, sk_c9), sk_c10) = multiply(multiply(sk_c10, sk_c2), sk_c10)),
% 0.62/0.83 inference(monotonicity,[status(thm)],[323])).
% 0.62/0.83 tff(325,plain,
% 0.62/0.83 (multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9),
% 0.62/0.83 inference(transitivity,[status(thm)],[235, 324, 143, 322, 315])).
% 0.62/0.83 tff(326,plain,
% 0.62/0.83 (sk_c10 = sk_c9),
% 0.62/0.83 inference(transitivity,[status(thm)],[72, 238, 143, 322, 315])).
% 0.62/0.83 tff(327,plain,
% 0.62/0.83 (inverse(sk_c2) = sk_c9),
% 0.62/0.83 inference(transitivity,[status(thm)],[224, 72, 238, 143, 322, 315])).
% 0.62/0.83 tff(328,plain,
% 0.62/0.83 (multiply(inverse(sk_c2), sk_c10) = multiply(sk_c9, sk_c9)),
% 0.62/0.83 inference(monotonicity,[status(thm)],[327, 326])).
% 0.62/0.83 tff(329,plain,
% 0.62/0.83 (multiply(sk_c9, sk_c9) = multiply(inverse(sk_c2), sk_c10)),
% 0.62/0.83 inference(symmetry,[status(thm)],[328])).
% 0.62/0.83 tff(330,plain,
% 0.62/0.83 ((multiply(sk_c9, sk_c9) = sk_c10) <=> (multiply(inverse(sk_c2), sk_c10) = sk_c9)),
% 0.62/0.83 inference(monotonicity,[status(thm)],[329, 326])).
% 0.62/0.83 tff(331,plain,
% 0.62/0.83 ((multiply(inverse(sk_c2), sk_c10) = sk_c9) <=> (multiply(sk_c9, sk_c9) = sk_c10)),
% 0.62/0.83 inference(symmetry,[status(thm)],[330])).
% 0.62/0.83 tff(332,plain,
% 0.62/0.83 (((inverse(sk_c1) = sk_c9) | (inverse(sk_c7) = sk_c10)) <=> ((inverse(sk_c1) = sk_c9) | (inverse(sk_c7) = sk_c10))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(333,axiom,((inverse(sk_c1) = sk_c9) | (inverse(sk_c7) = sk_c10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_32')).
% 0.62/0.83 tff(334,plain,
% 0.62/0.83 ((inverse(sk_c1) = sk_c9) | (inverse(sk_c7) = sk_c10)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[333, 332])).
% 0.62/0.83 tff(335,plain,
% 0.62/0.83 (inverse(sk_c1) = sk_c9),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[334, 298])).
% 0.62/0.83 tff(336,plain,
% 0.62/0.83 (sk_c9 = inverse(sk_c1)),
% 0.62/0.83 inference(symmetry,[status(thm)],[335])).
% 0.62/0.83 tff(337,plain,
% 0.62/0.83 (multiply(sk_c9, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.62/0.83 inference(monotonicity,[status(thm)],[336])).
% 0.62/0.83 tff(338,plain,
% 0.62/0.83 (multiply(sk_c9, sk_c1) = identity),
% 0.62/0.83 inference(transitivity,[status(thm)],[337, 248])).
% 0.62/0.83 tff(339,plain,
% 0.62/0.83 (multiply(multiply(sk_c9, sk_c1), sk_c9) = multiply(identity, sk_c9)),
% 0.62/0.83 inference(monotonicity,[status(thm)],[338])).
% 0.62/0.83 tff(340,plain,
% 0.62/0.83 (((inverse(sk_c7) = sk_c10) | (multiply(sk_c1, sk_c9) = sk_c10)) <=> ((inverse(sk_c7) = sk_c10) | (multiply(sk_c1, sk_c9) = sk_c10))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(341,plain,
% 0.62/0.83 (((multiply(sk_c1, sk_c9) = sk_c10) | (inverse(sk_c7) = sk_c10)) <=> ((inverse(sk_c7) = sk_c10) | (multiply(sk_c1, sk_c9) = sk_c10))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(342,axiom,((multiply(sk_c1, sk_c9) = sk_c10) | (inverse(sk_c7) = sk_c10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_24')).
% 0.62/0.83 tff(343,plain,
% 0.62/0.83 ((inverse(sk_c7) = sk_c10) | (multiply(sk_c1, sk_c9) = sk_c10)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[342, 341])).
% 0.62/0.83 tff(344,plain,
% 0.62/0.83 ((inverse(sk_c7) = sk_c10) | (multiply(sk_c1, sk_c9) = sk_c10)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[343, 340])).
% 0.62/0.83 tff(345,plain,
% 0.62/0.83 (multiply(sk_c1, sk_c9) = sk_c10),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[344, 298])).
% 0.62/0.83 tff(346,plain,
% 0.62/0.83 (sk_c10 = multiply(sk_c1, sk_c9)),
% 0.62/0.83 inference(symmetry,[status(thm)],[345])).
% 0.62/0.83 tff(347,plain,
% 0.62/0.83 (multiply(inverse(sk_c10), sk_c10) = multiply(sk_c9, multiply(sk_c1, sk_c9))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[126, 346])).
% 0.62/0.83 tff(348,plain,
% 0.62/0.83 (multiply(sk_c10, sk_c3) = multiply(sk_c10, multiply(sk_c2, sk_c10))),
% 0.62/0.83 inference(symmetry,[status(thm)],[322])).
% 0.62/0.83 tff(349,plain,
% 0.62/0.83 (sk_c9 = multiply(sk_c10, sk_c3)),
% 0.62/0.83 inference(symmetry,[status(thm)],[315])).
% 0.62/0.83 tff(350,plain,
% 0.62/0.83 (sk_c9 = sk_c10),
% 0.62/0.83 inference(transitivity,[status(thm)],[349, 348, 267, 266, 71])).
% 0.62/0.83 tff(351,plain,
% 0.62/0.83 (multiply(sk_c9, sk_c9) = multiply(sk_c10, sk_c9)),
% 0.62/0.83 inference(monotonicity,[status(thm)],[350])).
% 0.62/0.83 tff(352,plain,
% 0.62/0.83 (multiply(inverse(sk_c2), sk_c10) = sk_c9),
% 0.62/0.83 inference(transitivity,[status(thm)],[328, 351, 306, 12, 10, 347, 259, 339, 246])).
% 0.62/0.83 tff(353,plain,
% 0.62/0.83 (multiply(sk_c9, sk_c9) = sk_c10),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[352, 331])).
% 0.62/0.83 tff(354,plain,
% 0.62/0.83 (multiply(inverse(sk_c10), sk_c10) = sk_c9),
% 0.62/0.83 inference(transitivity,[status(thm)],[347, 259, 339, 246])).
% 0.62/0.83 tff(355,plain,
% 0.62/0.83 ((~(multiply(inverse(sk_c10), sk_c10) = sk_c9)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c9)) | (~(multiply(sk_c9, sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9))),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[280, 126, 304, 345, 335, 214])).
% 0.62/0.83 tff(356,plain,
% 0.62/0.83 (~(multiply(sk_c10, inverse(sk_c10)) = sk_c9)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[355, 354, 353, 325])).
% 0.62/0.83 tff(357,plain,
% 0.62/0.83 (~(multiply(inverse(sk_c10), sk_c10) = sk_c9)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[356, 309])).
% 0.62/0.83 tff(358,plain,
% 0.62/0.83 ($false),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[354, 357])).
% 0.62/0.83 tff(359,plain,(inverse(sk_c7) = sk_c10), inference(lemma,lemma(discharge,[]))).
% 0.62/0.83 tff(360,plain,
% 0.62/0.83 (sk_c10 = inverse(sk_c7)),
% 0.62/0.83 inference(symmetry,[status(thm)],[359])).
% 0.62/0.83 tff(361,plain,
% 0.62/0.83 (multiply(sk_c10, sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.62/0.83 inference(monotonicity,[status(thm)],[360])).
% 0.62/0.83 tff(362,plain,
% 0.62/0.83 (multiply(sk_c10, sk_c7) = identity),
% 0.62/0.83 inference(transitivity,[status(thm)],[361, 56])).
% 0.62/0.83 tff(363,plain,
% 0.62/0.83 (multiply(multiply(sk_c10, sk_c7), sk_c10) = multiply(identity, sk_c10)),
% 0.62/0.83 inference(monotonicity,[status(thm)],[362])).
% 0.62/0.83 tff(364,assumption,(~(inverse(sk_c9) = sk_c10)), introduced(assumption)).
% 0.62/0.83 tff(365,plain,
% 0.62/0.83 (((inverse(sk_c9) = sk_c10) | (multiply(sk_c7, sk_c10) = sk_c8)) <=> ((inverse(sk_c9) = sk_c10) | (multiply(sk_c7, sk_c10) = sk_c8))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(366,axiom,((inverse(sk_c9) = sk_c10) | (multiply(sk_c7, sk_c10) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_15')).
% 0.62/0.83 tff(367,plain,
% 0.62/0.83 ((inverse(sk_c9) = sk_c10) | (multiply(sk_c7, sk_c10) = sk_c8)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[366, 365])).
% 0.62/0.83 tff(368,plain,
% 0.62/0.83 (multiply(sk_c7, sk_c10) = sk_c8),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[367, 364])).
% 0.62/0.83 tff(369,plain,
% 0.62/0.83 (sk_c8 = multiply(sk_c7, sk_c10)),
% 0.62/0.83 inference(symmetry,[status(thm)],[368])).
% 0.62/0.83 tff(370,plain,
% 0.62/0.83 (multiply(sk_c10, sk_c8) = multiply(sk_c10, multiply(sk_c7, sk_c10))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[369])).
% 0.62/0.83 tff(371,plain,
% 0.62/0.83 (sk_c9 = multiply(sk_c10, sk_c8)),
% 0.62/0.83 inference(symmetry,[status(thm)],[285])).
% 0.62/0.83 tff(372,plain,
% 0.62/0.83 (sk_c9 = sk_c10),
% 0.62/0.83 inference(transitivity,[status(thm)],[371, 370, 166, 363, 71])).
% 0.62/0.83 tff(373,plain,
% 0.62/0.83 (inverse(sk_c9) = inverse(sk_c10)),
% 0.62/0.83 inference(monotonicity,[status(thm)],[372])).
% 0.62/0.83 tff(374,plain,
% 0.62/0.83 (inverse(sk_c9) = sk_c10),
% 0.62/0.83 inference(transitivity,[status(thm)],[373, 126, 371, 370, 166, 363, 71])).
% 0.62/0.83 tff(375,plain,
% 0.62/0.83 ($false),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[364, 374])).
% 0.62/0.83 tff(376,plain,(inverse(sk_c9) = sk_c10), inference(lemma,lemma(discharge,[]))).
% 0.62/0.83 tff(377,plain,
% 0.62/0.83 (sk_c10 = inverse(sk_c9)),
% 0.62/0.83 inference(symmetry,[status(thm)],[376])).
% 0.62/0.83 tff(378,plain,
% 0.62/0.83 (multiply(sk_c10, sk_c9) = multiply(inverse(sk_c9), sk_c9)),
% 0.62/0.83 inference(monotonicity,[status(thm)],[377])).
% 0.62/0.83 tff(379,plain,
% 0.62/0.83 (multiply(sk_c10, sk_c9) = multiply(sk_c10, sk_c2)),
% 0.62/0.83 inference(transitivity,[status(thm)],[378, 12, 230, 227])).
% 0.62/0.83 tff(380,plain,
% 0.62/0.83 (multiply(multiply(sk_c10, sk_c9), sk_c10) = multiply(multiply(sk_c10, sk_c2), sk_c10)),
% 0.62/0.83 inference(monotonicity,[status(thm)],[379])).
% 0.62/0.83 tff(381,plain,
% 0.62/0.83 (multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9),
% 0.62/0.83 inference(transitivity,[status(thm)],[235, 380, 143, 297, 290])).
% 0.62/0.83 tff(382,plain,
% 0.62/0.83 (multiply(sk_c10, sk_c2) = identity),
% 0.62/0.83 inference(transitivity,[status(thm)],[226, 229])).
% 0.62/0.83 tff(383,plain,
% 0.62/0.83 (multiply(multiply(sk_c10, sk_c2), sk_c10) = multiply(identity, sk_c10)),
% 0.62/0.83 inference(monotonicity,[status(thm)],[382])).
% 0.62/0.83 tff(384,plain,
% 0.62/0.83 (sk_c9 = multiply(sk_c10, sk_c3)),
% 0.62/0.83 inference(symmetry,[status(thm)],[290])).
% 0.62/0.83 tff(385,plain,
% 0.62/0.83 (((inverse(sk_c1) = sk_c9) | (multiply(sk_c7, sk_c10) = sk_c8)) <=> ((inverse(sk_c1) = sk_c9) | (multiply(sk_c7, sk_c10) = sk_c8))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(386,axiom,((inverse(sk_c1) = sk_c9) | (multiply(sk_c7, sk_c10) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_31')).
% 0.62/0.83 tff(387,plain,
% 0.62/0.83 ((inverse(sk_c1) = sk_c9) | (multiply(sk_c7, sk_c10) = sk_c8)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[386, 385])).
% 0.62/0.83 tff(388,plain,
% 0.62/0.83 (inverse(sk_c1) = sk_c9),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[387, 286])).
% 0.62/0.83 tff(389,plain,
% 0.62/0.83 (sk_c9 = inverse(sk_c1)),
% 0.62/0.83 inference(symmetry,[status(thm)],[388])).
% 0.62/0.83 tff(390,plain,
% 0.62/0.83 (multiply(sk_c9, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.62/0.83 inference(monotonicity,[status(thm)],[389])).
% 0.62/0.83 tff(391,plain,
% 0.62/0.83 (multiply(sk_c9, sk_c1) = identity),
% 0.62/0.83 inference(transitivity,[status(thm)],[390, 248])).
% 0.62/0.83 tff(392,plain,
% 0.62/0.83 (multiply(multiply(sk_c9, sk_c1), sk_c9) = multiply(identity, sk_c9)),
% 0.62/0.83 inference(monotonicity,[status(thm)],[391])).
% 0.62/0.83 tff(393,plain,
% 0.62/0.83 (((multiply(sk_c1, sk_c9) = sk_c10) | (multiply(sk_c7, sk_c10) = sk_c8)) <=> ((multiply(sk_c1, sk_c9) = sk_c10) | (multiply(sk_c7, sk_c10) = sk_c8))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(394,axiom,((multiply(sk_c1, sk_c9) = sk_c10) | (multiply(sk_c7, sk_c10) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_23')).
% 0.62/0.83 tff(395,plain,
% 0.62/0.83 ((multiply(sk_c1, sk_c9) = sk_c10) | (multiply(sk_c7, sk_c10) = sk_c8)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[394, 393])).
% 0.62/0.83 tff(396,plain,
% 0.62/0.83 (multiply(sk_c1, sk_c9) = sk_c10),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[395, 286])).
% 0.62/0.83 tff(397,plain,
% 0.62/0.83 (sk_c10 = multiply(sk_c1, sk_c9)),
% 0.62/0.83 inference(symmetry,[status(thm)],[396])).
% 0.62/0.83 tff(398,plain,
% 0.62/0.83 (multiply(inverse(sk_c10), sk_c10) = multiply(sk_c9, multiply(sk_c1, sk_c9))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[126, 397])).
% 0.62/0.83 tff(399,plain,
% 0.62/0.83 (multiply(identity, sk_c10) = multiply(multiply(sk_c10, sk_c2), sk_c10)),
% 0.62/0.83 inference(symmetry,[status(thm)],[383])).
% 0.62/0.83 tff(400,plain,
% 0.62/0.83 (sk_c10 = sk_c9),
% 0.62/0.83 inference(transitivity,[status(thm)],[72, 399, 143, 297, 290])).
% 0.62/0.83 tff(401,plain,
% 0.62/0.83 (multiply(inverse(sk_c2), sk_c10) = multiply(sk_c10, sk_c9)),
% 0.62/0.83 inference(monotonicity,[status(thm)],[224, 400])).
% 0.62/0.83 tff(402,plain,
% 0.62/0.83 (sk_c9 = sk_c10),
% 0.62/0.83 inference(transitivity,[status(thm)],[384, 296, 267, 383, 71])).
% 0.62/0.83 tff(403,plain,
% 0.62/0.83 (sk_c9 = inverse(sk_c2)),
% 0.62/0.83 inference(transitivity,[status(thm)],[384, 296, 267, 383, 71, 225])).
% 0.62/0.83 tff(404,plain,
% 0.62/0.83 (multiply(sk_c9, sk_c9) = multiply(inverse(sk_c2), sk_c10)),
% 0.62/0.83 inference(monotonicity,[status(thm)],[403, 402])).
% 0.62/0.83 tff(405,plain,
% 0.62/0.83 (multiply(sk_c9, sk_c9) = sk_c10),
% 0.62/0.83 inference(transitivity,[status(thm)],[404, 401, 378, 12, 10, 398, 259, 392, 246, 384, 296, 267, 383, 71])).
% 0.62/0.83 tff(406,plain,
% 0.62/0.83 (multiply(sk_c10, sk_c7) = multiply(sk_c10, sk_c2)),
% 0.62/0.83 inference(transitivity,[status(thm)],[361, 56, 230, 227])).
% 0.62/0.83 tff(407,plain,
% 0.62/0.83 (multiply(multiply(sk_c10, sk_c7), sk_c10) = multiply(multiply(sk_c10, sk_c2), sk_c10)),
% 0.62/0.83 inference(monotonicity,[status(thm)],[406])).
% 0.62/0.83 tff(408,plain,
% 0.62/0.83 (multiply(sk_c10, multiply(sk_c7, sk_c10)) = sk_c9),
% 0.62/0.83 inference(transitivity,[status(thm)],[166, 407, 143, 297, 290])).
% 0.62/0.83 tff(409,plain,
% 0.62/0.83 (multiply(sk_c10, inverse(sk_c10)) = multiply(inverse(sk_c10), sk_c10)),
% 0.62/0.83 inference(transitivity,[status(thm)],[127, 378, 12, 10])).
% 0.62/0.83 tff(410,plain,
% 0.62/0.83 ((multiply(sk_c10, inverse(sk_c10)) = sk_c9) <=> (multiply(inverse(sk_c10), sk_c10) = sk_c9)),
% 0.62/0.83 inference(monotonicity,[status(thm)],[409])).
% 0.62/0.83 tff(411,plain,
% 0.62/0.83 ((multiply(inverse(sk_c10), sk_c10) = sk_c9) <=> (multiply(sk_c10, inverse(sk_c10)) = sk_c9)),
% 0.62/0.83 inference(symmetry,[status(thm)],[410])).
% 0.62/0.83 tff(412,plain,
% 0.62/0.83 (multiply(sk_c10, sk_c9) = multiply(inverse(sk_c10), sk_c10)),
% 0.62/0.83 inference(transitivity,[status(thm)],[378, 12, 10])).
% 0.62/0.83 tff(413,plain,
% 0.62/0.83 ((multiply(sk_c10, sk_c9) = sk_c10) <=> (multiply(inverse(sk_c10), sk_c10) = sk_c9)),
% 0.62/0.83 inference(monotonicity,[status(thm)],[412, 400])).
% 0.62/0.83 tff(414,plain,
% 0.62/0.83 ((multiply(sk_c10, sk_c9) = sk_c10) <=> (multiply(sk_c10, inverse(sk_c10)) = sk_c9)),
% 0.62/0.83 inference(transitivity,[status(thm)],[413, 411])).
% 0.62/0.83 tff(415,plain,
% 0.62/0.83 (multiply(sk_c10, sk_c9) = sk_c10),
% 0.62/0.83 inference(transitivity,[status(thm)],[378, 12, 10, 398, 259, 392, 246, 384, 296, 267, 383, 71])).
% 0.62/0.83 tff(416,plain,
% 0.62/0.83 (multiply(sk_c10, inverse(sk_c10)) = sk_c9),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[415, 414])).
% 0.62/0.83 tff(417,plain,
% 0.62/0.83 (multiply(inverse(sk_c10), sk_c10) = sk_c9),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[415, 413])).
% 0.62/0.83 tff(418,plain,
% 0.62/0.83 (((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c7) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c7, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c10) = sk_c9)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c9)) | (~(multiply(sk_c9, sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)))) <=> ((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c7) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c7, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c10) = sk_c9)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c9)) | (~(multiply(sk_c9, sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(419,plain,
% 0.62/0.83 (((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c7) = sk_c10)) | (~(multiply(sk_c9, sk_c9) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c7, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c10) = sk_c9)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(inverse(sk_c10) = sk_c9))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c7) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c7, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c10) = sk_c9)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c9)) | (~(multiply(sk_c9, sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(420,plain,
% 0.62/0.83 (((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c7) = sk_c10)) | (~(multiply(sk_c9, sk_c9) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c7, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c10) = sk_c9)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)))) <=> ((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c7) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c7, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c10) = sk_c9)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c9)) | (~(multiply(sk_c9, sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9))))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[419])).
% 0.62/0.83 tff(421,plain,
% 0.62/0.83 (((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c7) = sk_c10)) | (~(multiply(sk_c9, sk_c9) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c7, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c10) = sk_c9)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)))) <=> ((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c7) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c7, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c10) = sk_c9)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c9)) | (~(multiply(sk_c9, sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)))),
% 0.62/0.83 inference(transitivity,[status(thm)],[420, 418])).
% 0.62/0.83 tff(422,plain,
% 0.62/0.83 ((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c7) = sk_c10)) | (~(multiply(sk_c9, sk_c9) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c7, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c10) = sk_c9)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(423,plain,
% 0.62/0.83 ((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c7) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c7, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c10) = sk_c9)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c9)) | (~(multiply(sk_c9, sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[422, 421])).
% 0.62/0.83 tff(424,plain,
% 0.62/0.83 ((~(multiply(sk_c10, multiply(sk_c7, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c10) = sk_c9)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c9)) | (~(multiply(sk_c9, sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9))),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[423, 126, 359, 376, 214])).
% 0.62/0.83 tff(425,plain,
% 0.62/0.83 ($false),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[424, 417, 415, 416, 408, 405, 381])).
% 0.62/0.83 tff(426,plain,(multiply(sk_c7, sk_c10) = sk_c8), inference(lemma,lemma(discharge,[]))).
% 0.62/0.83 tff(427,plain,
% 0.62/0.83 (sk_c8 = multiply(sk_c7, sk_c10)),
% 0.62/0.83 inference(symmetry,[status(thm)],[426])).
% 0.62/0.83 tff(428,plain,
% 0.62/0.83 (multiply(sk_c10, sk_c8) = multiply(sk_c10, multiply(sk_c7, sk_c10))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[427])).
% 0.62/0.83 tff(429,plain,
% 0.62/0.83 (multiply(sk_c10, multiply(sk_c7, sk_c10)) = multiply(sk_c10, sk_c8)),
% 0.62/0.83 inference(symmetry,[status(thm)],[428])).
% 0.62/0.83 tff(430,plain,
% 0.62/0.83 (multiply(inverse(sk_c7), sk_c7) = multiply(sk_c10, sk_c7)),
% 0.62/0.83 inference(symmetry,[status(thm)],[361])).
% 0.62/0.83 tff(431,plain,
% 0.62/0.83 (identity = multiply(sk_c10, sk_c7)),
% 0.62/0.83 inference(transitivity,[status(thm)],[77, 430])).
% 0.62/0.83 tff(432,plain,
% 0.62/0.83 (multiply(identity, sk_c10) = multiply(multiply(sk_c10, sk_c7), sk_c10)),
% 0.62/0.83 inference(monotonicity,[status(thm)],[431])).
% 0.62/0.83 tff(433,plain,
% 0.62/0.83 (sk_c10 = sk_c9),
% 0.62/0.83 inference(transitivity,[status(thm)],[72, 432, 54, 429, 285])).
% 0.62/0.83 tff(434,plain,
% 0.62/0.83 (sk_c9 = sk_c10),
% 0.62/0.83 inference(transitivity,[status(thm)],[371, 428, 166, 363, 71])).
% 0.62/0.83 tff(435,plain,
% 0.62/0.83 (multiply(sk_c9, sk_c9) = multiply(sk_c10, sk_c9)),
% 0.62/0.83 inference(monotonicity,[status(thm)],[434])).
% 0.62/0.83 tff(436,plain,
% 0.62/0.83 (multiply(identity, sk_c10) = multiply(multiply(sk_c10, sk_c7), sk_c10)),
% 0.62/0.83 inference(symmetry,[status(thm)],[363])).
% 0.62/0.83 tff(437,plain,
% 0.62/0.83 (sk_c10 = sk_c9),
% 0.62/0.83 inference(transitivity,[status(thm)],[72, 436, 54, 429, 285])).
% 0.62/0.83 tff(438,plain,
% 0.62/0.83 (multiply(multiply(sk_c10, sk_c7), sk_c10) = multiply(identity, sk_c10)),
% 0.62/0.83 inference(symmetry,[status(thm)],[432])).
% 0.62/0.83 tff(439,plain,
% 0.62/0.83 (sk_c9 = sk_c10),
% 0.62/0.83 inference(transitivity,[status(thm)],[371, 428, 166, 438, 71])).
% 0.62/0.83 tff(440,plain,
% 0.62/0.83 (multiply(sk_c9, sk_c9) = multiply(sk_c10, sk_c9)),
% 0.62/0.83 inference(monotonicity,[status(thm)],[439])).
% 0.62/0.83 tff(441,assumption,(~(inverse(sk_c4) = sk_c10)), introduced(assumption)).
% 0.62/0.83 tff(442,plain,
% 0.62/0.83 (((inverse(sk_c1) = sk_c9) | (inverse(sk_c4) = sk_c10)) <=> ((inverse(sk_c1) = sk_c9) | (inverse(sk_c4) = sk_c10))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(443,axiom,((inverse(sk_c1) = sk_c9) | (inverse(sk_c4) = sk_c10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_25')).
% 0.62/0.83 tff(444,plain,
% 0.62/0.83 ((inverse(sk_c1) = sk_c9) | (inverse(sk_c4) = sk_c10)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[443, 442])).
% 0.62/0.83 tff(445,plain,
% 0.62/0.83 (inverse(sk_c1) = sk_c9),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[444, 441])).
% 0.62/0.83 tff(446,plain,
% 0.62/0.83 (multiply(inverse(sk_c1), sk_c10) = multiply(sk_c9, sk_c9)),
% 0.62/0.83 inference(monotonicity,[status(thm)],[445, 433])).
% 0.62/0.83 tff(447,plain,
% 0.62/0.83 (multiply(inverse(sk_c1), sk_c10) = multiply(inverse(sk_c10), sk_c10)),
% 0.62/0.83 inference(transitivity,[status(thm)],[446, 440, 378, 12, 10])).
% 0.62/0.83 tff(448,plain,
% 0.62/0.83 ((multiply(inverse(sk_c1), sk_c10) = sk_c9) <=> (multiply(inverse(sk_c10), sk_c10) = sk_c9)),
% 0.62/0.83 inference(monotonicity,[status(thm)],[447])).
% 0.62/0.83 tff(449,plain,
% 0.62/0.83 ((~(multiply(inverse(sk_c1), sk_c10) = sk_c9)) <=> (~(multiply(inverse(sk_c10), sk_c10) = sk_c9))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[448])).
% 0.62/0.84 tff(450,plain,
% 0.62/0.84 (((inverse(sk_c4) = sk_c10) | (multiply(sk_c1, sk_c9) = sk_c10)) <=> ((inverse(sk_c4) = sk_c10) | (multiply(sk_c1, sk_c9) = sk_c10))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(451,plain,
% 0.62/0.84 (((multiply(sk_c1, sk_c9) = sk_c10) | (inverse(sk_c4) = sk_c10)) <=> ((inverse(sk_c4) = sk_c10) | (multiply(sk_c1, sk_c9) = sk_c10))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(452,axiom,((multiply(sk_c1, sk_c9) = sk_c10) | (inverse(sk_c4) = sk_c10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_17')).
% 0.62/0.84 tff(453,plain,
% 0.62/0.84 ((inverse(sk_c4) = sk_c10) | (multiply(sk_c1, sk_c9) = sk_c10)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[452, 451])).
% 0.62/0.84 tff(454,plain,
% 0.62/0.84 ((inverse(sk_c4) = sk_c10) | (multiply(sk_c1, sk_c9) = sk_c10)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[453, 450])).
% 0.62/0.84 tff(455,plain,
% 0.62/0.84 (multiply(sk_c1, sk_c9) = sk_c10),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[454, 441])).
% 0.62/0.84 tff(456,plain,
% 0.62/0.84 (multiply(sk_c1, inverse(sk_c1)) = multiply(sk_c1, sk_c9)),
% 0.62/0.84 inference(monotonicity,[status(thm)],[445])).
% 0.62/0.84 tff(457,plain,
% 0.62/0.84 (multiply(sk_c1, inverse(sk_c1)) = sk_c9),
% 0.62/0.84 inference(transitivity,[status(thm)],[456, 455, 72, 432, 54, 429, 285])).
% 0.62/0.84 tff(458,plain,
% 0.62/0.84 (inverse(sk_c1) = sk_c10),
% 0.62/0.84 inference(transitivity,[status(thm)],[445, 371, 428, 166, 438, 71])).
% 0.62/0.84 tff(459,plain,
% 0.62/0.84 (multiply(sk_c10, sk_c9) = multiply(sk_c10, sk_c7)),
% 0.62/0.84 inference(transitivity,[status(thm)],[378, 12, 77, 430])).
% 0.62/0.84 tff(460,plain,
% 0.62/0.84 (multiply(multiply(sk_c10, sk_c9), sk_c10) = multiply(multiply(sk_c10, sk_c7), sk_c10)),
% 0.62/0.84 inference(monotonicity,[status(thm)],[459])).
% 0.62/0.84 tff(461,plain,
% 0.62/0.84 (multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9),
% 0.62/0.84 inference(transitivity,[status(thm)],[235, 460, 54, 429, 285])).
% 0.62/0.84 tff(462,plain,
% 0.62/0.84 (((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(inverse(sk_c1) = sk_c10)) | (~(multiply(inverse(sk_c1), sk_c10) = sk_c9)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c9)) | (~(multiply(sk_c1, sk_c9) = sk_c10)) | (~(inverse(sk_c1) = sk_c9)))) <=> ((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(inverse(sk_c1) = sk_c10)) | (~(multiply(inverse(sk_c1), sk_c10) = sk_c9)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c9)) | (~(multiply(sk_c1, sk_c9) = sk_c10)) | (~(inverse(sk_c1) = sk_c9)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(463,plain,
% 0.62/0.84 (((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c1, sk_c9) = sk_c10)) | (~(inverse(sk_c1) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(sk_c1, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c1), sk_c10) = sk_c9)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(inverse(sk_c1) = sk_c9))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(inverse(sk_c1) = sk_c10)) | (~(multiply(inverse(sk_c1), sk_c10) = sk_c9)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c9)) | (~(multiply(sk_c1, sk_c9) = sk_c10)) | (~(inverse(sk_c1) = sk_c9)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(464,plain,
% 0.62/0.84 (((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c1, sk_c9) = sk_c10)) | (~(inverse(sk_c1) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(sk_c1, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c1), sk_c10) = sk_c9)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)))) <=> ((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(inverse(sk_c1) = sk_c10)) | (~(multiply(inverse(sk_c1), sk_c10) = sk_c9)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c9)) | (~(multiply(sk_c1, sk_c9) = sk_c10)) | (~(inverse(sk_c1) = sk_c9))))),
% 0.62/0.84 inference(monotonicity,[status(thm)],[463])).
% 0.62/0.84 tff(465,plain,
% 0.62/0.84 (((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c1, sk_c9) = sk_c10)) | (~(inverse(sk_c1) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(sk_c1, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c1), sk_c10) = sk_c9)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)))) <=> ((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(inverse(sk_c1) = sk_c10)) | (~(multiply(inverse(sk_c1), sk_c10) = sk_c9)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c9)) | (~(multiply(sk_c1, sk_c9) = sk_c10)) | (~(inverse(sk_c1) = sk_c9)))),
% 0.62/0.84 inference(transitivity,[status(thm)],[464, 462])).
% 0.62/0.84 tff(466,plain,
% 0.62/0.84 ((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c1, sk_c9) = sk_c10)) | (~(inverse(sk_c1) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(sk_c1, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c1), sk_c10) = sk_c9)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(inverse(sk_c1) = sk_c9)))),
% 0.62/0.84 inference(quant_inst,[status(thm)],[])).
% 0.62/0.84 tff(467,plain,
% 0.62/0.84 ((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(inverse(sk_c1) = sk_c10)) | (~(multiply(inverse(sk_c1), sk_c10) = sk_c9)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c9)) | (~(multiply(sk_c1, sk_c9) = sk_c10)) | (~(inverse(sk_c1) = sk_c9))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[466, 465])).
% 0.62/0.84 tff(468,plain,
% 0.62/0.84 ((~(multiply(inverse(sk_c1), sk_c10) = sk_c9)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c9))),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[467, 126, 376, 455, 445, 214, 461, 458])).
% 0.62/0.84 tff(469,plain,
% 0.62/0.84 (~(multiply(inverse(sk_c1), sk_c10) = sk_c9)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[468, 457])).
% 0.62/0.84 tff(470,plain,
% 0.62/0.84 (~(multiply(inverse(sk_c10), sk_c10) = sk_c9)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[469, 449])).
% 0.62/0.84 tff(471,plain,
% 0.62/0.84 (sk_c9 = inverse(sk_c1)),
% 0.62/0.84 inference(symmetry,[status(thm)],[445])).
% 0.62/0.84 tff(472,plain,
% 0.62/0.84 (multiply(sk_c9, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.62/0.84 inference(monotonicity,[status(thm)],[471])).
% 0.62/0.84 tff(473,plain,
% 0.62/0.84 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c9, sk_c1)),
% 0.62/0.84 inference(symmetry,[status(thm)],[472])).
% 0.62/0.84 tff(474,plain,
% 0.62/0.84 (identity = multiply(inverse(sk_c1), sk_c1)),
% 0.62/0.84 inference(symmetry,[status(thm)],[248])).
% 0.62/0.84 tff(475,plain,
% 0.62/0.84 (multiply(sk_c10, sk_c7) = multiply(sk_c9, sk_c1)),
% 0.62/0.84 inference(transitivity,[status(thm)],[361, 56, 474, 473])).
% 0.62/0.84 tff(476,plain,
% 0.62/0.84 (multiply(multiply(sk_c10, sk_c7), sk_c10) = multiply(multiply(sk_c9, sk_c1), sk_c9)),
% 0.62/0.84 inference(monotonicity,[status(thm)],[475, 433])).
% 0.62/0.84 tff(477,plain,
% 0.62/0.84 (multiply(multiply(sk_c9, sk_c1), sk_c9) = multiply(multiply(sk_c10, sk_c7), sk_c10)),
% 0.62/0.84 inference(symmetry,[status(thm)],[476])).
% 0.62/0.84 tff(478,plain,
% 0.62/0.84 (multiply(sk_c1, sk_c9) = sk_c9),
% 0.62/0.84 inference(transitivity,[status(thm)],[455, 72, 432, 54, 429, 285])).
% 0.62/0.84 tff(479,plain,
% 0.62/0.84 (multiply(sk_c9, multiply(sk_c1, sk_c9)) = multiply(sk_c9, sk_c9)),
% 0.62/0.84 inference(monotonicity,[status(thm)],[478])).
% 0.62/0.84 tff(480,plain,
% 0.62/0.84 (multiply(sk_c9, sk_c9) = multiply(sk_c9, multiply(sk_c1, sk_c9))),
% 0.62/0.84 inference(symmetry,[status(thm)],[479])).
% 0.62/0.84 tff(481,plain,
% 0.62/0.84 (multiply(sk_c10, sk_c9) = multiply(sk_c9, sk_c9)),
% 0.62/0.84 inference(symmetry,[status(thm)],[440])).
% 0.62/0.84 tff(482,plain,
% 0.62/0.84 (multiply(inverse(sk_c9), sk_c9) = multiply(sk_c10, sk_c9)),
% 0.62/0.84 inference(symmetry,[status(thm)],[378])).
% 0.62/0.84 tff(483,plain,
% 0.62/0.84 (identity = multiply(inverse(sk_c9), sk_c9)),
% 0.62/0.84 inference(symmetry,[status(thm)],[12])).
% 0.62/0.84 tff(484,plain,
% 0.62/0.84 (multiply(inverse(sk_c10), sk_c10) = sk_c9),
% 0.62/0.84 inference(transitivity,[status(thm)],[9, 483, 482, 481, 480, 259, 477, 54, 429, 285])).
% 0.62/0.84 tff(485,plain,
% 0.62/0.84 ($false),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[484, 470])).
% 0.62/0.84 tff(486,plain,(inverse(sk_c4) = sk_c10), inference(lemma,lemma(discharge,[]))).
% 0.62/0.84 tff(487,plain,
% 0.62/0.84 (inverse(sk_c4) = sk_c9),
% 0.62/0.84 inference(transitivity,[status(thm)],[486, 72, 436, 54, 429, 285])).
% 0.62/0.84 tff(488,plain,
% 0.62/0.84 (multiply(inverse(sk_c4), sk_c10) = multiply(sk_c9, sk_c9)),
% 0.62/0.84 inference(monotonicity,[status(thm)],[487, 437])).
% 0.62/0.84 tff(489,plain,
% 0.62/0.84 (multiply(inverse(sk_c4), sk_c10) = multiply(inverse(sk_c10), sk_c10)),
% 0.62/0.84 inference(transitivity,[status(thm)],[488, 435, 378, 12, 10])).
% 0.62/0.84 tff(490,plain,
% 0.62/0.84 ((multiply(inverse(sk_c4), sk_c10) = sk_c9) <=> (multiply(inverse(sk_c10), sk_c10) = sk_c9)),
% 0.62/0.84 inference(monotonicity,[status(thm)],[489])).
% 0.62/0.84 tff(491,plain,
% 0.62/0.84 ((multiply(inverse(sk_c10), sk_c10) = sk_c9) <=> (multiply(inverse(sk_c4), sk_c10) = sk_c9)),
% 0.62/0.84 inference(symmetry,[status(thm)],[490])).
% 0.62/0.84 tff(492,plain,
% 0.62/0.84 (sk_c9 = inverse(sk_c10)),
% 0.62/0.84 inference(symmetry,[status(thm)],[126])).
% 0.62/0.84 tff(493,plain,
% 0.62/0.84 (multiply(sk_c9, sk_c10) = multiply(inverse(sk_c10), sk_c10)),
% 0.62/0.84 inference(monotonicity,[status(thm)],[492])).
% 0.62/0.84 tff(494,plain,
% 0.62/0.84 (multiply(inverse(sk_c10), sk_c10) = multiply(sk_c9, sk_c10)),
% 0.62/0.84 inference(symmetry,[status(thm)],[493])).
% 0.62/0.84 tff(495,plain,
% 0.62/0.84 (sk_c10 = inverse(sk_c4)),
% 0.62/0.84 inference(symmetry,[status(thm)],[486])).
% 0.62/0.84 tff(496,plain,
% 0.62/0.84 (sk_c9 = inverse(sk_c4)),
% 0.62/0.84 inference(transitivity,[status(thm)],[371, 428, 166, 363, 71, 495])).
% 0.62/0.84 tff(497,plain,
% 0.62/0.84 (multiply(sk_c9, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.62/0.84 inference(monotonicity,[status(thm)],[496])).
% 0.62/0.84 tff(498,plain,
% 0.62/0.84 (multiply(sk_c9, sk_c4) = multiply(sk_c9, sk_c10)),
% 0.62/0.84 inference(transitivity,[status(thm)],[497, 98, 10, 494])).
% 0.62/0.84 tff(499,plain,
% 0.62/0.84 (multiply(sk_c9, multiply(sk_c9, sk_c4)) = multiply(sk_c10, multiply(sk_c9, sk_c10))),
% 0.62/0.84 inference(monotonicity,[status(thm)],[434, 498])).
% 0.62/0.84 tff(500,plain,
% 0.62/0.84 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c9, sk_c9), sk_c4) = multiply(sk_c9, multiply(sk_c9, sk_c4)))),
% 0.62/0.84 inference(quant_inst,[status(thm)],[])).
% 0.62/0.84 tff(501,plain,
% 0.62/0.84 (multiply(multiply(sk_c9, sk_c9), sk_c4) = multiply(sk_c9, multiply(sk_c9, sk_c4))),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[500, 52])).
% 0.62/0.84 tff(502,plain,
% 0.62/0.84 (multiply(sk_c10, sk_c9) = multiply(sk_c9, sk_c9)),
% 0.62/0.84 inference(symmetry,[status(thm)],[435])).
% 0.62/0.84 tff(503,plain,
% 0.62/0.84 (identity = multiply(sk_c9, sk_c9)),
% 0.62/0.84 inference(transitivity,[status(thm)],[483, 482, 502])).
% 0.62/0.84 tff(504,plain,
% 0.62/0.84 (multiply(identity, sk_c4) = multiply(multiply(sk_c9, sk_c9), sk_c4)),
% 0.62/0.84 inference(monotonicity,[status(thm)],[503])).
% 0.62/0.84 tff(505,plain,
% 0.62/0.84 (sk_c4 = multiply(identity, sk_c4)),
% 0.62/0.84 inference(symmetry,[status(thm)],[75])).
% 0.62/0.84 tff(506,plain,
% 0.62/0.84 (sk_c4 = sk_c9),
% 0.62/0.84 inference(transitivity,[status(thm)],[505, 504, 501, 499, 235, 460, 54, 429, 285])).
% 0.62/0.84 tff(507,plain,
% 0.62/0.84 (multiply(sk_c4, sk_c9) = multiply(sk_c9, sk_c9)),
% 0.62/0.84 inference(monotonicity,[status(thm)],[506])).
% 0.62/0.84 tff(508,plain,
% 0.62/0.84 (multiply(sk_c4, sk_c9) = multiply(inverse(sk_c10), sk_c10)),
% 0.62/0.84 inference(transitivity,[status(thm)],[507, 435, 378, 12, 10])).
% 0.62/0.84 tff(509,plain,
% 0.62/0.84 ((multiply(sk_c4, sk_c9) = sk_c10) <=> (multiply(inverse(sk_c10), sk_c10) = sk_c9)),
% 0.62/0.84 inference(monotonicity,[status(thm)],[508, 437])).
% 0.62/0.84 tff(510,plain,
% 0.62/0.84 ((multiply(sk_c4, sk_c9) = sk_c10) <=> (multiply(inverse(sk_c4), sk_c10) = sk_c9)),
% 0.62/0.84 inference(transitivity,[status(thm)],[509, 491])).
% 0.62/0.84 tff(511,plain,
% 0.62/0.84 (multiply(inverse(sk_c4), sk_c10) = sk_c9),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[90, 510])).
% 0.62/0.84 tff(512,plain,
% 0.62/0.84 (multiply(sk_c4, inverse(sk_c4)) = multiply(sk_c4, sk_c9)),
% 0.62/0.84 inference(monotonicity,[status(thm)],[487])).
% 0.62/0.84 tff(513,plain,
% 0.62/0.84 ((multiply(sk_c4, inverse(sk_c4)) = sk_c9) <=> (multiply(sk_c4, sk_c9) = sk_c10)),
% 0.62/0.84 inference(monotonicity,[status(thm)],[512, 434])).
% 0.62/0.84 tff(514,plain,
% 0.62/0.84 ((multiply(sk_c4, sk_c9) = sk_c10) <=> (multiply(sk_c4, inverse(sk_c4)) = sk_c9)),
% 0.62/0.84 inference(symmetry,[status(thm)],[513])).
% 0.62/0.84 tff(515,plain,
% 0.62/0.84 (multiply(sk_c4, inverse(sk_c4)) = sk_c9),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[90, 514])).
% 0.62/0.84 tff(516,plain,
% 0.62/0.84 (((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c4) = sk_c10)) | (~(multiply(sk_c4, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c4), sk_c10) = sk_c9)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c9)) | (~(inverse(sk_c4) = sk_c9)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)))) <=> ((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c4) = sk_c10)) | (~(multiply(sk_c4, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c4), sk_c10) = sk_c9)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c9)) | (~(inverse(sk_c4) = sk_c9)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(517,plain,
% 0.62/0.84 (((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c4, sk_c9) = sk_c10)) | (~(inverse(sk_c4) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(sk_c4, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c4), sk_c10) = sk_c9)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(inverse(sk_c4) = sk_c9))) <=> ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c4) = sk_c10)) | (~(multiply(sk_c4, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c4), sk_c10) = sk_c9)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c9)) | (~(inverse(sk_c4) = sk_c9)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(518,plain,
% 0.62/0.84 (((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c4, sk_c9) = sk_c10)) | (~(inverse(sk_c4) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(sk_c4, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c4), sk_c10) = sk_c9)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(inverse(sk_c4) = sk_c9)))) <=> ((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c4) = sk_c10)) | (~(multiply(sk_c4, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c4), sk_c10) = sk_c9)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c9)) | (~(inverse(sk_c4) = sk_c9)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9))))),
% 0.62/0.84 inference(monotonicity,[status(thm)],[517])).
% 0.62/0.84 tff(519,plain,
% 0.62/0.84 (((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c4, sk_c9) = sk_c10)) | (~(inverse(sk_c4) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(sk_c4, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c4), sk_c10) = sk_c9)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(inverse(sk_c4) = sk_c9)))) <=> ((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c4) = sk_c10)) | (~(multiply(sk_c4, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c4), sk_c10) = sk_c9)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c9)) | (~(inverse(sk_c4) = sk_c9)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)))),
% 0.62/0.84 inference(transitivity,[status(thm)],[518, 516])).
% 0.62/0.84 tff(520,plain,
% 0.62/0.84 ((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c4, sk_c9) = sk_c10)) | (~(inverse(sk_c4) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(sk_c4, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c4), sk_c10) = sk_c9)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(inverse(sk_c4) = sk_c9)))),
% 0.62/0.84 inference(quant_inst,[status(thm)],[])).
% 0.62/0.84 tff(521,plain,
% 0.62/0.84 ((~![X6: $i, X4: $i, X3: $i, X8: $i, X1: $i] : ((~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(X8) = sk_c10)) | (~(multiply(X1, sk_c9) = sk_c10)) | (~(inverse(X1) = sk_c10)) | (~(multiply(sk_c10, multiply(X8, sk_c10)) = sk_c9)) | (~(multiply(X4, sk_c9) = sk_c10)) | (~(multiply(inverse(X3), sk_c10) = sk_c9)) | (~(multiply(X3, inverse(X3)) = sk_c9)) | (~(inverse(X6) = sk_c10)) | (~(multiply(sk_c10, multiply(X6, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c9)))) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c4) = sk_c10)) | (~(multiply(sk_c4, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c4), sk_c10) = sk_c9)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c9)) | (~(inverse(sk_c4) = sk_c9)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[520, 519])).
% 0.62/0.84 tff(522,plain,
% 0.62/0.84 ((~(multiply(sk_c4, sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c4), sk_c10) = sk_c9)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c9))),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[521, 126, 486, 376, 214, 461, 487])).
% 0.62/0.84 tff(523,plain,
% 0.62/0.84 ($false),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[522, 515, 511, 90])).
% 0.62/0.84 tff(524,plain,(~(multiply(sk_c4, sk_c9) = sk_c10)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.84 tff(525,plain,
% 0.62/0.84 (((inverse(sk_c1) = sk_c9) | (multiply(sk_c4, sk_c9) = sk_c10)) <=> ((inverse(sk_c1) = sk_c9) | (multiply(sk_c4, sk_c9) = sk_c10))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(526,axiom,((inverse(sk_c1) = sk_c9) | (multiply(sk_c4, sk_c9) = sk_c10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_26')).
% 0.62/0.84 tff(527,plain,
% 0.62/0.84 ((inverse(sk_c1) = sk_c9) | (multiply(sk_c4, sk_c9) = sk_c10)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[526, 525])).
% 0.62/0.84 tff(528,plain,
% 0.62/0.84 (inverse(sk_c1) = sk_c9),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[527, 524])).
% 0.62/0.84 tff(529,plain,
% 0.62/0.84 (sk_c9 = inverse(sk_c1)),
% 0.62/0.84 inference(symmetry,[status(thm)],[528])).
% 0.62/0.84 tff(530,plain,
% 0.62/0.84 (multiply(sk_c9, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.62/0.84 inference(monotonicity,[status(thm)],[529])).
% 0.62/0.84 tff(531,plain,
% 0.62/0.84 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c9, sk_c1)),
% 0.62/0.84 inference(symmetry,[status(thm)],[530])).
% 0.62/0.84 tff(532,plain,
% 0.62/0.84 (multiply(sk_c10, sk_c7) = multiply(sk_c9, sk_c1)),
% 0.62/0.84 inference(transitivity,[status(thm)],[361, 56, 474, 531])).
% 0.62/0.84 tff(533,plain,
% 0.62/0.84 (multiply(multiply(sk_c10, sk_c7), sk_c10) = multiply(multiply(sk_c9, sk_c1), sk_c9)),
% 0.62/0.84 inference(monotonicity,[status(thm)],[532, 433])).
% 0.62/0.84 tff(534,plain,
% 0.62/0.84 (multiply(multiply(sk_c9, sk_c1), sk_c9) = multiply(multiply(sk_c10, sk_c7), sk_c10)),
% 0.62/0.84 inference(symmetry,[status(thm)],[533])).
% 0.62/0.84 tff(535,plain,
% 0.62/0.84 (((multiply(sk_c1, sk_c9) = sk_c10) | (multiply(sk_c4, sk_c9) = sk_c10)) <=> ((multiply(sk_c1, sk_c9) = sk_c10) | (multiply(sk_c4, sk_c9) = sk_c10))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(536,axiom,((multiply(sk_c1, sk_c9) = sk_c10) | (multiply(sk_c4, sk_c9) = sk_c10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_18')).
% 0.62/0.84 tff(537,plain,
% 0.62/0.84 ((multiply(sk_c1, sk_c9) = sk_c10) | (multiply(sk_c4, sk_c9) = sk_c10)),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[536, 535])).
% 0.62/0.85 tff(538,plain,
% 0.62/0.85 (multiply(sk_c1, sk_c9) = sk_c10),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[537, 524])).
% 0.62/0.85 tff(539,plain,
% 0.62/0.85 (multiply(sk_c1, sk_c9) = sk_c9),
% 0.62/0.85 inference(transitivity,[status(thm)],[538, 72, 432, 54, 429, 285])).
% 0.62/0.85 tff(540,plain,
% 0.62/0.85 (multiply(sk_c9, multiply(sk_c1, sk_c9)) = multiply(sk_c9, sk_c9)),
% 0.62/0.85 inference(monotonicity,[status(thm)],[539])).
% 0.62/0.85 tff(541,plain,
% 0.62/0.85 (multiply(sk_c9, sk_c9) = multiply(sk_c9, multiply(sk_c1, sk_c9))),
% 0.62/0.85 inference(symmetry,[status(thm)],[540])).
% 0.62/0.85 tff(542,plain,
% 0.62/0.85 (multiply(inverse(sk_c10), sk_c10) = sk_c9),
% 0.62/0.85 inference(transitivity,[status(thm)],[9, 483, 482, 481, 541, 259, 534, 54, 429, 285])).
% 0.62/0.85 tff(543,plain,
% 0.62/0.85 (sk_c9 = inverse(sk_c4)),
% 0.62/0.85 inference(transitivity,[status(thm)],[371, 428, 166, 438, 71, 495])).
% 0.62/0.85 tff(544,plain,
% 0.62/0.85 (multiply(sk_c9, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.62/0.85 inference(monotonicity,[status(thm)],[543])).
% 0.62/0.85 tff(545,plain,
% 0.62/0.85 (multiply(sk_c9, sk_c4) = multiply(sk_c9, sk_c10)),
% 0.62/0.85 inference(transitivity,[status(thm)],[544, 98, 10, 494])).
% 0.62/0.85 tff(546,plain,
% 0.62/0.85 (multiply(sk_c9, multiply(sk_c9, sk_c4)) = multiply(sk_c10, multiply(sk_c9, sk_c10))),
% 0.62/0.85 inference(monotonicity,[status(thm)],[439, 545])).
% 0.62/0.85 tff(547,plain,
% 0.62/0.85 (identity = multiply(sk_c9, sk_c9)),
% 0.62/0.85 inference(transitivity,[status(thm)],[483, 482, 481])).
% 0.62/0.85 tff(548,plain,
% 0.62/0.85 (multiply(identity, sk_c4) = multiply(multiply(sk_c9, sk_c9), sk_c4)),
% 0.62/0.85 inference(monotonicity,[status(thm)],[547])).
% 0.62/0.85 tff(549,plain,
% 0.62/0.85 (sk_c4 = sk_c9),
% 0.62/0.85 inference(transitivity,[status(thm)],[505, 548, 501, 546, 235, 460, 54, 429, 285])).
% 0.62/0.85 tff(550,plain,
% 0.62/0.85 (multiply(sk_c4, sk_c9) = multiply(sk_c9, sk_c9)),
% 0.62/0.85 inference(monotonicity,[status(thm)],[549])).
% 0.62/0.85 tff(551,plain,
% 0.62/0.85 (multiply(sk_c4, sk_c9) = multiply(inverse(sk_c10), sk_c10)),
% 0.62/0.85 inference(transitivity,[status(thm)],[550, 440, 378, 12, 10])).
% 0.62/0.85 tff(552,plain,
% 0.62/0.85 ((multiply(sk_c4, sk_c9) = sk_c10) <=> (multiply(inverse(sk_c10), sk_c10) = sk_c9)),
% 0.62/0.85 inference(monotonicity,[status(thm)],[551, 433])).
% 0.62/0.85 tff(553,plain,
% 0.62/0.85 ((~(multiply(sk_c4, sk_c9) = sk_c10)) <=> (~(multiply(inverse(sk_c10), sk_c10) = sk_c9))),
% 0.62/0.85 inference(monotonicity,[status(thm)],[552])).
% 0.62/0.85 tff(554,plain,
% 0.62/0.85 (~(multiply(inverse(sk_c10), sk_c10) = sk_c9)),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[524, 553])).
% 0.62/0.85 tff(555,plain,
% 0.62/0.85 ($false),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[554, 542])).
% 0.62/0.85 % SZS output end Proof
% 0.62/0.85 % E exiting
%------------------------------------------------------------------------------