%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP362-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:07:39 AM UTC 2025
% Result : Unsatisfiable 0.53s 0.70s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP362-1 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 16:00:56 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.53/0.70 % SZS status Unsatisfiable
% 0.53/0.70 % SZS output start Proof
% 0.53/0.70 tff(sk_c8_type, type, (
% 0.53/0.70 sk_c8: $i)).
% 0.53/0.70 tff(multiply_type, type, (
% 0.53/0.70 multiply: ( $i * $i ) > $i)).
% 0.53/0.70 tff(sk_c9_type, type, (
% 0.53/0.70 sk_c9: $i)).
% 0.53/0.70 tff(inverse_type, type, (
% 0.53/0.70 inverse: $i > $i)).
% 0.53/0.70 tff(identity_type, type, (
% 0.53/0.70 identity: $i)).
% 0.53/0.70 tff(sk_c10_type, type, (
% 0.53/0.70 sk_c10: $i)).
% 0.53/0.70 tff(sk_c3_type, type, (
% 0.53/0.70 sk_c3: $i)).
% 0.53/0.70 tff(sk_c4_type, type, (
% 0.53/0.70 sk_c4: $i)).
% 0.53/0.70 tff(sk_c1_type, type, (
% 0.53/0.70 sk_c1: $i)).
% 0.53/0.70 tff(sk_c2_type, type, (
% 0.53/0.70 sk_c2: $i)).
% 0.53/0.70 tff(sk_c7_type, type, (
% 0.53/0.70 sk_c7: $i)).
% 0.53/0.70 tff(sk_c5_type, type, (
% 0.53/0.70 sk_c5: $i)).
% 0.53/0.70 tff(sk_c6_type, type, (
% 0.53/0.70 sk_c6: $i)).
% 0.53/0.70 tff(1,plain,
% 0.53/0.70 (^[X: $i] : refl((multiply(inverse(X), X) = identity) <=> (multiply(inverse(X), X) = identity))),
% 0.53/0.70 inference(bind,[status(th)],[])).
% 0.53/0.70 tff(2,plain,
% 0.53/0.70 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.53/0.70 inference(quant_intro,[status(thm)],[1])).
% 0.53/0.70 tff(3,plain,
% 0.53/0.70 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(4,axiom,(![X: $i] : (multiply(inverse(X), X) = identity)), file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax','left_inverse')).
% 0.53/0.70 tff(5,plain,
% 0.53/0.70 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.53/0.70 tff(6,plain,(
% 0.53/0.70 ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.53/0.70 inference(skolemize,[status(sab)],[5])).
% 0.53/0.70 tff(7,plain,
% 0.53/0.70 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.53/0.70 tff(8,plain,
% 0.53/0.70 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c9), sk_c9) = identity)),
% 0.53/0.70 inference(quant_inst,[status(thm)],[])).
% 0.53/0.70 tff(9,plain,
% 0.53/0.70 (multiply(inverse(sk_c9), sk_c9) = identity),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.53/0.70 tff(10,plain,
% 0.53/0.70 (identity = multiply(inverse(sk_c9), sk_c9)),
% 0.53/0.70 inference(symmetry,[status(thm)],[9])).
% 0.53/0.70 tff(11,plain,
% 0.53/0.70 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c10), sk_c10) = identity)),
% 0.53/0.70 inference(quant_inst,[status(thm)],[])).
% 0.53/0.70 tff(12,plain,
% 0.53/0.70 (multiply(inverse(sk_c10), sk_c10) = identity),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[11, 7])).
% 0.53/0.70 tff(13,plain,
% 0.53/0.70 (^[X: $i] : refl((multiply(identity, X) = X) <=> (multiply(identity, X) = X))),
% 0.53/0.70 inference(bind,[status(th)],[])).
% 0.53/0.70 tff(14,plain,
% 0.53/0.70 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.53/0.70 inference(quant_intro,[status(thm)],[13])).
% 0.53/0.70 tff(15,plain,
% 0.53/0.70 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(16,axiom,(![X: $i] : (multiply(identity, X) = X)), file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax','left_identity')).
% 0.53/0.70 tff(17,plain,
% 0.53/0.70 (![X: $i] : (multiply(identity, X) = X)),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.53/0.70 tff(18,plain,(
% 0.53/0.70 ![X: $i] : (multiply(identity, X) = X)),
% 0.53/0.70 inference(skolemize,[status(sab)],[17])).
% 0.53/0.70 tff(19,plain,
% 0.53/0.70 (![X: $i] : (multiply(identity, X) = X)),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.53/0.70 tff(20,plain,
% 0.53/0.70 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c10) = sk_c10)),
% 0.53/0.70 inference(quant_inst,[status(thm)],[])).
% 0.53/0.70 tff(21,plain,
% 0.53/0.70 (multiply(identity, sk_c10) = sk_c10),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.53/0.70 tff(22,plain,
% 0.53/0.70 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c3), sk_c3) = identity)),
% 0.53/0.70 inference(quant_inst,[status(thm)],[])).
% 0.53/0.70 tff(23,plain,
% 0.53/0.70 (multiply(inverse(sk_c3), sk_c3) = identity),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[22, 7])).
% 0.53/0.70 tff(24,assumption,(~(inverse(sk_c9) = sk_c10)), introduced(assumption)).
% 0.53/0.70 tff(25,plain,
% 0.53/0.70 (((inverse(sk_c3) = sk_c10) | (inverse(sk_c9) = sk_c10)) <=> ((inverse(sk_c3) = sk_c10) | (inverse(sk_c9) = sk_c10))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(26,plain,
% 0.53/0.70 (((inverse(sk_c9) = sk_c10) | (inverse(sk_c3) = sk_c10)) <=> ((inverse(sk_c3) = sk_c10) | (inverse(sk_c9) = sk_c10))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(27,axiom,((inverse(sk_c9) = sk_c10) | (inverse(sk_c3) = sk_c10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_13')).
% 0.53/0.71 tff(28,plain,
% 0.53/0.71 ((inverse(sk_c3) = sk_c10) | (inverse(sk_c9) = sk_c10)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.53/0.71 tff(29,plain,
% 0.53/0.71 ((inverse(sk_c3) = sk_c10) | (inverse(sk_c9) = sk_c10)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.53/0.71 tff(30,plain,
% 0.53/0.71 (inverse(sk_c3) = sk_c10),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[29, 24])).
% 0.53/0.71 tff(31,plain,
% 0.53/0.71 (sk_c10 = inverse(sk_c3)),
% 0.53/0.71 inference(symmetry,[status(thm)],[30])).
% 0.53/0.71 tff(32,plain,
% 0.53/0.71 (multiply(sk_c10, sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.53/0.71 inference(monotonicity,[status(thm)],[31])).
% 0.53/0.71 tff(33,plain,
% 0.53/0.71 (multiply(sk_c10, sk_c3) = identity),
% 0.53/0.71 inference(transitivity,[status(thm)],[32, 23])).
% 0.53/0.71 tff(34,plain,
% 0.53/0.71 (multiply(multiply(sk_c10, sk_c3), sk_c10) = multiply(identity, sk_c10)),
% 0.53/0.71 inference(monotonicity,[status(thm)],[33])).
% 0.53/0.71 tff(35,plain,
% 0.53/0.71 (^[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))))),
% 0.53/0.71 inference(bind,[status(th)],[])).
% 0.53/0.71 tff(36,plain,
% 0.53/0.71 (![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)))),
% 0.53/0.71 inference(quant_intro,[status(thm)],[35])).
% 0.53/0.71 tff(37,plain,
% 0.53/0.71 (![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)))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(38,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')).
% 0.53/0.71 tff(39,plain,
% 0.53/0.71 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.53/0.71 tff(40,plain,(
% 0.53/0.71 ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.53/0.71 inference(skolemize,[status(sab)],[39])).
% 0.53/0.71 tff(41,plain,
% 0.53/0.71 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.53/0.71 tff(42,plain,
% 0.53/0.71 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c10, sk_c3), sk_c10) = multiply(sk_c10, multiply(sk_c3, sk_c10)))),
% 0.53/0.71 inference(quant_inst,[status(thm)],[])).
% 0.53/0.71 tff(43,plain,
% 0.53/0.71 (multiply(multiply(sk_c10, sk_c3), sk_c10) = multiply(sk_c10, multiply(sk_c3, sk_c10))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.53/0.71 tff(44,plain,
% 0.53/0.71 (multiply(sk_c10, multiply(sk_c3, sk_c10)) = multiply(multiply(sk_c10, sk_c3), sk_c10)),
% 0.53/0.71 inference(symmetry,[status(thm)],[43])).
% 0.53/0.71 tff(45,plain,
% 0.53/0.71 (((inverse(sk_c9) = sk_c10) | (multiply(sk_c3, sk_c10) = sk_c4)) <=> ((inverse(sk_c9) = sk_c10) | (multiply(sk_c3, sk_c10) = sk_c4))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(46,axiom,((inverse(sk_c9) = sk_c10) | (multiply(sk_c3, sk_c10) = sk_c4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_12')).
% 0.53/0.71 tff(47,plain,
% 0.53/0.71 ((inverse(sk_c9) = sk_c10) | (multiply(sk_c3, sk_c10) = sk_c4)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.53/0.71 tff(48,plain,
% 0.53/0.71 (multiply(sk_c3, sk_c10) = sk_c4),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[47, 24])).
% 0.53/0.71 tff(49,plain,
% 0.53/0.71 (sk_c4 = multiply(sk_c3, sk_c10)),
% 0.53/0.71 inference(symmetry,[status(thm)],[48])).
% 0.53/0.71 tff(50,plain,
% 0.53/0.71 (multiply(sk_c10, sk_c4) = multiply(sk_c10, multiply(sk_c3, sk_c10))),
% 0.53/0.71 inference(monotonicity,[status(thm)],[49])).
% 0.53/0.71 tff(51,plain,
% 0.53/0.71 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c8) = sk_c8)),
% 0.53/0.71 inference(quant_inst,[status(thm)],[])).
% 0.53/0.71 tff(52,plain,
% 0.53/0.71 (multiply(identity, sk_c8) = sk_c8),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[51, 19])).
% 0.53/0.71 tff(53,assumption,(~(multiply(sk_c10, sk_c4) = sk_c9)), introduced(assumption)).
% 0.53/0.71 tff(54,plain,
% 0.53/0.71 (((multiply(sk_c10, sk_c2) = sk_c9) | (multiply(sk_c10, sk_c4) = sk_c9)) <=> ((multiply(sk_c10, sk_c2) = sk_c9) | (multiply(sk_c10, sk_c4) = sk_c9))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(55,axiom,((multiply(sk_c10, sk_c2) = sk_c9) | (multiply(sk_c10, sk_c4) = sk_c9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_29')).
% 0.53/0.71 tff(56,plain,
% 0.53/0.71 ((multiply(sk_c10, sk_c2) = sk_c9) | (multiply(sk_c10, sk_c4) = sk_c9)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.53/0.71 tff(57,plain,
% 0.53/0.71 (multiply(sk_c10, sk_c2) = sk_c9),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[56, 53])).
% 0.53/0.71 tff(58,plain,
% 0.53/0.71 (((multiply(sk_c1, sk_c10) = sk_c2) | (multiply(sk_c10, sk_c4) = sk_c9)) <=> ((multiply(sk_c1, sk_c10) = sk_c2) | (multiply(sk_c10, sk_c4) = sk_c9))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(59,axiom,((multiply(sk_c1, sk_c10) = sk_c2) | (multiply(sk_c10, sk_c4) = sk_c9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_38')).
% 0.53/0.71 tff(60,plain,
% 0.53/0.71 ((multiply(sk_c1, sk_c10) = sk_c2) | (multiply(sk_c10, sk_c4) = sk_c9)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.53/0.71 tff(61,plain,
% 0.53/0.71 (multiply(sk_c1, sk_c10) = sk_c2),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[60, 53])).
% 0.53/0.71 tff(62,plain,
% 0.53/0.71 (sk_c2 = multiply(sk_c1, sk_c10)),
% 0.53/0.71 inference(symmetry,[status(thm)],[61])).
% 0.53/0.71 tff(63,plain,
% 0.53/0.71 (multiply(sk_c10, sk_c2) = multiply(sk_c10, multiply(sk_c1, sk_c10))),
% 0.53/0.71 inference(monotonicity,[status(thm)],[62])).
% 0.53/0.71 tff(64,plain,
% 0.53/0.71 (multiply(sk_c10, multiply(sk_c1, sk_c10)) = multiply(sk_c10, sk_c2)),
% 0.53/0.71 inference(symmetry,[status(thm)],[63])).
% 0.53/0.71 tff(65,plain,
% 0.53/0.71 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c10, sk_c1), sk_c10) = multiply(sk_c10, multiply(sk_c1, sk_c10)))),
% 0.53/0.71 inference(quant_inst,[status(thm)],[])).
% 0.53/0.71 tff(66,plain,
% 0.53/0.71 (multiply(multiply(sk_c10, sk_c1), sk_c10) = multiply(sk_c10, multiply(sk_c1, sk_c10))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[65, 41])).
% 0.53/0.71 tff(67,plain,
% 0.53/0.71 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c1), sk_c1) = identity)),
% 0.53/0.71 inference(quant_inst,[status(thm)],[])).
% 0.53/0.71 tff(68,plain,
% 0.53/0.71 (multiply(inverse(sk_c1), sk_c1) = identity),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[67, 7])).
% 0.53/0.71 tff(69,assumption,(~(inverse(sk_c1) = sk_c10)), introduced(assumption)).
% 0.53/0.71 tff(70,plain,
% 0.53/0.71 (((inverse(sk_c1) = sk_c10) | (inverse(sk_c3) = sk_c10)) <=> ((inverse(sk_c1) = sk_c10) | (inverse(sk_c3) = sk_c10))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(71,axiom,((inverse(sk_c1) = sk_c10) | (inverse(sk_c3) = sk_c10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_49')).
% 0.53/0.71 tff(72,plain,
% 0.53/0.71 ((inverse(sk_c1) = sk_c10) | (inverse(sk_c3) = sk_c10)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.53/0.71 tff(73,plain,
% 0.53/0.71 (inverse(sk_c3) = sk_c10),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[72, 69])).
% 0.53/0.71 tff(74,plain,
% 0.53/0.71 (sk_c10 = inverse(sk_c3)),
% 0.53/0.71 inference(symmetry,[status(thm)],[73])).
% 0.53/0.71 tff(75,plain,
% 0.53/0.71 (multiply(sk_c10, sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.53/0.71 inference(monotonicity,[status(thm)],[74])).
% 0.53/0.71 tff(76,plain,
% 0.53/0.71 (multiply(sk_c10, sk_c3) = identity),
% 0.53/0.71 inference(transitivity,[status(thm)],[75, 23])).
% 0.53/0.71 tff(77,plain,
% 0.53/0.71 (multiply(multiply(sk_c10, sk_c3), sk_c10) = multiply(identity, sk_c10)),
% 0.53/0.71 inference(monotonicity,[status(thm)],[76])).
% 0.53/0.71 tff(78,plain,
% 0.53/0.71 (((inverse(sk_c1) = sk_c10) | (multiply(sk_c3, sk_c10) = sk_c4)) <=> ((inverse(sk_c1) = sk_c10) | (multiply(sk_c3, sk_c10) = sk_c4))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(79,axiom,((inverse(sk_c1) = sk_c10) | (multiply(sk_c3, sk_c10) = sk_c4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_48')).
% 0.53/0.71 tff(80,plain,
% 0.53/0.71 ((inverse(sk_c1) = sk_c10) | (multiply(sk_c3, sk_c10) = sk_c4)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.53/0.71 tff(81,plain,
% 0.53/0.71 (multiply(sk_c3, sk_c10) = sk_c4),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[80, 69])).
% 0.53/0.71 tff(82,plain,
% 0.53/0.71 (sk_c4 = multiply(sk_c3, sk_c10)),
% 0.53/0.71 inference(symmetry,[status(thm)],[81])).
% 0.53/0.71 tff(83,plain,
% 0.53/0.71 (multiply(sk_c10, sk_c4) = multiply(sk_c10, multiply(sk_c3, sk_c10))),
% 0.53/0.71 inference(monotonicity,[status(thm)],[82])).
% 0.53/0.71 tff(84,plain,
% 0.53/0.71 (((inverse(sk_c1) = sk_c10) | (multiply(sk_c10, sk_c4) = sk_c9)) <=> ((inverse(sk_c1) = sk_c10) | (multiply(sk_c10, sk_c4) = sk_c9))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(85,axiom,((inverse(sk_c1) = sk_c10) | (multiply(sk_c10, sk_c4) = sk_c9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_47')).
% 0.53/0.71 tff(86,plain,
% 0.53/0.71 ((inverse(sk_c1) = sk_c10) | (multiply(sk_c10, sk_c4) = sk_c9)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.53/0.71 tff(87,plain,
% 0.53/0.71 (multiply(sk_c10, sk_c4) = sk_c9),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[86, 69])).
% 0.53/0.71 tff(88,plain,
% 0.53/0.71 (sk_c9 = multiply(sk_c10, sk_c4)),
% 0.53/0.71 inference(symmetry,[status(thm)],[87])).
% 0.53/0.71 tff(89,plain,
% 0.53/0.71 (sk_c9 = sk_c10),
% 0.53/0.71 inference(transitivity,[status(thm)],[88, 83, 44, 77, 21])).
% 0.53/0.71 tff(90,plain,
% 0.53/0.71 (multiply(sk_c9, sk_c8) = multiply(sk_c10, sk_c8)),
% 0.53/0.71 inference(monotonicity,[status(thm)],[89])).
% 0.53/0.71 tff(91,plain,
% 0.53/0.71 ((multiply(sk_c9, sk_c8) = sk_c10) <=> (multiply(sk_c10, sk_c8) = sk_c10)),
% 0.53/0.71 inference(monotonicity,[status(thm)],[90])).
% 0.53/0.71 tff(92,plain,
% 0.53/0.71 ((multiply(sk_c10, sk_c8) = sk_c10) <=> (multiply(sk_c9, sk_c8) = sk_c10)),
% 0.53/0.71 inference(symmetry,[status(thm)],[91])).
% 0.53/0.71 tff(93,plain,
% 0.53/0.71 (multiply(inverse(sk_c3), sk_c3) = multiply(sk_c10, sk_c3)),
% 0.53/0.71 inference(symmetry,[status(thm)],[75])).
% 0.53/0.71 tff(94,plain,
% 0.53/0.71 (identity = multiply(inverse(sk_c3), sk_c3)),
% 0.53/0.71 inference(symmetry,[status(thm)],[23])).
% 0.53/0.71 tff(95,plain,
% 0.53/0.71 (((inverse(sk_c1) = sk_c10) | (inverse(sk_c10) = sk_c9)) <=> ((inverse(sk_c1) = sk_c10) | (inverse(sk_c10) = sk_c9))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(96,axiom,((inverse(sk_c1) = sk_c10) | (inverse(sk_c10) = sk_c9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_46')).
% 0.53/0.71 tff(97,plain,
% 0.53/0.71 ((inverse(sk_c1) = sk_c10) | (inverse(sk_c10) = sk_c9)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.53/0.71 tff(98,plain,
% 0.53/0.71 (inverse(sk_c10) = sk_c9),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[97, 69])).
% 0.53/0.71 tff(99,plain,
% 0.53/0.71 (sk_c9 = inverse(sk_c10)),
% 0.53/0.71 inference(symmetry,[status(thm)],[98])).
% 0.53/0.71 tff(100,plain,
% 0.53/0.71 (multiply(sk_c9, sk_c10) = multiply(inverse(sk_c10), sk_c10)),
% 0.53/0.71 inference(monotonicity,[status(thm)],[99])).
% 0.53/0.71 tff(101,plain,
% 0.53/0.71 (multiply(sk_c9, sk_c10) = multiply(sk_c10, sk_c3)),
% 0.53/0.71 inference(transitivity,[status(thm)],[100, 12, 94, 93])).
% 0.53/0.71 tff(102,plain,
% 0.53/0.71 (multiply(multiply(sk_c9, sk_c10), sk_c10) = multiply(multiply(sk_c10, sk_c3), sk_c10)),
% 0.53/0.71 inference(monotonicity,[status(thm)],[101])).
% 0.53/0.71 tff(103,plain,
% 0.53/0.71 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c9, sk_c10), sk_c10) = multiply(sk_c9, multiply(sk_c10, sk_c10)))),
% 0.53/0.71 inference(quant_inst,[status(thm)],[])).
% 0.53/0.71 tff(104,plain,
% 0.53/0.71 (multiply(multiply(sk_c9, sk_c10), sk_c10) = multiply(sk_c9, multiply(sk_c10, sk_c10))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[103, 41])).
% 0.53/0.71 tff(105,plain,
% 0.53/0.71 (multiply(sk_c9, multiply(sk_c10, sk_c10)) = multiply(multiply(sk_c9, sk_c10), sk_c10)),
% 0.53/0.71 inference(symmetry,[status(thm)],[104])).
% 0.53/0.71 tff(106,plain,
% 0.53/0.71 (multiply(sk_c10, multiply(sk_c3, sk_c10)) = multiply(sk_c10, sk_c4)),
% 0.53/0.71 inference(symmetry,[status(thm)],[83])).
% 0.53/0.71 tff(107,plain,
% 0.53/0.71 (multiply(identity, sk_c10) = multiply(multiply(sk_c10, sk_c3), sk_c10)),
% 0.53/0.71 inference(symmetry,[status(thm)],[77])).
% 0.53/0.71 tff(108,plain,
% 0.53/0.71 (sk_c10 = multiply(identity, sk_c10)),
% 0.53/0.71 inference(symmetry,[status(thm)],[21])).
% 0.53/0.71 tff(109,plain,
% 0.53/0.71 (sk_c10 = sk_c9),
% 0.53/0.71 inference(transitivity,[status(thm)],[108, 107, 43, 106, 87])).
% 0.53/0.71 tff(110,plain,
% 0.53/0.71 (multiply(sk_c10, multiply(sk_c10, sk_c10)) = multiply(sk_c9, multiply(sk_c10, sk_c10))),
% 0.53/0.71 inference(monotonicity,[status(thm)],[109])).
% 0.53/0.71 tff(111,plain,
% 0.53/0.71 (sk_c10 = inverse(sk_c10)),
% 0.53/0.71 inference(transitivity,[status(thm)],[108, 107, 43, 106, 87, 99])).
% 0.53/0.71 tff(112,plain,
% 0.53/0.71 (multiply(sk_c10, sk_c10) = multiply(inverse(sk_c10), sk_c10)),
% 0.53/0.71 inference(monotonicity,[status(thm)],[111])).
% 0.53/0.71 tff(113,plain,
% 0.53/0.71 (multiply(inverse(sk_c10), sk_c10) = multiply(sk_c10, sk_c10)),
% 0.53/0.71 inference(symmetry,[status(thm)],[112])).
% 0.53/0.71 tff(114,plain,
% 0.53/0.71 (((inverse(sk_c1) = sk_c10) | (multiply(sk_c7, sk_c8) = sk_c10)) <=> ((inverse(sk_c1) = sk_c10) | (multiply(sk_c7, sk_c8) = sk_c10))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(115,axiom,((inverse(sk_c1) = sk_c10) | (multiply(sk_c7, sk_c8) = sk_c10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_54')).
% 0.53/0.71 tff(116,plain,
% 0.53/0.71 ((inverse(sk_c1) = sk_c10) | (multiply(sk_c7, sk_c8) = sk_c10)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.53/0.71 tff(117,plain,
% 0.53/0.71 (multiply(sk_c7, sk_c8) = sk_c10),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[116, 69])).
% 0.53/0.71 tff(118,plain,
% 0.53/0.71 (multiply(sk_c9, multiply(sk_c7, sk_c8)) = multiply(inverse(sk_c10), sk_c10)),
% 0.53/0.71 inference(monotonicity,[status(thm)],[99, 117])).
% 0.53/0.71 tff(119,plain,
% 0.53/0.71 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c9, sk_c7), sk_c8) = multiply(sk_c9, multiply(sk_c7, sk_c8)))),
% 0.53/0.71 inference(quant_inst,[status(thm)],[])).
% 0.53/0.71 tff(120,plain,
% 0.53/0.71 (multiply(multiply(sk_c9, sk_c7), sk_c8) = multiply(sk_c9, multiply(sk_c7, sk_c8))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[119, 41])).
% 0.53/0.71 tff(121,plain,
% 0.53/0.71 (((inverse(sk_c1) = sk_c10) | (inverse(sk_c7) = sk_c10)) <=> ((inverse(sk_c1) = sk_c10) | (inverse(sk_c7) = sk_c10))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(122,axiom,((inverse(sk_c1) = sk_c10) | (inverse(sk_c7) = sk_c10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_53')).
% 0.53/0.71 tff(123,plain,
% 0.53/0.71 ((inverse(sk_c1) = sk_c10) | (inverse(sk_c7) = sk_c10)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.53/0.71 tff(124,plain,
% 0.53/0.71 (inverse(sk_c7) = sk_c10),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[123, 69])).
% 0.53/0.71 tff(125,plain,
% 0.53/0.71 (sk_c10 = inverse(sk_c7)),
% 0.53/0.71 inference(symmetry,[status(thm)],[124])).
% 0.53/0.71 tff(126,plain,
% 0.53/0.71 (sk_c9 = inverse(sk_c7)),
% 0.53/0.71 inference(transitivity,[status(thm)],[88, 83, 44, 77, 21, 125])).
% 0.53/0.71 tff(127,plain,
% 0.53/0.71 (multiply(sk_c9, sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.53/0.71 inference(monotonicity,[status(thm)],[126])).
% 0.53/0.71 tff(128,plain,
% 0.53/0.71 (multiply(inverse(sk_c7), sk_c7) = multiply(sk_c9, sk_c7)),
% 0.53/0.71 inference(symmetry,[status(thm)],[127])).
% 0.53/0.71 tff(129,plain,
% 0.53/0.71 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c7), sk_c7) = identity)),
% 0.53/0.71 inference(quant_inst,[status(thm)],[])).
% 0.53/0.71 tff(130,plain,
% 0.53/0.71 (multiply(inverse(sk_c7), sk_c7) = identity),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[129, 7])).
% 0.53/0.71 tff(131,plain,
% 0.53/0.71 (identity = multiply(inverse(sk_c7), sk_c7)),
% 0.53/0.71 inference(symmetry,[status(thm)],[130])).
% 0.53/0.71 tff(132,plain,
% 0.53/0.71 (identity = multiply(sk_c9, sk_c7)),
% 0.53/0.71 inference(transitivity,[status(thm)],[131, 128])).
% 0.53/0.71 tff(133,plain,
% 0.53/0.71 (multiply(identity, sk_c8) = multiply(multiply(sk_c9, sk_c7), sk_c8)),
% 0.53/0.71 inference(monotonicity,[status(thm)],[132])).
% 0.53/0.71 tff(134,plain,
% 0.53/0.71 (sk_c8 = multiply(identity, sk_c8)),
% 0.53/0.71 inference(symmetry,[status(thm)],[52])).
% 0.53/0.71 tff(135,plain,
% 0.53/0.71 (sk_c8 = multiply(sk_c10, sk_c10)),
% 0.53/0.71 inference(transitivity,[status(thm)],[134, 133, 120, 118, 113])).
% 0.53/0.71 tff(136,plain,
% 0.53/0.71 (multiply(sk_c10, sk_c8) = multiply(sk_c10, multiply(sk_c10, sk_c10))),
% 0.53/0.71 inference(monotonicity,[status(thm)],[135])).
% 0.53/0.71 tff(137,plain,
% 0.53/0.71 (multiply(sk_c10, sk_c8) = sk_c10),
% 0.53/0.71 inference(transitivity,[status(thm)],[136, 110, 105, 102, 77, 21])).
% 0.53/0.71 tff(138,plain,
% 0.53/0.71 (multiply(sk_c9, sk_c8) = sk_c10),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[137, 92])).
% 0.53/0.71 tff(139,plain,
% 0.53/0.71 (((inverse(sk_c1) = sk_c10) | (multiply(sk_c5, sk_c6) = sk_c8)) <=> ((inverse(sk_c1) = sk_c10) | (multiply(sk_c5, sk_c6) = sk_c8))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(140,axiom,((inverse(sk_c1) = sk_c10) | (multiply(sk_c5, sk_c6) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_50')).
% 0.53/0.71 tff(141,plain,
% 0.53/0.71 ((inverse(sk_c1) = sk_c10) | (multiply(sk_c5, sk_c6) = sk_c8)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.53/0.71 tff(142,plain,
% 0.53/0.71 (multiply(sk_c5, sk_c6) = sk_c8),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[141, 69])).
% 0.53/0.71 tff(143,plain,
% 0.53/0.71 (((inverse(sk_c1) = sk_c10) | (inverse(sk_c5) = sk_c6)) <=> ((inverse(sk_c1) = sk_c10) | (inverse(sk_c5) = sk_c6))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(144,axiom,((inverse(sk_c1) = sk_c10) | (inverse(sk_c5) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_51')).
% 0.53/0.71 tff(145,plain,
% 0.53/0.71 ((inverse(sk_c1) = sk_c10) | (inverse(sk_c5) = sk_c6)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.53/0.71 tff(146,plain,
% 0.53/0.71 (inverse(sk_c5) = sk_c6),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[145, 69])).
% 0.53/0.71 tff(147,plain,
% 0.53/0.71 (multiply(sk_c5, inverse(sk_c5)) = multiply(sk_c5, sk_c6)),
% 0.53/0.71 inference(monotonicity,[status(thm)],[146])).
% 0.53/0.71 tff(148,plain,
% 0.53/0.71 (multiply(sk_c5, inverse(sk_c5)) = sk_c8),
% 0.53/0.71 inference(transitivity,[status(thm)],[147, 142])).
% 0.53/0.71 tff(149,plain,
% 0.53/0.71 (((inverse(sk_c1) = sk_c10) | (multiply(sk_c6, sk_c9) = sk_c8)) <=> ((inverse(sk_c1) = sk_c10) | (multiply(sk_c6, sk_c9) = sk_c8))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(150,axiom,((inverse(sk_c1) = sk_c10) | (multiply(sk_c6, sk_c9) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_52')).
% 0.53/0.71 tff(151,plain,
% 0.53/0.71 ((inverse(sk_c1) = sk_c10) | (multiply(sk_c6, sk_c9) = sk_c8)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.53/0.71 tff(152,plain,
% 0.53/0.71 (multiply(sk_c6, sk_c9) = sk_c8),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[151, 69])).
% 0.53/0.71 tff(153,plain,
% 0.53/0.71 (multiply(inverse(sk_c5), sk_c9) = multiply(sk_c6, sk_c9)),
% 0.53/0.71 inference(monotonicity,[status(thm)],[146])).
% 0.53/0.71 tff(154,plain,
% 0.53/0.71 (multiply(inverse(sk_c5), sk_c9) = sk_c8),
% 0.53/0.71 inference(transitivity,[status(thm)],[153, 152])).
% 0.53/0.71 tff(155,plain,
% 0.53/0.71 (multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9),
% 0.53/0.71 inference(transitivity,[status(thm)],[110, 105, 102, 43, 106, 87])).
% 0.53/0.71 tff(156,plain,
% 0.53/0.71 (inverse(sk_c10) = sk_c10),
% 0.53/0.71 inference(transitivity,[status(thm)],[98, 88, 83, 44, 77, 21])).
% 0.53/0.71 tff(157,plain,
% 0.53/0.71 (inverse(sk_c9) = inverse(sk_c10)),
% 0.53/0.71 inference(monotonicity,[status(thm)],[89])).
% 0.53/0.71 tff(158,plain,
% 0.53/0.71 (inverse(sk_c9) = sk_c10),
% 0.53/0.71 inference(transitivity,[status(thm)],[157, 98, 88, 83, 44, 77, 21])).
% 0.53/0.71 tff(159,assumption,(inverse(sk_c3) = sk_c10), introduced(assumption)).
% 0.53/0.71 tff(160,plain,
% 0.53/0.71 (sk_c10 = inverse(sk_c3)),
% 0.53/0.71 inference(symmetry,[status(thm)],[159])).
% 0.53/0.71 tff(161,plain,
% 0.53/0.71 (multiply(sk_c10, sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.53/0.71 inference(monotonicity,[status(thm)],[160])).
% 0.53/0.71 tff(162,plain,
% 0.53/0.71 (multiply(sk_c10, sk_c3) = identity),
% 0.53/0.71 inference(transitivity,[status(thm)],[161, 23])).
% 0.53/0.71 tff(163,plain,
% 0.53/0.71 (multiply(multiply(sk_c10, sk_c3), sk_c10) = multiply(identity, sk_c10)),
% 0.53/0.71 inference(monotonicity,[status(thm)],[162])).
% 0.53/0.71 tff(164,assumption,(multiply(sk_c3, sk_c10) = sk_c4), introduced(assumption)).
% 0.53/0.71 tff(165,plain,
% 0.53/0.71 (sk_c4 = multiply(sk_c3, sk_c10)),
% 0.53/0.71 inference(symmetry,[status(thm)],[164])).
% 0.53/0.71 tff(166,plain,
% 0.53/0.71 (multiply(sk_c10, sk_c4) = multiply(sk_c10, multiply(sk_c3, sk_c10))),
% 0.53/0.71 inference(monotonicity,[status(thm)],[165])).
% 0.53/0.71 tff(167,assumption,(multiply(sk_c10, sk_c4) = sk_c9), introduced(assumption)).
% 0.53/0.71 tff(168,plain,
% 0.53/0.71 (sk_c9 = multiply(sk_c10, sk_c4)),
% 0.53/0.71 inference(symmetry,[status(thm)],[167])).
% 0.53/0.71 tff(169,plain,
% 0.53/0.71 (sk_c9 = sk_c10),
% 0.53/0.71 inference(transitivity,[status(thm)],[168, 166, 44, 163, 21])).
% 0.53/0.71 tff(170,plain,
% 0.53/0.71 ((multiply(sk_c10, sk_c8) = sk_c9) <=> (multiply(sk_c10, sk_c8) = sk_c10)),
% 0.53/0.71 inference(monotonicity,[status(thm)],[169])).
% 0.53/0.71 tff(171,plain,
% 0.53/0.71 ((~(multiply(sk_c10, sk_c8) = sk_c9)) <=> (~(multiply(sk_c10, sk_c8) = sk_c10))),
% 0.53/0.71 inference(monotonicity,[status(thm)],[170])).
% 0.53/0.71 tff(172,assumption,(~(multiply(sk_c10, sk_c8) = sk_c9)), introduced(assumption)).
% 0.53/0.71 tff(173,plain,
% 0.53/0.71 (~(multiply(sk_c10, sk_c8) = sk_c10)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.53/0.71 tff(174,assumption,(multiply(sk_c10, sk_c8) = sk_c10), introduced(assumption)).
% 0.53/0.71 tff(175,plain,
% 0.53/0.71 ($false),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[174, 173])).
% 0.53/0.71 tff(176,plain,((multiply(sk_c10, sk_c8) = sk_c9) | (~(multiply(sk_c10, sk_c8) = sk_c10)) | (~(multiply(sk_c10, sk_c4) = sk_c9)) | (~(inverse(sk_c3) = sk_c10)) | (~(multiply(sk_c3, sk_c10) = sk_c4))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.71 tff(177,plain,
% 0.53/0.71 (multiply(sk_c10, sk_c8) = sk_c9),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[176, 137, 87, 73, 81])).
% 0.53/0.71 tff(178,plain,
% 0.53/0.71 (^[X4: $i, X2: $i, X7: $i, X5: $i] : refl(((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9))))),
% 0.53/0.71 inference(bind,[status(th)],[])).
% 0.53/0.71 tff(179,plain,
% 0.53/0.71 (![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9))) <=> ![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))),
% 0.53/0.71 inference(quant_intro,[status(thm)],[178])).
% 0.53/0.71 tff(180,plain,
% 0.53/0.71 (![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9))) <=> ![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(181,plain,
% 0.53/0.71 (^[X4: $i, X2: $i, X7: $i, X5: $i] : rewrite(((~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(inverse(X2) = sk_c10)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c10))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9))))),
% 0.53/0.72 inference(bind,[status(th)],[])).
% 0.53/0.72 tff(182,plain,
% 0.53/0.72 (![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(inverse(X2) = sk_c10)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c10))) <=> ![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))),
% 0.53/0.72 inference(quant_intro,[status(thm)],[181])).
% 0.53/0.72 tff(183,plain,
% 0.53/0.72 (![X6: $i, X4: $i, X3: $i, X2: $i, X7: $i, X5: $i, X1: $i] : ((~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(inverse(X2) = sk_c10)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c10))) <=> ![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(inverse(X2) = sk_c10)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c10)))),
% 0.53/0.72 inference(elim_unused_vars,[status(thm)],[])).
% 0.53/0.72 tff(184,plain,
% 0.53/0.72 (![X6: $i, X4: $i, X3: $i, X2: $i, X7: $i, X5: $i, X1: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(X6, sk_c9) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X2) = sk_c10)) | (~(multiply(X2, sk_c10) = X1)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))) <=> ![X6: $i, X4: $i, X3: $i, X2: $i, X7: $i, X5: $i, X1: $i] : ((~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(inverse(X2) = sk_c10)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c10)))),
% 0.53/0.72 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.53/0.72 tff(185,plain,
% 0.53/0.72 (![X6: $i, X4: $i, X3: $i, X2: $i, X7: $i, X5: $i, X1: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(X6, sk_c9) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X2) = sk_c10)) | (~(multiply(X2, sk_c10) = X1)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))) <=> ![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(inverse(X2) = sk_c10)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)) | (~(inverse(X4) = sk_c10)))),
% 0.53/0.72 inference(transitivity,[status(thm)],[184, 183])).
% 0.53/0.72 tff(186,plain,
% 0.53/0.72 (![X6: $i, X4: $i, X3: $i, X2: $i, X7: $i, X5: $i, X1: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(X6, sk_c9) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X2) = sk_c10)) | (~(multiply(X2, sk_c10) = X1)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))) <=> ![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))),
% 0.53/0.72 inference(transitivity,[status(thm)],[185, 182])).
% 0.53/0.72 tff(187,plain,
% 0.53/0.72 (^[X6: $i, X4: $i, X3: $i, X2: $i, X7: $i, X5: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)))), ((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(sk_c10, sk_c8) = sk_c9))) <=> (((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(sk_c10, sk_c8) = sk_c9))))), rewrite((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(sk_c10, sk_c8) = sk_c9))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)))), ((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(sk_c10, sk_c8) = sk_c9))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9))))), (((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(sk_c10, sk_c8) = sk_c9))) | (~(multiply(sk_c10, X3) = sk_c9))) <=> (((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9))) | (~(multiply(sk_c10, X3) = sk_c9))))), rewrite((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9))) | (~(multiply(sk_c10, X3) = sk_c9))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(multiply(sk_c10, X3) = sk_c9)))), (((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(sk_c10, sk_c8) = sk_c9))) | (~(multiply(sk_c10, X3) = sk_c9))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(multiply(sk_c10, X3) = sk_c9))))), ((((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(sk_c10, sk_c8) = sk_c9))) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X4, sk_c10) = X3))) <=> (((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X4, sk_c10) = X3))))), rewrite((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X4, sk_c10) = X3))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9)))), ((((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(sk_c10, sk_c8) = sk_c9))) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X4, sk_c10) = X3))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))))), (((((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(sk_c10, sk_c8) = sk_c9))) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X4, sk_c10) = X3))) | (~(inverse(X4) = sk_c10))) <=> (((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(inverse(X4) = sk_c10))))), rewrite((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(inverse(X4) = sk_c10))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9)))), (((((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(sk_c10, sk_c8) = sk_c9))) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X4, sk_c10) = X3))) | (~(inverse(X4) = sk_c10))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))))), ((((((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(sk_c10, sk_c8) = sk_c9))) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X4, sk_c10) = X3))) | (~(inverse(X4) = sk_c10))) | (~(inverse(sk_c10) = sk_c9))) <=> (((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(inverse(sk_c10) = sk_c9))))), rewrite((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(inverse(sk_c10) = sk_c9))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9)))), ((((((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(sk_c10, sk_c8) = sk_c9))) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X4, sk_c10) = X3))) | (~(inverse(X4) = sk_c10))) | (~(inverse(sk_c10) = sk_c9))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))))), (((((((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(sk_c10, sk_c8) = sk_c9))) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X4, sk_c10) = X3))) | (~(inverse(X4) = sk_c10))) | (~(inverse(sk_c10) = sk_c9))) | (~(multiply(sk_c10, X1) = sk_c9))) <=> (((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(sk_c10, X1) = sk_c9))))), rewrite((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(sk_c10, X1) = sk_c9))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9)))), (((((((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(sk_c10, sk_c8) = sk_c9))) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X4, sk_c10) = X3))) | (~(inverse(X4) = sk_c10))) | (~(inverse(sk_c10) = sk_c9))) | (~(multiply(sk_c10, X1) = sk_c9))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))))), ((((((((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(sk_c10, sk_c8) = sk_c9))) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X4, sk_c10) = X3))) | (~(inverse(X4) = sk_c10))) | (~(inverse(sk_c10) = sk_c9))) | (~(multiply(sk_c10, X1) = sk_c9))) | (~(multiply(X2, sk_c10) = X1))) <=> (((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X2, sk_c10) = X1))))), rewrite((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X2, sk_c10) = X1))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(X2, sk_c10) = X1)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9)))), ((((((((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(sk_c10, sk_c8) = sk_c9))) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X4, sk_c10) = X3))) | (~(inverse(X4) = sk_c10))) | (~(inverse(sk_c10) = sk_c9))) | (~(multiply(sk_c10, X1) = sk_c9))) | (~(multiply(X2, sk_c10) = X1))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(X2, sk_c10) = X1)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))))), (((((((((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(sk_c10, sk_c8) = sk_c9))) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X4, sk_c10) = X3))) | (~(inverse(X4) = sk_c10))) | (~(inverse(sk_c10) = sk_c9))) | (~(multiply(sk_c10, X1) = sk_c9))) | (~(multiply(X2, sk_c10) = X1))) | (~(inverse(X2) = sk_c10))) <=> (((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(X2, sk_c10) = X1)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(inverse(X2) = sk_c10))))), rewrite((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(X2, sk_c10) = X1)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(inverse(X2) = sk_c10))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(multiply(X2, sk_c10) = X1)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9)))), (((((((((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(sk_c10, sk_c8) = sk_c9))) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X4, sk_c10) = X3))) | (~(inverse(X4) = sk_c10))) | (~(inverse(sk_c10) = sk_c9))) | (~(multiply(sk_c10, X1) = sk_c9))) | (~(multiply(X2, sk_c10) = X1))) | (~(inverse(X2) = sk_c10))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(multiply(X2, sk_c10) = X1)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))))), ((((((((((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(sk_c10, sk_c8) = sk_c9))) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X4, sk_c10) = X3))) | (~(inverse(X4) = sk_c10))) | (~(inverse(sk_c10) = sk_c9))) | (~(multiply(sk_c10, X1) = sk_c9))) | (~(multiply(X2, sk_c10) = X1))) | (~(inverse(X2) = sk_c10))) | (~(multiply(X5, X6) = sk_c8))) <=> (((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(multiply(X2, sk_c10) = X1)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X5, X6) = sk_c8))))), rewrite((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(multiply(X2, sk_c10) = X1)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X5, X6) = sk_c8))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X2) = sk_c10)) | (~(multiply(X2, sk_c10) = X1)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9)))), ((((((((((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(sk_c10, sk_c8) = sk_c9))) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X4, sk_c10) = X3))) | (~(inverse(X4) = sk_c10))) | (~(inverse(sk_c10) = sk_c9))) | (~(multiply(sk_c10, X1) = sk_c9))) | (~(multiply(X2, sk_c10) = X1))) | (~(inverse(X2) = sk_c10))) | (~(multiply(X5, X6) = sk_c8))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X2) = sk_c10)) | (~(multiply(X2, sk_c10) = X1)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))))), (((((((((((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(sk_c10, sk_c8) = sk_c9))) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X4, sk_c10) = X3))) | (~(inverse(X4) = sk_c10))) | (~(inverse(sk_c10) = sk_c9))) | (~(multiply(sk_c10, X1) = sk_c9))) | (~(multiply(X2, sk_c10) = X1))) | (~(inverse(X2) = sk_c10))) | (~(multiply(X5, X6) = sk_c8))) | (~(inverse(X5) = X6))) <=> (((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X2) = sk_c10)) | (~(multiply(X2, sk_c10) = X1)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(inverse(X5) = X6))))), rewrite((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X2) = sk_c10)) | (~(multiply(X2, sk_c10) = X1)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(inverse(X5) = X6))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X2) = sk_c10)) | (~(multiply(X2, sk_c10) = X1)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9)))), (((((((((((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(sk_c10, sk_c8) = sk_c9))) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X4, sk_c10) = X3))) | (~(inverse(X4) = sk_c10))) | (~(inverse(sk_c10) = sk_c9))) | (~(multiply(sk_c10, X1) = sk_c9))) | (~(multiply(X2, sk_c10) = X1))) | (~(inverse(X2) = sk_c10))) | (~(multiply(X5, X6) = sk_c8))) | (~(inverse(X5) = X6))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X2) = sk_c10)) | (~(multiply(X2, sk_c10) = X1)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))))), ((((((((((((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(sk_c10, sk_c8) = sk_c9))) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X4, sk_c10) = X3))) | (~(inverse(X4) = sk_c10))) | (~(inverse(sk_c10) = sk_c9))) | (~(multiply(sk_c10, X1) = sk_c9))) | (~(multiply(X2, sk_c10) = X1))) | (~(inverse(X2) = sk_c10))) | (~(multiply(X5, X6) = sk_c8))) | (~(inverse(X5) = X6))) | (~(multiply(X6, sk_c9) = sk_c8))) <=> (((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X2) = sk_c10)) | (~(multiply(X2, sk_c10) = X1)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X6, sk_c9) = sk_c8))))), rewrite((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X2) = sk_c10)) | (~(multiply(X2, sk_c10) = X1)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X6, sk_c9) = sk_c8))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(X6, sk_c9) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X2) = sk_c10)) | (~(multiply(X2, sk_c10) = X1)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9)))), ((((((((((((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(sk_c10, sk_c8) = sk_c9))) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X4, sk_c10) = X3))) | (~(inverse(X4) = sk_c10))) | (~(inverse(sk_c10) = sk_c9))) | (~(multiply(sk_c10, X1) = sk_c9))) | (~(multiply(X2, sk_c10) = X1))) | (~(inverse(X2) = sk_c10))) | (~(multiply(X5, X6) = sk_c8))) | (~(inverse(X5) = X6))) | (~(multiply(X6, sk_c9) = sk_c8))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(X6, sk_c9) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X2) = sk_c10)) | (~(multiply(X2, sk_c10) = X1)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))))), (((((((((((((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(sk_c10, sk_c8) = sk_c9))) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X4, sk_c10) = X3))) | (~(inverse(X4) = sk_c10))) | (~(inverse(sk_c10) = sk_c9))) | (~(multiply(sk_c10, X1) = sk_c9))) | (~(multiply(X2, sk_c10) = X1))) | (~(inverse(X2) = sk_c10))) | (~(multiply(X5, X6) = sk_c8))) | (~(inverse(X5) = X6))) | (~(multiply(X6, sk_c9) = sk_c8))) | (~(inverse(X7) = sk_c10))) <=> (((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(X6, sk_c9) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X2) = sk_c10)) | (~(multiply(X2, sk_c10) = X1)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(inverse(X7) = sk_c10))))), rewrite((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(X6, sk_c9) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X2) = sk_c10)) | (~(multiply(X2, sk_c10) = X1)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(inverse(X7) = sk_c10))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X7) = sk_c10)) | (~(multiply(X6, sk_c9) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X2) = sk_c10)) | (~(multiply(X2, sk_c10) = X1)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9)))), (((((((((((((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(sk_c10, sk_c8) = sk_c9))) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X4, sk_c10) = X3))) | (~(inverse(X4) = sk_c10))) | (~(inverse(sk_c10) = sk_c9))) | (~(multiply(sk_c10, X1) = sk_c9))) | (~(multiply(X2, sk_c10) = X1))) | (~(inverse(X2) = sk_c10))) | (~(multiply(X5, X6) = sk_c8))) | (~(inverse(X5) = X6))) | (~(multiply(X6, sk_c9) = sk_c8))) | (~(inverse(X7) = sk_c10))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X7) = sk_c10)) | (~(multiply(X6, sk_c9) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X2) = sk_c10)) | (~(multiply(X2, sk_c10) = X1)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))))), ((((((((((((((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(sk_c10, sk_c8) = sk_c9))) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X4, sk_c10) = X3))) | (~(inverse(X4) = sk_c10))) | (~(inverse(sk_c10) = sk_c9))) | (~(multiply(sk_c10, X1) = sk_c9))) | (~(multiply(X2, sk_c10) = X1))) | (~(inverse(X2) = sk_c10))) | (~(multiply(X5, X6) = sk_c8))) | (~(inverse(X5) = X6))) | (~(multiply(X6, sk_c9) = sk_c8))) | (~(inverse(X7) = sk_c10))) | (~(multiply(X7, sk_c8) = sk_c10))) <=> (((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X7) = sk_c10)) | (~(multiply(X6, sk_c9) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X2) = sk_c10)) | (~(multiply(X2, sk_c10) = X1)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X7, sk_c8) = sk_c10))))), rewrite((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X7) = sk_c10)) | (~(multiply(X6, sk_c9) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X2) = sk_c10)) | (~(multiply(X2, sk_c10) = X1)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X7, sk_c8) = sk_c10))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(X6, sk_c9) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X2) = sk_c10)) | (~(multiply(X2, sk_c10) = X1)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9)))), ((((((((((((((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(sk_c10, sk_c8) = sk_c9))) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X4, sk_c10) = X3))) | (~(inverse(X4) = sk_c10))) | (~(inverse(sk_c10) = sk_c9))) | (~(multiply(sk_c10, X1) = sk_c9))) | (~(multiply(X2, sk_c10) = X1))) | (~(inverse(X2) = sk_c10))) | (~(multiply(X5, X6) = sk_c8))) | (~(inverse(X5) = X6))) | (~(multiply(X6, sk_c9) = sk_c8))) | (~(inverse(X7) = sk_c10))) | (~(multiply(X7, sk_c8) = sk_c10))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(X6, sk_c9) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X2) = sk_c10)) | (~(multiply(X2, sk_c10) = X1)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9)))))),
% 0.53/0.73 inference(bind,[status(th)],[])).
% 0.53/0.73 tff(188,plain,
% 0.53/0.73 (![X6: $i, X4: $i, X3: $i, X2: $i, X7: $i, X5: $i, X1: $i] : (((((((((((((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(sk_c10, sk_c8) = sk_c9))) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X4, sk_c10) = X3))) | (~(inverse(X4) = sk_c10))) | (~(inverse(sk_c10) = sk_c9))) | (~(multiply(sk_c10, X1) = sk_c9))) | (~(multiply(X2, sk_c10) = X1))) | (~(inverse(X2) = sk_c10))) | (~(multiply(X5, X6) = sk_c8))) | (~(inverse(X5) = X6))) | (~(multiply(X6, sk_c9) = sk_c8))) | (~(inverse(X7) = sk_c10))) | (~(multiply(X7, sk_c8) = sk_c10))) <=> ![X6: $i, X4: $i, X3: $i, X2: $i, X7: $i, X5: $i, X1: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(X6, sk_c9) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X2) = sk_c10)) | (~(multiply(X2, sk_c10) = X1)) | (~(multiply(sk_c10, X1) = sk_c9)) | (~(inverse(X4) = sk_c10)) | (~(multiply(X4, sk_c10) = X3)) | (~(multiply(sk_c10, X3) = sk_c9)))),
% 0.53/0.73 inference(quant_intro,[status(thm)],[187])).
% 0.53/0.73 tff(189,plain,
% 0.53/0.73 (![X6: $i, X4: $i, X3: $i, X2: $i, X7: $i, X5: $i, X1: $i] : (((((((((((((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(sk_c10, sk_c8) = sk_c9))) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X4, sk_c10) = X3))) | (~(inverse(X4) = sk_c10))) | (~(inverse(sk_c10) = sk_c9))) | (~(multiply(sk_c10, X1) = sk_c9))) | (~(multiply(X2, sk_c10) = X1))) | (~(inverse(X2) = sk_c10))) | (~(multiply(X5, X6) = sk_c8))) | (~(inverse(X5) = X6))) | (~(multiply(X6, sk_c9) = sk_c8))) | (~(inverse(X7) = sk_c10))) | (~(multiply(X7, sk_c8) = sk_c10))) <=> ![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))),
% 0.53/0.73 inference(transitivity,[status(thm)],[188, 186])).
% 0.53/0.73 tff(190,axiom,(![X6: $i, X4: $i, X3: $i, X2: $i, X7: $i, X5: $i, X1: $i] : (((((((((((((((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10))) | (~(multiply(sk_c10, sk_c8) = sk_c9))) | (~(multiply(sk_c10, X3) = sk_c9))) | (~(multiply(X4, sk_c10) = X3))) | (~(inverse(X4) = sk_c10))) | (~(inverse(sk_c10) = sk_c9))) | (~(multiply(sk_c10, X1) = sk_c9))) | (~(multiply(X2, sk_c10) = X1))) | (~(inverse(X2) = sk_c10))) | (~(multiply(X5, X6) = sk_c8))) | (~(inverse(X5) = X6))) | (~(multiply(X6, sk_c9) = sk_c8))) | (~(inverse(X7) = sk_c10))) | (~(multiply(X7, sk_c8) = sk_c10)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_55')).
% 0.53/0.73 tff(191,plain,
% 0.53/0.73 (![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.53/0.73 tff(192,plain,
% 0.53/0.73 (![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[191, 180])).
% 0.53/0.73 tff(193,plain,(
% 0.53/0.73 ![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))),
% 0.53/0.73 inference(skolemize,[status(sab)],[192])).
% 0.53/0.73 tff(194,plain,
% 0.53/0.73 (![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[193, 179])).
% 0.53/0.73 tff(195,plain,
% 0.53/0.73 (((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c10) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c8) = sk_c10)) | (~(multiply(inverse(sk_c5), sk_c9) = sk_c8)) | (~(multiply(sk_c5, inverse(sk_c5)) = sk_c8)))) <=> ((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | (~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c10) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c8) = sk_c10)) | (~(multiply(inverse(sk_c5), sk_c9) = sk_c8)) | (~(multiply(sk_c5, inverse(sk_c5)) = sk_c8)))),
% 0.53/0.74 inference(rewrite,[status(thm)],[])).
% 0.53/0.74 tff(196,plain,
% 0.53/0.74 (((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c10) = sk_c10)) | (~(inverse(sk_c10) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c8) = sk_c10)) | (~(inverse(sk_c10) = sk_c10)) | (~(multiply(inverse(sk_c5), sk_c9) = sk_c8)) | (~(multiply(sk_c5, inverse(sk_c5)) = sk_c8)) | (~(multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c10) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c8) = sk_c10)) | (~(multiply(inverse(sk_c5), sk_c9) = sk_c8)) | (~(multiply(sk_c5, inverse(sk_c5)) = sk_c8)))),
% 0.53/0.74 inference(rewrite,[status(thm)],[])).
% 0.53/0.74 tff(197,plain,
% 0.53/0.74 (((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c10) = sk_c10)) | (~(inverse(sk_c10) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c8) = sk_c10)) | (~(inverse(sk_c10) = sk_c10)) | (~(multiply(inverse(sk_c5), sk_c9) = sk_c8)) | (~(multiply(sk_c5, inverse(sk_c5)) = sk_c8)) | (~(multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9)))) <=> ((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c10) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c8) = sk_c10)) | (~(multiply(inverse(sk_c5), sk_c9) = sk_c8)) | (~(multiply(sk_c5, inverse(sk_c5)) = sk_c8))))),
% 0.53/0.74 inference(monotonicity,[status(thm)],[196])).
% 0.53/0.74 tff(198,plain,
% 0.53/0.74 (((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c10) = sk_c10)) | (~(inverse(sk_c10) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c8) = sk_c10)) | (~(inverse(sk_c10) = sk_c10)) | (~(multiply(inverse(sk_c5), sk_c9) = sk_c8)) | (~(multiply(sk_c5, inverse(sk_c5)) = sk_c8)) | (~(multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9)))) <=> ((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | (~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c10) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c8) = sk_c10)) | (~(multiply(inverse(sk_c5), sk_c9) = sk_c8)) | (~(multiply(sk_c5, inverse(sk_c5)) = sk_c8)))),
% 0.53/0.74 inference(transitivity,[status(thm)],[197, 195])).
% 0.53/0.74 tff(199,plain,
% 0.53/0.74 ((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c10) = sk_c10)) | (~(inverse(sk_c10) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c8) = sk_c10)) | (~(inverse(sk_c10) = sk_c10)) | (~(multiply(inverse(sk_c5), sk_c9) = sk_c8)) | (~(multiply(sk_c5, inverse(sk_c5)) = sk_c8)) | (~(multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9)))),
% 0.53/0.74 inference(quant_inst,[status(thm)],[])).
% 0.53/0.74 tff(200,plain,
% 0.53/0.74 ((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | (~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c10) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c8) = sk_c10)) | (~(multiply(inverse(sk_c5), sk_c9) = sk_c8)) | (~(multiply(sk_c5, inverse(sk_c5)) = sk_c8))),
% 0.53/0.74 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.53/0.74 tff(201,plain,
% 0.53/0.74 ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c8) = sk_c10)) | (~(multiply(inverse(sk_c5), sk_c9) = sk_c8)) | (~(multiply(sk_c5, inverse(sk_c5)) = sk_c8))),
% 0.53/0.74 inference(unit_resolution,[status(thm)],[200, 98, 194])).
% 0.53/0.74 tff(202,plain,
% 0.53/0.74 (~(multiply(sk_c9, sk_c8) = sk_c10)),
% 0.53/0.74 inference(unit_resolution,[status(thm)],[201, 177, 158, 156, 155, 137, 154, 148])).
% 0.53/0.74 tff(203,plain,
% 0.53/0.74 ($false),
% 0.53/0.74 inference(unit_resolution,[status(thm)],[202, 138])).
% 0.53/0.74 tff(204,plain,(inverse(sk_c1) = sk_c10), inference(lemma,lemma(discharge,[]))).
% 0.53/0.74 tff(205,plain,
% 0.53/0.74 (sk_c10 = inverse(sk_c1)),
% 0.53/0.74 inference(symmetry,[status(thm)],[204])).
% 0.53/0.74 tff(206,plain,
% 0.53/0.74 (multiply(sk_c10, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.53/0.74 inference(monotonicity,[status(thm)],[205])).
% 0.53/0.74 tff(207,plain,
% 0.53/0.74 (multiply(sk_c10, sk_c1) = identity),
% 0.53/0.74 inference(transitivity,[status(thm)],[206, 68])).
% 0.53/0.74 tff(208,plain,
% 0.53/0.74 (multiply(multiply(sk_c10, sk_c1), sk_c10) = multiply(identity, sk_c10)),
% 0.53/0.74 inference(monotonicity,[status(thm)],[207])).
% 0.53/0.74 tff(209,plain,
% 0.53/0.74 (multiply(identity, sk_c10) = multiply(multiply(sk_c10, sk_c1), sk_c10)),
% 0.53/0.74 inference(symmetry,[status(thm)],[208])).
% 0.53/0.74 tff(210,plain,
% 0.53/0.74 (sk_c10 = sk_c9),
% 0.53/0.74 inference(transitivity,[status(thm)],[108, 209, 66, 64, 57])).
% 0.53/0.74 tff(211,plain,
% 0.53/0.74 (multiply(sk_c10, sk_c10) = multiply(inverse(sk_c1), sk_c9)),
% 0.53/0.74 inference(monotonicity,[status(thm)],[205, 210])).
% 0.53/0.74 tff(212,plain,
% 0.53/0.74 (multiply(inverse(sk_c1), sk_c9) = multiply(sk_c10, sk_c10)),
% 0.53/0.74 inference(symmetry,[status(thm)],[211])).
% 0.53/0.74 tff(213,plain,
% 0.53/0.74 (((inverse(sk_c9) = sk_c10) | (multiply(sk_c10, sk_c4) = sk_c9)) <=> ((inverse(sk_c9) = sk_c10) | (multiply(sk_c10, sk_c4) = sk_c9))),
% 0.53/0.74 inference(rewrite,[status(thm)],[])).
% 0.53/0.74 tff(214,axiom,((inverse(sk_c9) = sk_c10) | (multiply(sk_c10, sk_c4) = sk_c9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_11')).
% 0.53/0.74 tff(215,plain,
% 0.53/0.74 ((inverse(sk_c9) = sk_c10) | (multiply(sk_c10, sk_c4) = sk_c9)),
% 0.53/0.74 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.53/0.74 tff(216,plain,
% 0.53/0.74 (inverse(sk_c9) = sk_c10),
% 0.53/0.74 inference(unit_resolution,[status(thm)],[215, 53])).
% 0.53/0.74 tff(217,plain,
% 0.53/0.74 (inverse(sk_c9) = inverse(sk_c1)),
% 0.53/0.74 inference(transitivity,[status(thm)],[216, 205])).
% 0.53/0.74 tff(218,plain,
% 0.53/0.74 (multiply(inverse(sk_c9), sk_c9) = multiply(inverse(sk_c1), sk_c9)),
% 0.53/0.74 inference(monotonicity,[status(thm)],[217])).
% 0.53/0.74 tff(219,plain,
% 0.53/0.74 (identity = multiply(sk_c10, sk_c10)),
% 0.53/0.74 inference(transitivity,[status(thm)],[10, 218, 212])).
% 0.53/0.74 tff(220,plain,
% 0.53/0.74 (multiply(identity, sk_c8) = multiply(multiply(sk_c10, sk_c10), sk_c8)),
% 0.53/0.74 inference(monotonicity,[status(thm)],[219])).
% 0.53/0.74 tff(221,plain,
% 0.53/0.74 (multiply(multiply(sk_c10, sk_c10), sk_c8) = multiply(identity, sk_c8)),
% 0.53/0.74 inference(symmetry,[status(thm)],[220])).
% 0.53/0.74 tff(222,plain,
% 0.53/0.74 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c10, sk_c10), sk_c8) = multiply(sk_c10, multiply(sk_c10, sk_c8)))),
% 0.53/0.74 inference(quant_inst,[status(thm)],[])).
% 0.53/0.74 tff(223,plain,
% 0.53/0.74 (multiply(multiply(sk_c10, sk_c10), sk_c8) = multiply(sk_c10, multiply(sk_c10, sk_c8))),
% 0.53/0.74 inference(unit_resolution,[status(thm)],[222, 41])).
% 0.53/0.74 tff(224,plain,
% 0.53/0.74 (multiply(sk_c10, multiply(sk_c10, sk_c8)) = multiply(multiply(sk_c10, sk_c10), sk_c8)),
% 0.53/0.74 inference(symmetry,[status(thm)],[223])).
% 0.53/0.74 tff(225,plain,
% 0.53/0.74 (((multiply(sk_c10, sk_c4) = sk_c9) | (multiply(sk_c10, sk_c8) = sk_c9)) <=> ((multiply(sk_c10, sk_c4) = sk_c9) | (multiply(sk_c10, sk_c8) = sk_c9))),
% 0.53/0.74 inference(rewrite,[status(thm)],[])).
% 0.53/0.74 tff(226,plain,
% 0.53/0.74 (((multiply(sk_c10, sk_c8) = sk_c9) | (multiply(sk_c10, sk_c4) = sk_c9)) <=> ((multiply(sk_c10, sk_c4) = sk_c9) | (multiply(sk_c10, sk_c8) = sk_c9))),
% 0.53/0.74 inference(rewrite,[status(thm)],[])).
% 0.53/0.74 tff(227,axiom,((multiply(sk_c10, sk_c8) = sk_c9) | (multiply(sk_c10, sk_c4) = sk_c9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_20')).
% 0.53/0.74 tff(228,plain,
% 0.53/0.74 ((multiply(sk_c10, sk_c4) = sk_c9) | (multiply(sk_c10, sk_c8) = sk_c9)),
% 0.53/0.74 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.53/0.74 tff(229,plain,
% 0.53/0.74 ((multiply(sk_c10, sk_c4) = sk_c9) | (multiply(sk_c10, sk_c8) = sk_c9)),
% 0.53/0.74 inference(modus_ponens,[status(thm)],[228, 225])).
% 0.53/0.74 tff(230,plain,
% 0.53/0.74 (multiply(sk_c10, sk_c8) = sk_c9),
% 0.53/0.74 inference(unit_resolution,[status(thm)],[229, 53])).
% 0.53/0.74 tff(231,plain,
% 0.53/0.74 (multiply(sk_c10, multiply(sk_c10, sk_c8)) = multiply(inverse(sk_c1), sk_c9)),
% 0.53/0.74 inference(monotonicity,[status(thm)],[205, 230])).
% 0.53/0.74 tff(232,plain,
% 0.53/0.74 (multiply(inverse(sk_c1), sk_c9) = multiply(sk_c10, multiply(sk_c10, sk_c8))),
% 0.53/0.74 inference(symmetry,[status(thm)],[231])).
% 0.53/0.74 tff(233,plain,
% 0.53/0.74 (inverse(sk_c10) = inverse(sk_c9)),
% 0.53/0.74 inference(monotonicity,[status(thm)],[210])).
% 0.53/0.74 tff(234,plain,
% 0.53/0.74 (inverse(sk_c10) = sk_c10),
% 0.53/0.74 inference(transitivity,[status(thm)],[233, 216])).
% 0.53/0.74 tff(235,plain,
% 0.53/0.74 (multiply(sk_c10, inverse(sk_c10)) = multiply(sk_c10, sk_c10)),
% 0.53/0.74 inference(monotonicity,[status(thm)],[234])).
% 0.53/0.74 tff(236,plain,
% 0.53/0.74 (multiply(sk_c10, inverse(sk_c10)) = sk_c8),
% 0.53/0.74 inference(transitivity,[status(thm)],[235, 211, 232, 224, 221, 52])).
% 0.53/0.74 tff(237,plain,
% 0.53/0.74 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c10, sk_c1)),
% 0.53/0.74 inference(symmetry,[status(thm)],[206])).
% 0.53/0.74 tff(238,plain,
% 0.53/0.74 (identity = multiply(inverse(sk_c1), sk_c1)),
% 0.53/0.74 inference(symmetry,[status(thm)],[68])).
% 0.53/0.74 tff(239,plain,
% 0.53/0.74 (multiply(inverse(sk_c1), sk_c9) = multiply(inverse(sk_c9), sk_c9)),
% 0.53/0.74 inference(symmetry,[status(thm)],[218])).
% 0.53/0.74 tff(240,plain,
% 0.53/0.74 (multiply(sk_c10, sk_c9) = multiply(inverse(sk_c1), sk_c9)),
% 0.53/0.74 inference(monotonicity,[status(thm)],[205])).
% 0.53/0.74 tff(241,plain,
% 0.53/0.74 (multiply(sk_c10, sk_c9) = multiply(sk_c10, sk_c1)),
% 0.53/0.74 inference(transitivity,[status(thm)],[240, 239, 9, 238, 237])).
% 0.53/0.74 tff(242,plain,
% 0.53/0.74 (multiply(multiply(sk_c10, sk_c9), sk_c10) = multiply(multiply(sk_c10, sk_c1), sk_c10)),
% 0.53/0.74 inference(monotonicity,[status(thm)],[241])).
% 0.53/0.74 tff(243,plain,
% 0.53/0.74 ((~![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)))),
% 0.53/0.74 inference(quant_inst,[status(thm)],[])).
% 0.53/0.74 tff(244,plain,
% 0.53/0.74 (multiply(multiply(sk_c10, sk_c9), sk_c10) = multiply(sk_c10, multiply(sk_c9, sk_c10))),
% 0.53/0.74 inference(unit_resolution,[status(thm)],[243, 41])).
% 0.53/0.74 tff(245,plain,
% 0.53/0.74 (multiply(sk_c10, multiply(sk_c9, sk_c10)) = multiply(multiply(sk_c10, sk_c9), sk_c10)),
% 0.53/0.74 inference(symmetry,[status(thm)],[244])).
% 0.53/0.74 tff(246,plain,
% 0.53/0.74 (multiply(sk_c10, multiply(sk_c1, sk_c10)) = multiply(multiply(sk_c10, sk_c1), sk_c10)),
% 0.53/0.74 inference(symmetry,[status(thm)],[66])).
% 0.53/0.74 tff(247,plain,
% 0.53/0.74 (sk_c9 = multiply(sk_c10, sk_c2)),
% 0.53/0.74 inference(symmetry,[status(thm)],[57])).
% 0.53/0.74 tff(248,plain,
% 0.53/0.74 (sk_c9 = sk_c10),
% 0.53/0.74 inference(transitivity,[status(thm)],[247, 63, 246, 208, 21])).
% 0.53/0.74 tff(249,plain,
% 0.53/0.74 (multiply(sk_c9, sk_c10) = multiply(sk_c10, sk_c10)),
% 0.53/0.74 inference(monotonicity,[status(thm)],[248])).
% 0.53/0.74 tff(250,plain,
% 0.53/0.74 (multiply(sk_c10, sk_c10) = multiply(sk_c9, sk_c10)),
% 0.53/0.74 inference(symmetry,[status(thm)],[249])).
% 0.53/0.74 tff(251,plain,
% 0.53/0.74 (identity = multiply(sk_c9, sk_c10)),
% 0.53/0.74 inference(transitivity,[status(thm)],[10, 218, 212, 250])).
% 0.53/0.74 tff(252,plain,
% 0.53/0.74 (multiply(sk_c10, identity) = multiply(sk_c10, multiply(sk_c9, sk_c10))),
% 0.53/0.74 inference(monotonicity,[status(thm)],[251])).
% 0.53/0.74 tff(253,plain,
% 0.53/0.74 (multiply(sk_c10, sk_c10) = identity),
% 0.53/0.74 inference(transitivity,[status(thm)],[211, 239, 9])).
% 0.53/0.74 tff(254,plain,
% 0.53/0.74 (multiply(sk_c10, multiply(sk_c10, sk_c10)) = multiply(sk_c10, identity)),
% 0.53/0.74 inference(monotonicity,[status(thm)],[253])).
% 0.53/0.74 tff(255,plain,
% 0.53/0.74 (multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9),
% 0.53/0.74 inference(transitivity,[status(thm)],[254, 252, 245, 242, 66, 64, 57])).
% 0.53/0.74 tff(256,plain,
% 0.53/0.74 (multiply(inverse(sk_c10), sk_c9) = multiply(sk_c10, sk_c10)),
% 0.53/0.74 inference(monotonicity,[status(thm)],[234, 248])).
% 0.53/0.74 tff(257,plain,
% 0.53/0.74 (multiply(inverse(sk_c10), sk_c9) = sk_c8),
% 0.53/0.74 inference(transitivity,[status(thm)],[256, 211, 232, 224, 221, 52])).
% 0.53/0.74 tff(258,plain,
% 0.53/0.74 (multiply(sk_c10, sk_c8) = sk_c10),
% 0.53/0.74 inference(transitivity,[status(thm)],[230, 247, 63, 246, 208, 21])).
% 0.53/0.74 tff(259,plain,
% 0.53/0.74 (inverse(sk_c10) = sk_c9),
% 0.53/0.74 inference(transitivity,[status(thm)],[233, 216, 108, 209, 66, 64, 57])).
% 0.53/0.74 tff(260,plain,
% 0.53/0.74 (((multiply(sk_c9, sk_c8) = sk_c10) | (multiply(sk_c10, sk_c4) = sk_c9)) <=> ((multiply(sk_c9, sk_c8) = sk_c10) | (multiply(sk_c10, sk_c4) = sk_c9))),
% 0.53/0.74 inference(rewrite,[status(thm)],[])).
% 0.53/0.74 tff(261,axiom,((multiply(sk_c9, sk_c8) = sk_c10) | (multiply(sk_c10, sk_c4) = sk_c9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_2')).
% 0.53/0.74 tff(262,plain,
% 0.53/0.74 ((multiply(sk_c9, sk_c8) = sk_c10) | (multiply(sk_c10, sk_c4) = sk_c9)),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.53/0.75 tff(263,plain,
% 0.53/0.75 ((multiply(sk_c9, sk_c8) = sk_c10) | (multiply(sk_c10, sk_c4) = sk_c9)),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[262, 260])).
% 0.53/0.75 tff(264,plain,
% 0.53/0.75 ((multiply(sk_c9, sk_c8) = sk_c10) | (multiply(sk_c10, sk_c4) = sk_c9)),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[263, 260])).
% 0.53/0.75 tff(265,plain,
% 0.53/0.75 ((multiply(sk_c9, sk_c8) = sk_c10) | (multiply(sk_c10, sk_c4) = sk_c9)),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[264, 260])).
% 0.53/0.75 tff(266,plain,
% 0.53/0.75 ((multiply(sk_c9, sk_c8) = sk_c10) | (multiply(sk_c10, sk_c4) = sk_c9)),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[265, 260])).
% 0.53/0.75 tff(267,plain,
% 0.53/0.75 (multiply(sk_c9, sk_c8) = sk_c10),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[266, 53])).
% 0.53/0.75 tff(268,plain,
% 0.53/0.75 (((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c10) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c8) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c9) = sk_c8)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c8)))) <=> ((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | (~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c10) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c8) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c9) = sk_c8)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c8)))),
% 0.53/0.75 inference(rewrite,[status(thm)],[])).
% 0.53/0.75 tff(269,plain,
% 0.53/0.75 (((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c10) = sk_c10)) | (~(inverse(sk_c10) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c8) = sk_c10)) | (~(inverse(sk_c10) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c9) = sk_c8)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c8)) | (~(multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c10) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c8) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c9) = sk_c8)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c8)))),
% 0.53/0.75 inference(rewrite,[status(thm)],[])).
% 0.53/0.75 tff(270,plain,
% 0.53/0.75 (((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c10) = sk_c10)) | (~(inverse(sk_c10) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c8) = sk_c10)) | (~(inverse(sk_c10) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c9) = sk_c8)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c8)) | (~(multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9)))) <=> ((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c10) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c8) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c9) = sk_c8)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c8))))),
% 0.53/0.75 inference(monotonicity,[status(thm)],[269])).
% 0.53/0.75 tff(271,plain,
% 0.53/0.75 (((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c10) = sk_c10)) | (~(inverse(sk_c10) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c8) = sk_c10)) | (~(inverse(sk_c10) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c9) = sk_c8)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c8)) | (~(multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9)))) <=> ((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | (~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c10) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c8) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c9) = sk_c8)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c8)))),
% 0.53/0.75 inference(transitivity,[status(thm)],[270, 268])).
% 0.53/0.75 tff(272,plain,
% 0.53/0.75 ((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c10) = sk_c10)) | (~(inverse(sk_c10) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c8) = sk_c10)) | (~(inverse(sk_c10) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c9) = sk_c8)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c8)) | (~(multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9)))),
% 0.53/0.75 inference(quant_inst,[status(thm)],[])).
% 0.53/0.75 tff(273,plain,
% 0.53/0.75 ((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | (~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c10) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9)) | (~(multiply(sk_c10, sk_c8) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c9) = sk_c8)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c8))),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.53/0.75 tff(274,plain,
% 0.53/0.75 ((~(multiply(sk_c10, multiply(sk_c10, sk_c10)) = sk_c9)) | (~(multiply(inverse(sk_c10), sk_c9) = sk_c8)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c8))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[273, 267, 259, 216, 230, 194, 258, 234])).
% 0.53/0.75 tff(275,plain,
% 0.53/0.75 ($false),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[274, 257, 255, 236])).
% 0.53/0.75 tff(276,plain,(multiply(sk_c10, sk_c4) = sk_c9), inference(lemma,lemma(discharge,[]))).
% 0.53/0.75 tff(277,plain,
% 0.53/0.75 (sk_c9 = multiply(sk_c10, sk_c4)),
% 0.53/0.75 inference(symmetry,[status(thm)],[276])).
% 0.53/0.75 tff(278,assumption,(~(inverse(sk_c10) = sk_c9)), introduced(assumption)).
% 0.53/0.75 tff(279,plain,
% 0.53/0.75 (((inverse(sk_c10) = sk_c9) | (multiply(sk_c10, sk_c2) = sk_c9)) <=> ((inverse(sk_c10) = sk_c9) | (multiply(sk_c10, sk_c2) = sk_c9))),
% 0.53/0.75 inference(rewrite,[status(thm)],[])).
% 0.53/0.75 tff(280,plain,
% 0.53/0.75 (((multiply(sk_c10, sk_c2) = sk_c9) | (inverse(sk_c10) = sk_c9)) <=> ((inverse(sk_c10) = sk_c9) | (multiply(sk_c10, sk_c2) = sk_c9))),
% 0.53/0.75 inference(rewrite,[status(thm)],[])).
% 0.53/0.75 tff(281,axiom,((multiply(sk_c10, sk_c2) = sk_c9) | (inverse(sk_c10) = sk_c9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_28')).
% 0.53/0.75 tff(282,plain,
% 0.53/0.75 ((inverse(sk_c10) = sk_c9) | (multiply(sk_c10, sk_c2) = sk_c9)),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.53/0.75 tff(283,plain,
% 0.53/0.75 ((inverse(sk_c10) = sk_c9) | (multiply(sk_c10, sk_c2) = sk_c9)),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[282, 279])).
% 0.53/0.75 tff(284,plain,
% 0.53/0.75 (multiply(sk_c10, sk_c2) = sk_c9),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[283, 278])).
% 0.53/0.75 tff(285,plain,
% 0.53/0.75 (((inverse(sk_c10) = sk_c9) | (multiply(sk_c1, sk_c10) = sk_c2)) <=> ((inverse(sk_c10) = sk_c9) | (multiply(sk_c1, sk_c10) = sk_c2))),
% 0.53/0.75 inference(rewrite,[status(thm)],[])).
% 0.53/0.75 tff(286,plain,
% 0.53/0.75 (((multiply(sk_c1, sk_c10) = sk_c2) | (inverse(sk_c10) = sk_c9)) <=> ((inverse(sk_c10) = sk_c9) | (multiply(sk_c1, sk_c10) = sk_c2))),
% 0.53/0.75 inference(rewrite,[status(thm)],[])).
% 0.53/0.75 tff(287,axiom,((multiply(sk_c1, sk_c10) = sk_c2) | (inverse(sk_c10) = sk_c9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_37')).
% 0.53/0.75 tff(288,plain,
% 0.53/0.75 ((inverse(sk_c10) = sk_c9) | (multiply(sk_c1, sk_c10) = sk_c2)),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.53/0.75 tff(289,plain,
% 0.53/0.75 ((inverse(sk_c10) = sk_c9) | (multiply(sk_c1, sk_c10) = sk_c2)),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[288, 285])).
% 0.53/0.75 tff(290,plain,
% 0.53/0.75 (multiply(sk_c1, sk_c10) = sk_c2),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[289, 278])).
% 0.53/0.75 tff(291,plain,
% 0.53/0.75 (sk_c2 = multiply(sk_c1, sk_c10)),
% 0.53/0.75 inference(symmetry,[status(thm)],[290])).
% 0.53/0.75 tff(292,plain,
% 0.53/0.75 (multiply(sk_c10, sk_c2) = multiply(sk_c10, multiply(sk_c1, sk_c10))),
% 0.53/0.75 inference(monotonicity,[status(thm)],[291])).
% 0.53/0.75 tff(293,plain,
% 0.53/0.75 (multiply(sk_c10, multiply(sk_c1, sk_c10)) = multiply(sk_c10, sk_c2)),
% 0.53/0.75 inference(symmetry,[status(thm)],[292])).
% 0.53/0.75 tff(294,plain,
% 0.53/0.75 (((inverse(sk_c10) = sk_c9) | (inverse(sk_c9) = sk_c10)) <=> ((inverse(sk_c10) = sk_c9) | (inverse(sk_c9) = sk_c10))),
% 0.53/0.75 inference(rewrite,[status(thm)],[])).
% 0.53/0.75 tff(295,plain,
% 0.53/0.75 (((inverse(sk_c9) = sk_c10) | (inverse(sk_c10) = sk_c9)) <=> ((inverse(sk_c10) = sk_c9) | (inverse(sk_c9) = sk_c10))),
% 0.53/0.75 inference(rewrite,[status(thm)],[])).
% 0.53/0.75 tff(296,axiom,((inverse(sk_c9) = sk_c10) | (inverse(sk_c10) = sk_c9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_10')).
% 0.53/0.75 tff(297,plain,
% 0.53/0.75 ((inverse(sk_c10) = sk_c9) | (inverse(sk_c9) = sk_c10)),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[296, 295])).
% 0.53/0.75 tff(298,plain,
% 0.53/0.75 ((inverse(sk_c10) = sk_c9) | (inverse(sk_c9) = sk_c10)),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[297, 294])).
% 0.53/0.75 tff(299,plain,
% 0.53/0.75 (inverse(sk_c9) = sk_c10),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[298, 278])).
% 0.53/0.75 tff(300,plain,
% 0.53/0.75 (sk_c10 = sk_c9),
% 0.53/0.75 inference(transitivity,[status(thm)],[108, 209, 66, 293, 284])).
% 0.53/0.75 tff(301,plain,
% 0.53/0.75 (inverse(sk_c10) = inverse(sk_c9)),
% 0.53/0.75 inference(monotonicity,[status(thm)],[300])).
% 0.53/0.75 tff(302,plain,
% 0.53/0.75 (inverse(sk_c10) = sk_c9),
% 0.53/0.75 inference(transitivity,[status(thm)],[301, 299, 108, 209, 66, 293, 284])).
% 0.53/0.75 tff(303,plain,
% 0.53/0.75 ($false),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[278, 302])).
% 0.53/0.75 tff(304,plain,(inverse(sk_c10) = sk_c9), inference(lemma,lemma(discharge,[]))).
% 0.53/0.75 tff(305,plain,
% 0.53/0.75 (sk_c9 = sk_c10),
% 0.53/0.75 inference(transitivity,[status(thm)],[277, 50, 44, 34, 21])).
% 0.53/0.75 tff(306,plain,
% 0.53/0.75 (inverse(sk_c9) = inverse(sk_c10)),
% 0.53/0.75 inference(monotonicity,[status(thm)],[305])).
% 0.53/0.75 tff(307,plain,
% 0.53/0.75 (inverse(sk_c9) = sk_c10),
% 0.53/0.75 inference(transitivity,[status(thm)],[306, 304, 277, 50, 44, 34, 21])).
% 0.53/0.75 tff(308,plain,
% 0.53/0.75 ($false),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[24, 307])).
% 0.53/0.75 tff(309,plain,(inverse(sk_c9) = sk_c10), inference(lemma,lemma(discharge,[]))).
% 0.53/0.75 tff(310,plain,
% 0.53/0.75 (sk_c9 = inverse(sk_c10)),
% 0.53/0.75 inference(symmetry,[status(thm)],[304])).
% 0.53/0.75 tff(311,plain,
% 0.53/0.75 (multiply(sk_c9, inverse(sk_c9)) = multiply(inverse(sk_c10), sk_c10)),
% 0.53/0.75 inference(monotonicity,[status(thm)],[310, 309])).
% 0.53/0.75 tff(312,plain,
% 0.53/0.75 (multiply(sk_c9, inverse(sk_c9)) = multiply(inverse(sk_c9), sk_c9)),
% 0.53/0.75 inference(transitivity,[status(thm)],[311, 12, 10])).
% 0.53/0.75 tff(313,plain,
% 0.53/0.75 ((multiply(sk_c9, inverse(sk_c9)) = sk_c8) <=> (multiply(inverse(sk_c9), sk_c9) = sk_c8)),
% 0.53/0.75 inference(monotonicity,[status(thm)],[312])).
% 0.53/0.75 tff(314,plain,
% 0.53/0.75 ((~(multiply(sk_c9, inverse(sk_c9)) = sk_c8)) <=> (~(multiply(inverse(sk_c9), sk_c9) = sk_c8))),
% 0.53/0.75 inference(monotonicity,[status(thm)],[313])).
% 0.53/0.75 tff(315,plain,
% 0.53/0.75 (sk_c10 = inverse(sk_c9)),
% 0.53/0.75 inference(symmetry,[status(thm)],[309])).
% 0.53/0.75 tff(316,plain,
% 0.53/0.75 (inverse(sk_c1) = inverse(sk_c9)),
% 0.53/0.75 inference(transitivity,[status(thm)],[204, 315])).
% 0.53/0.75 tff(317,plain,
% 0.53/0.75 (multiply(inverse(sk_c1), sk_c9) = multiply(inverse(sk_c9), sk_c9)),
% 0.53/0.75 inference(monotonicity,[status(thm)],[316])).
% 0.53/0.75 tff(318,plain,
% 0.53/0.75 (multiply(inverse(sk_c9), sk_c9) = multiply(inverse(sk_c1), sk_c9)),
% 0.53/0.75 inference(symmetry,[status(thm)],[317])).
% 0.53/0.75 tff(319,plain,
% 0.53/0.75 ((multiply(inverse(sk_c9), sk_c9) = sk_c8) <=> (multiply(inverse(sk_c1), sk_c9) = sk_c8)),
% 0.53/0.75 inference(monotonicity,[status(thm)],[318])).
% 0.53/0.75 tff(320,plain,
% 0.53/0.75 ((multiply(inverse(sk_c1), sk_c9) = sk_c8) <=> (multiply(inverse(sk_c9), sk_c9) = sk_c8)),
% 0.53/0.75 inference(symmetry,[status(thm)],[319])).
% 0.53/0.75 tff(321,plain,
% 0.53/0.75 (multiply(sk_c10, inverse(sk_c10)) = multiply(inverse(sk_c1), sk_c9)),
% 0.53/0.75 inference(monotonicity,[status(thm)],[205, 304])).
% 0.53/0.75 tff(322,plain,
% 0.53/0.75 ((multiply(sk_c10, inverse(sk_c10)) = sk_c8) <=> (multiply(inverse(sk_c1), sk_c9) = sk_c8)),
% 0.53/0.75 inference(monotonicity,[status(thm)],[321])).
% 0.53/0.75 tff(323,plain,
% 0.53/0.75 ((multiply(sk_c10, inverse(sk_c10)) = sk_c8) <=> (multiply(inverse(sk_c9), sk_c9) = sk_c8)),
% 0.53/0.75 inference(transitivity,[status(thm)],[322, 320])).
% 0.53/0.75 tff(324,plain,
% 0.53/0.75 ((~(multiply(sk_c10, inverse(sk_c10)) = sk_c8)) <=> (~(multiply(inverse(sk_c9), sk_c9) = sk_c8))),
% 0.53/0.75 inference(monotonicity,[status(thm)],[323])).
% 0.53/0.75 tff(325,assumption,(~(multiply(sk_c3, sk_c10) = sk_c4)), introduced(assumption)).
% 0.53/0.75 tff(326,plain,
% 0.53/0.75 (((multiply(sk_c10, sk_c2) = sk_c9) | (multiply(sk_c3, sk_c10) = sk_c4)) <=> ((multiply(sk_c10, sk_c2) = sk_c9) | (multiply(sk_c3, sk_c10) = sk_c4))),
% 0.53/0.75 inference(rewrite,[status(thm)],[])).
% 0.53/0.75 tff(327,axiom,((multiply(sk_c10, sk_c2) = sk_c9) | (multiply(sk_c3, sk_c10) = sk_c4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_30')).
% 0.53/0.75 tff(328,plain,
% 0.53/0.75 ((multiply(sk_c10, sk_c2) = sk_c9) | (multiply(sk_c3, sk_c10) = sk_c4)),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.53/0.75 tff(329,plain,
% 0.53/0.75 (multiply(sk_c10, sk_c2) = sk_c9),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[328, 325])).
% 0.53/0.75 tff(330,plain,
% 0.53/0.75 (((multiply(sk_c1, sk_c10) = sk_c2) | (multiply(sk_c3, sk_c10) = sk_c4)) <=> ((multiply(sk_c1, sk_c10) = sk_c2) | (multiply(sk_c3, sk_c10) = sk_c4))),
% 0.53/0.75 inference(rewrite,[status(thm)],[])).
% 0.53/0.75 tff(331,axiom,((multiply(sk_c1, sk_c10) = sk_c2) | (multiply(sk_c3, sk_c10) = sk_c4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_39')).
% 0.53/0.75 tff(332,plain,
% 0.53/0.75 ((multiply(sk_c1, sk_c10) = sk_c2) | (multiply(sk_c3, sk_c10) = sk_c4)),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.53/0.75 tff(333,plain,
% 0.53/0.75 (multiply(sk_c1, sk_c10) = sk_c2),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[332, 325])).
% 0.53/0.75 tff(334,plain,
% 0.53/0.75 (sk_c2 = multiply(sk_c1, sk_c10)),
% 0.53/0.75 inference(symmetry,[status(thm)],[333])).
% 0.53/0.75 tff(335,plain,
% 0.53/0.75 (multiply(sk_c10, sk_c2) = multiply(sk_c10, multiply(sk_c1, sk_c10))),
% 0.53/0.75 inference(monotonicity,[status(thm)],[334])).
% 0.53/0.75 tff(336,plain,
% 0.53/0.75 (multiply(sk_c10, multiply(sk_c1, sk_c10)) = multiply(sk_c10, sk_c2)),
% 0.53/0.75 inference(symmetry,[status(thm)],[335])).
% 0.53/0.75 tff(337,plain,
% 0.53/0.75 (multiply(sk_c10, sk_c9) = multiply(sk_c10, sk_c1)),
% 0.53/0.75 inference(transitivity,[status(thm)],[240, 317, 9, 238, 237])).
% 0.53/0.75 tff(338,plain,
% 0.53/0.75 (multiply(multiply(sk_c10, sk_c9), sk_c10) = multiply(multiply(sk_c10, sk_c1), sk_c10)),
% 0.53/0.75 inference(monotonicity,[status(thm)],[337])).
% 0.53/0.75 tff(339,plain,
% 0.53/0.75 (multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9),
% 0.53/0.75 inference(transitivity,[status(thm)],[245, 338, 66, 336, 329])).
% 0.53/0.75 tff(340,plain,
% 0.53/0.75 (((multiply(sk_c9, sk_c8) = sk_c10) | (multiply(sk_c3, sk_c10) = sk_c4)) <=> ((multiply(sk_c9, sk_c8) = sk_c10) | (multiply(sk_c3, sk_c10) = sk_c4))),
% 0.53/0.75 inference(rewrite,[status(thm)],[])).
% 0.53/0.75 tff(341,axiom,((multiply(sk_c9, sk_c8) = sk_c10) | (multiply(sk_c3, sk_c10) = sk_c4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_3')).
% 0.53/0.75 tff(342,plain,
% 0.53/0.75 ((multiply(sk_c9, sk_c8) = sk_c10) | (multiply(sk_c3, sk_c10) = sk_c4)),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[341, 340])).
% 0.53/0.75 tff(343,plain,
% 0.53/0.75 ((multiply(sk_c9, sk_c8) = sk_c10) | (multiply(sk_c3, sk_c10) = sk_c4)),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[342, 340])).
% 0.53/0.75 tff(344,plain,
% 0.53/0.75 ((multiply(sk_c9, sk_c8) = sk_c10) | (multiply(sk_c3, sk_c10) = sk_c4)),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[343, 340])).
% 0.53/0.75 tff(345,plain,
% 0.53/0.75 ((multiply(sk_c9, sk_c8) = sk_c10) | (multiply(sk_c3, sk_c10) = sk_c4)),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[344, 340])).
% 0.53/0.75 tff(346,plain,
% 0.53/0.75 ((multiply(sk_c9, sk_c8) = sk_c10) | (multiply(sk_c3, sk_c10) = sk_c4)),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[345, 340])).
% 0.53/0.75 tff(347,plain,
% 0.53/0.75 (multiply(sk_c9, sk_c8) = sk_c10),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[346, 325])).
% 0.53/0.75 tff(348,plain,
% 0.53/0.75 (multiply(inverse(sk_c1), sk_c9) = multiply(sk_c10, sk_c9)),
% 0.53/0.75 inference(symmetry,[status(thm)],[240])).
% 0.53/0.75 tff(349,plain,
% 0.53/0.75 (identity = multiply(sk_c10, sk_c9)),
% 0.53/0.75 inference(transitivity,[status(thm)],[10, 318, 348])).
% 0.53/0.75 tff(350,plain,
% 0.53/0.75 (multiply(identity, sk_c8) = multiply(multiply(sk_c10, sk_c9), sk_c8)),
% 0.53/0.75 inference(monotonicity,[status(thm)],[349])).
% 0.53/0.75 tff(351,plain,
% 0.53/0.75 (multiply(multiply(sk_c10, sk_c9), sk_c8) = multiply(identity, sk_c8)),
% 0.53/0.75 inference(symmetry,[status(thm)],[350])).
% 0.53/0.75 tff(352,plain,
% 0.53/0.75 (multiply(sk_c9, sk_c10) = multiply(inverse(sk_c10), sk_c10)),
% 0.53/0.75 inference(monotonicity,[status(thm)],[310])).
% 0.53/0.75 tff(353,plain,
% 0.53/0.75 (multiply(sk_c9, sk_c10) = multiply(sk_c10, sk_c9)),
% 0.53/0.75 inference(transitivity,[status(thm)],[352, 12, 10, 318, 348])).
% 0.53/0.75 tff(354,plain,
% 0.53/0.75 (multiply(multiply(sk_c9, sk_c10), sk_c8) = multiply(multiply(sk_c10, sk_c9), sk_c8)),
% 0.53/0.75 inference(monotonicity,[status(thm)],[353])).
% 0.53/0.75 tff(355,plain,
% 0.53/0.75 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c9, sk_c10), sk_c8) = multiply(sk_c9, multiply(sk_c10, sk_c8)))),
% 0.53/0.75 inference(quant_inst,[status(thm)],[])).
% 0.53/0.75 tff(356,plain,
% 0.53/0.75 (multiply(multiply(sk_c9, sk_c10), sk_c8) = multiply(sk_c9, multiply(sk_c10, sk_c8))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[355, 41])).
% 0.53/0.75 tff(357,plain,
% 0.53/0.75 (multiply(sk_c9, multiply(sk_c10, sk_c8)) = multiply(multiply(sk_c9, sk_c10), sk_c8)),
% 0.53/0.75 inference(symmetry,[status(thm)],[356])).
% 0.53/0.75 tff(358,plain,
% 0.53/0.75 (((inverse(sk_c3) = sk_c10) | (multiply(sk_c10, sk_c8) = sk_c9)) <=> ((inverse(sk_c3) = sk_c10) | (multiply(sk_c10, sk_c8) = sk_c9))),
% 0.53/0.75 inference(rewrite,[status(thm)],[])).
% 0.53/0.75 tff(359,plain,
% 0.53/0.75 (((multiply(sk_c10, sk_c8) = sk_c9) | (inverse(sk_c3) = sk_c10)) <=> ((inverse(sk_c3) = sk_c10) | (multiply(sk_c10, sk_c8) = sk_c9))),
% 0.53/0.75 inference(rewrite,[status(thm)],[])).
% 0.53/0.75 tff(360,axiom,((multiply(sk_c10, sk_c8) = sk_c9) | (inverse(sk_c3) = sk_c10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_22')).
% 0.53/0.75 tff(361,plain,
% 0.53/0.75 ((inverse(sk_c3) = sk_c10) | (multiply(sk_c10, sk_c8) = sk_c9)),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[360, 359])).
% 0.53/0.75 tff(362,plain,
% 0.53/0.75 ((inverse(sk_c3) = sk_c10) | (multiply(sk_c10, sk_c8) = sk_c9)),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[361, 358])).
% 0.53/0.75 tff(363,plain,
% 0.53/0.75 (inverse(sk_c3) = sk_c10),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[362, 172])).
% 0.53/0.75 tff(364,plain,
% 0.53/0.75 (sk_c10 = inverse(sk_c3)),
% 0.53/0.75 inference(symmetry,[status(thm)],[363])).
% 0.53/0.75 tff(365,plain,
% 0.53/0.75 (multiply(sk_c10, sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.53/0.75 inference(monotonicity,[status(thm)],[364])).
% 0.53/0.75 tff(366,plain,
% 0.53/0.75 (multiply(sk_c10, sk_c3) = identity),
% 0.53/0.75 inference(transitivity,[status(thm)],[365, 23])).
% 0.53/0.75 tff(367,plain,
% 0.53/0.75 (multiply(multiply(sk_c10, sk_c3), sk_c10) = multiply(identity, sk_c10)),
% 0.53/0.75 inference(monotonicity,[status(thm)],[366])).
% 0.53/0.75 tff(368,plain,
% 0.53/0.75 (multiply(inverse(sk_c3), sk_c3) = multiply(sk_c10, sk_c3)),
% 0.53/0.75 inference(symmetry,[status(thm)],[365])).
% 0.53/0.75 tff(369,plain,
% 0.53/0.75 (((inverse(sk_c10) = sk_c9) | (multiply(sk_c10, sk_c8) = sk_c9)) <=> ((inverse(sk_c10) = sk_c9) | (multiply(sk_c10, sk_c8) = sk_c9))),
% 0.53/0.75 inference(rewrite,[status(thm)],[])).
% 0.53/0.75 tff(370,plain,
% 0.53/0.75 (((multiply(sk_c10, sk_c8) = sk_c9) | (inverse(sk_c10) = sk_c9)) <=> ((inverse(sk_c10) = sk_c9) | (multiply(sk_c10, sk_c8) = sk_c9))),
% 0.53/0.75 inference(rewrite,[status(thm)],[])).
% 0.53/0.75 tff(371,axiom,((multiply(sk_c10, sk_c8) = sk_c9) | (inverse(sk_c10) = sk_c9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_19')).
% 0.53/0.75 tff(372,plain,
% 0.53/0.75 ((inverse(sk_c10) = sk_c9) | (multiply(sk_c10, sk_c8) = sk_c9)),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[371, 370])).
% 0.53/0.75 tff(373,plain,
% 0.53/0.75 ((inverse(sk_c10) = sk_c9) | (multiply(sk_c10, sk_c8) = sk_c9)),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[372, 369])).
% 0.53/0.75 tff(374,plain,
% 0.53/0.75 (inverse(sk_c10) = sk_c9),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[373, 172])).
% 0.53/0.75 tff(375,plain,
% 0.53/0.75 (sk_c9 = inverse(sk_c10)),
% 0.53/0.75 inference(symmetry,[status(thm)],[374])).
% 0.53/0.75 tff(376,plain,
% 0.53/0.75 (multiply(sk_c9, sk_c10) = multiply(inverse(sk_c10), sk_c10)),
% 0.53/0.75 inference(monotonicity,[status(thm)],[375])).
% 0.53/0.75 tff(377,plain,
% 0.53/0.75 (multiply(sk_c9, sk_c10) = multiply(sk_c10, sk_c3)),
% 0.53/0.75 inference(transitivity,[status(thm)],[376, 12, 94, 368])).
% 0.53/0.75 tff(378,plain,
% 0.53/0.75 (multiply(multiply(sk_c9, sk_c10), sk_c10) = multiply(multiply(sk_c10, sk_c3), sk_c10)),
% 0.53/0.75 inference(monotonicity,[status(thm)],[377])).
% 0.53/0.75 tff(379,plain,
% 0.53/0.75 (((multiply(sk_c10, sk_c8) = sk_c9) | (multiply(sk_c3, sk_c10) = sk_c4)) <=> ((multiply(sk_c10, sk_c8) = sk_c9) | (multiply(sk_c3, sk_c10) = sk_c4))),
% 0.53/0.75 inference(rewrite,[status(thm)],[])).
% 0.53/0.75 tff(380,axiom,((multiply(sk_c10, sk_c8) = sk_c9) | (multiply(sk_c3, sk_c10) = sk_c4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_21')).
% 0.53/0.75 tff(381,plain,
% 0.53/0.75 ((multiply(sk_c10, sk_c8) = sk_c9) | (multiply(sk_c3, sk_c10) = sk_c4)),
% 0.53/0.76 inference(modus_ponens,[status(thm)],[380, 379])).
% 0.53/0.76 tff(382,plain,
% 0.53/0.76 (multiply(sk_c3, sk_c10) = sk_c4),
% 0.53/0.76 inference(unit_resolution,[status(thm)],[381, 172])).
% 0.53/0.76 tff(383,plain,
% 0.53/0.76 (sk_c4 = multiply(sk_c3, sk_c10)),
% 0.53/0.76 inference(symmetry,[status(thm)],[382])).
% 0.53/0.76 tff(384,plain,
% 0.53/0.76 (multiply(sk_c10, sk_c4) = multiply(sk_c10, multiply(sk_c3, sk_c10))),
% 0.53/0.76 inference(monotonicity,[status(thm)],[383])).
% 0.53/0.76 tff(385,plain,
% 0.53/0.76 (multiply(sk_c10, multiply(sk_c3, sk_c10)) = multiply(sk_c10, sk_c4)),
% 0.53/0.76 inference(symmetry,[status(thm)],[384])).
% 0.53/0.76 tff(386,plain,
% 0.53/0.76 (multiply(identity, sk_c10) = multiply(multiply(sk_c10, sk_c3), sk_c10)),
% 0.53/0.76 inference(symmetry,[status(thm)],[367])).
% 0.53/0.76 tff(387,plain,
% 0.53/0.76 (sk_c10 = inverse(sk_c10)),
% 0.53/0.76 inference(transitivity,[status(thm)],[108, 386, 43, 385, 276, 375])).
% 0.53/0.76 tff(388,plain,
% 0.53/0.76 (multiply(sk_c10, sk_c10) = multiply(inverse(sk_c10), sk_c10)),
% 0.53/0.76 inference(monotonicity,[status(thm)],[387])).
% 0.53/0.76 tff(389,plain,
% 0.53/0.76 (multiply(inverse(sk_c10), sk_c10) = multiply(sk_c10, sk_c10)),
% 0.53/0.76 inference(symmetry,[status(thm)],[388])).
% 0.53/0.76 tff(390,plain,
% 0.53/0.76 (((multiply(sk_c10, sk_c8) = sk_c9) | (multiply(sk_c7, sk_c8) = sk_c10)) <=> ((multiply(sk_c10, sk_c8) = sk_c9) | (multiply(sk_c7, sk_c8) = sk_c10))),
% 0.53/0.76 inference(rewrite,[status(thm)],[])).
% 0.53/0.76 tff(391,axiom,((multiply(sk_c10, sk_c8) = sk_c9) | (multiply(sk_c7, sk_c8) = sk_c10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_27')).
% 0.53/0.76 tff(392,plain,
% 0.53/0.76 ((multiply(sk_c10, sk_c8) = sk_c9) | (multiply(sk_c7, sk_c8) = sk_c10)),
% 0.53/0.76 inference(modus_ponens,[status(thm)],[391, 390])).
% 0.53/0.76 tff(393,plain,
% 0.53/0.76 (multiply(sk_c7, sk_c8) = sk_c10),
% 0.53/0.76 inference(unit_resolution,[status(thm)],[392, 172])).
% 0.53/0.76 tff(394,plain,
% 0.53/0.76 (multiply(sk_c9, multiply(sk_c7, sk_c8)) = multiply(inverse(sk_c10), sk_c10)),
% 0.53/0.76 inference(monotonicity,[status(thm)],[375, 393])).
% 0.53/0.76 tff(395,plain,
% 0.53/0.76 (((inverse(sk_c7) = sk_c10) | (multiply(sk_c10, sk_c8) = sk_c9)) <=> ((inverse(sk_c7) = sk_c10) | (multiply(sk_c10, sk_c8) = sk_c9))),
% 0.53/0.76 inference(rewrite,[status(thm)],[])).
% 0.53/0.76 tff(396,plain,
% 0.53/0.76 (((multiply(sk_c10, sk_c8) = sk_c9) | (inverse(sk_c7) = sk_c10)) <=> ((inverse(sk_c7) = sk_c10) | (multiply(sk_c10, sk_c8) = sk_c9))),
% 0.53/0.76 inference(rewrite,[status(thm)],[])).
% 0.53/0.76 tff(397,axiom,((multiply(sk_c10, sk_c8) = sk_c9) | (inverse(sk_c7) = sk_c10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_26')).
% 0.53/0.76 tff(398,plain,
% 0.53/0.76 ((inverse(sk_c7) = sk_c10) | (multiply(sk_c10, sk_c8) = sk_c9)),
% 0.53/0.76 inference(modus_ponens,[status(thm)],[397, 396])).
% 0.53/0.76 tff(399,plain,
% 0.53/0.76 ((inverse(sk_c7) = sk_c10) | (multiply(sk_c10, sk_c8) = sk_c9)),
% 0.53/0.76 inference(modus_ponens,[status(thm)],[398, 395])).
% 0.53/0.76 tff(400,plain,
% 0.53/0.76 (inverse(sk_c7) = sk_c10),
% 0.53/0.76 inference(unit_resolution,[status(thm)],[399, 172])).
% 0.53/0.76 tff(401,plain,
% 0.53/0.76 (sk_c10 = inverse(sk_c7)),
% 0.53/0.76 inference(symmetry,[status(thm)],[400])).
% 0.53/0.76 tff(402,plain,
% 0.53/0.76 (sk_c9 = inverse(sk_c7)),
% 0.53/0.76 inference(transitivity,[status(thm)],[277, 384, 44, 367, 21, 401])).
% 0.53/0.76 tff(403,plain,
% 0.53/0.76 (multiply(sk_c9, sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.53/0.76 inference(monotonicity,[status(thm)],[402])).
% 0.53/0.76 tff(404,plain,
% 0.53/0.76 (multiply(inverse(sk_c7), sk_c7) = multiply(sk_c9, sk_c7)),
% 0.53/0.76 inference(symmetry,[status(thm)],[403])).
% 0.53/0.76 tff(405,plain,
% 0.53/0.76 (identity = multiply(sk_c9, sk_c7)),
% 0.53/0.76 inference(transitivity,[status(thm)],[131, 404])).
% 0.53/0.76 tff(406,plain,
% 0.53/0.76 (multiply(identity, sk_c8) = multiply(multiply(sk_c9, sk_c7), sk_c8)),
% 0.53/0.76 inference(monotonicity,[status(thm)],[405])).
% 0.53/0.76 tff(407,plain,
% 0.53/0.76 (sk_c8 = multiply(sk_c10, sk_c10)),
% 0.53/0.76 inference(transitivity,[status(thm)],[134, 406, 120, 394, 389])).
% 0.53/0.76 tff(408,plain,
% 0.53/0.76 (sk_c10 = sk_c9),
% 0.53/0.76 inference(transitivity,[status(thm)],[108, 386, 43, 385, 276])).
% 0.53/0.76 tff(409,plain,
% 0.53/0.76 (multiply(sk_c10, sk_c8) = multiply(sk_c9, multiply(sk_c10, sk_c10))),
% 0.53/0.76 inference(monotonicity,[status(thm)],[408, 407])).
% 0.53/0.76 tff(410,plain,
% 0.53/0.76 (multiply(sk_c10, sk_c8) = sk_c10),
% 0.53/0.76 inference(transitivity,[status(thm)],[409, 105, 378, 367, 21])).
% 0.53/0.76 tff(411,plain,
% 0.53/0.76 ((multiply(sk_c10, sk_c8) = sk_c9) | (~(multiply(sk_c10, sk_c8) = sk_c10)) | (~(inverse(sk_c3) = sk_c10)) | (~(multiply(sk_c3, sk_c10) = sk_c4))),
% 0.53/0.76 inference(unit_resolution,[status(thm)],[176, 276])).
% 0.53/0.76 tff(412,plain,
% 0.53/0.76 (~(multiply(sk_c10, sk_c8) = sk_c10)),
% 0.53/0.76 inference(unit_resolution,[status(thm)],[411, 382, 363, 172])).
% 0.53/0.76 tff(413,plain,
% 0.53/0.76 ($false),
% 0.53/0.76 inference(unit_resolution,[status(thm)],[412, 410])).
% 0.53/0.76 tff(414,plain,(multiply(sk_c10, sk_c8) = sk_c9), inference(lemma,lemma(discharge,[]))).
% 0.53/0.76 tff(415,plain,
% 0.53/0.76 (sk_c9 = multiply(sk_c10, sk_c8)),
% 0.53/0.76 inference(symmetry,[status(thm)],[414])).
% 0.53/0.76 tff(416,plain,
% 0.53/0.76 (multiply(inverse(sk_c10), sk_c9) = multiply(sk_c9, multiply(sk_c10, sk_c8))),
% 0.53/0.76 inference(monotonicity,[status(thm)],[304, 415])).
% 0.53/0.76 tff(417,plain,
% 0.53/0.76 (multiply(inverse(sk_c10), sk_c9) = sk_c8),
% 0.53/0.76 inference(transitivity,[status(thm)],[416, 357, 354, 351, 52])).
% 0.53/0.76 tff(418,plain,
% 0.53/0.76 (((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(inverse(sk_c10), sk_c9) = sk_c8)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c8)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)))) <=> ((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | (~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(inverse(sk_c10), sk_c9) = sk_c8)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c8)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)))),
% 0.53/0.76 inference(rewrite,[status(thm)],[])).
% 0.53/0.76 tff(419,plain,
% 0.53/0.76 (((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c9) = sk_c8)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c8)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(inverse(sk_c10), sk_c9) = sk_c8)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c8)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)))),
% 0.53/0.76 inference(rewrite,[status(thm)],[])).
% 0.53/0.76 tff(420,plain,
% 0.53/0.76 (((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c9) = sk_c8)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c8)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)))) <=> ((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(inverse(sk_c10), sk_c9) = sk_c8)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c8)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9))))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[419])).
% 0.60/0.76 tff(421,plain,
% 0.60/0.76 (((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c9) = sk_c8)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c8)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)))) <=> ((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | (~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(inverse(sk_c10), sk_c9) = sk_c8)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c8)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)))),
% 0.60/0.76 inference(transitivity,[status(thm)],[420, 418])).
% 0.60/0.76 tff(422,plain,
% 0.60/0.76 ((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c9) = sk_c8)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c8)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(423,plain,
% 0.60/0.76 ((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | (~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(inverse(sk_c10), sk_c9) = sk_c8)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c8)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[422, 421])).
% 0.60/0.76 tff(424,plain,
% 0.60/0.76 ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(multiply(inverse(sk_c10), sk_c9) = sk_c8)) | (~(multiply(sk_c10, inverse(sk_c10)) = sk_c8)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[423, 304, 309, 414, 194])).
% 0.60/0.76 tff(425,plain,
% 0.60/0.76 (~(multiply(sk_c10, inverse(sk_c10)) = sk_c8)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[424, 417, 347, 339])).
% 0.60/0.76 tff(426,plain,
% 0.60/0.76 (~(multiply(inverse(sk_c9), sk_c9) = sk_c8)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[425, 324])).
% 0.60/0.76 tff(427,plain,
% 0.60/0.76 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c10, sk_c9), sk_c8) = multiply(sk_c10, multiply(sk_c9, sk_c8)))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(428,plain,
% 0.60/0.76 (multiply(multiply(sk_c10, sk_c9), sk_c8) = multiply(sk_c10, multiply(sk_c9, sk_c8))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[427, 41])).
% 0.60/0.76 tff(429,plain,
% 0.60/0.76 (multiply(sk_c10, multiply(sk_c9, sk_c8)) = multiply(multiply(sk_c10, sk_c9), sk_c8)),
% 0.60/0.76 inference(symmetry,[status(thm)],[428])).
% 0.60/0.76 tff(430,plain,
% 0.60/0.76 (multiply(sk_c10, multiply(sk_c9, sk_c8)) = multiply(sk_c10, sk_c10)),
% 0.60/0.76 inference(monotonicity,[status(thm)],[347])).
% 0.60/0.76 tff(431,plain,
% 0.60/0.76 (multiply(sk_c10, sk_c10) = multiply(sk_c10, multiply(sk_c9, sk_c8))),
% 0.60/0.76 inference(symmetry,[status(thm)],[430])).
% 0.60/0.76 tff(432,plain,
% 0.60/0.76 (sk_c10 = sk_c9),
% 0.60/0.76 inference(transitivity,[status(thm)],[108, 209, 66, 336, 329])).
% 0.60/0.76 tff(433,plain,
% 0.60/0.76 (multiply(sk_c10, sk_c10) = multiply(inverse(sk_c1), sk_c9)),
% 0.60/0.76 inference(monotonicity,[status(thm)],[205, 432])).
% 0.60/0.76 tff(434,plain,
% 0.60/0.76 (multiply(inverse(sk_c1), sk_c9) = multiply(sk_c10, sk_c10)),
% 0.60/0.76 inference(symmetry,[status(thm)],[433])).
% 0.60/0.76 tff(435,plain,
% 0.60/0.76 (multiply(inverse(sk_c9), sk_c9) = sk_c8),
% 0.60/0.76 inference(transitivity,[status(thm)],[318, 434, 431, 429, 351, 52])).
% 0.60/0.76 tff(436,plain,
% 0.60/0.76 ($false),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[435, 426])).
% 0.60/0.76 tff(437,plain,(multiply(sk_c3, sk_c10) = sk_c4), inference(lemma,lemma(discharge,[]))).
% 0.60/0.76 tff(438,plain,
% 0.60/0.76 (multiply(sk_c10, multiply(sk_c3, sk_c10)) = multiply(sk_c10, sk_c4)),
% 0.60/0.76 inference(monotonicity,[status(thm)],[437])).
% 0.60/0.76 tff(439,assumption,(~(inverse(sk_c3) = sk_c10)), introduced(assumption)).
% 0.60/0.76 tff(440,plain,
% 0.60/0.76 (((inverse(sk_c3) = sk_c10) | (multiply(sk_c10, sk_c2) = sk_c9)) <=> ((inverse(sk_c3) = sk_c10) | (multiply(sk_c10, sk_c2) = sk_c9))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(441,plain,
% 0.60/0.76 (((multiply(sk_c10, sk_c2) = sk_c9) | (inverse(sk_c3) = sk_c10)) <=> ((inverse(sk_c3) = sk_c10) | (multiply(sk_c10, sk_c2) = sk_c9))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(442,axiom,((multiply(sk_c10, sk_c2) = sk_c9) | (inverse(sk_c3) = sk_c10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_31')).
% 0.60/0.76 tff(443,plain,
% 0.60/0.76 ((inverse(sk_c3) = sk_c10) | (multiply(sk_c10, sk_c2) = sk_c9)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[442, 441])).
% 0.60/0.76 tff(444,plain,
% 0.60/0.76 ((inverse(sk_c3) = sk_c10) | (multiply(sk_c10, sk_c2) = sk_c9)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[443, 440])).
% 0.60/0.76 tff(445,plain,
% 0.60/0.76 (multiply(sk_c10, sk_c2) = sk_c9),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[444, 439])).
% 0.60/0.76 tff(446,plain,
% 0.60/0.76 (((inverse(sk_c3) = sk_c10) | (multiply(sk_c1, sk_c10) = sk_c2)) <=> ((inverse(sk_c3) = sk_c10) | (multiply(sk_c1, sk_c10) = sk_c2))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(447,plain,
% 0.60/0.76 (((multiply(sk_c1, sk_c10) = sk_c2) | (inverse(sk_c3) = sk_c10)) <=> ((inverse(sk_c3) = sk_c10) | (multiply(sk_c1, sk_c10) = sk_c2))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(448,axiom,((multiply(sk_c1, sk_c10) = sk_c2) | (inverse(sk_c3) = sk_c10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_40')).
% 0.60/0.76 tff(449,plain,
% 0.60/0.76 ((inverse(sk_c3) = sk_c10) | (multiply(sk_c1, sk_c10) = sk_c2)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[448, 447])).
% 0.60/0.76 tff(450,plain,
% 0.60/0.76 ((inverse(sk_c3) = sk_c10) | (multiply(sk_c1, sk_c10) = sk_c2)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[449, 446])).
% 0.60/0.76 tff(451,plain,
% 0.60/0.76 (multiply(sk_c1, sk_c10) = sk_c2),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[450, 439])).
% 0.60/0.76 tff(452,plain,
% 0.60/0.76 (sk_c2 = multiply(sk_c1, sk_c10)),
% 0.60/0.76 inference(symmetry,[status(thm)],[451])).
% 0.60/0.76 tff(453,plain,
% 0.60/0.76 (multiply(sk_c10, sk_c2) = multiply(sk_c10, multiply(sk_c1, sk_c10))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[452])).
% 0.60/0.76 tff(454,plain,
% 0.60/0.76 (multiply(sk_c10, multiply(sk_c1, sk_c10)) = multiply(sk_c10, sk_c2)),
% 0.60/0.76 inference(symmetry,[status(thm)],[453])).
% 0.60/0.76 tff(455,plain,
% 0.60/0.76 (multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9),
% 0.60/0.76 inference(transitivity,[status(thm)],[245, 338, 66, 454, 445])).
% 0.60/0.76 tff(456,plain,
% 0.60/0.76 (((multiply(sk_c9, sk_c8) = sk_c10) | (inverse(sk_c3) = sk_c10)) <=> ((multiply(sk_c9, sk_c8) = sk_c10) | (inverse(sk_c3) = sk_c10))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(457,axiom,((multiply(sk_c9, sk_c8) = sk_c10) | (inverse(sk_c3) = sk_c10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_4')).
% 0.60/0.76 tff(458,plain,
% 0.60/0.76 ((multiply(sk_c9, sk_c8) = sk_c10) | (inverse(sk_c3) = sk_c10)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[457, 456])).
% 0.60/0.76 tff(459,plain,
% 0.60/0.76 ((multiply(sk_c9, sk_c8) = sk_c10) | (inverse(sk_c3) = sk_c10)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[458, 456])).
% 0.60/0.76 tff(460,plain,
% 0.60/0.76 ((multiply(sk_c9, sk_c8) = sk_c10) | (inverse(sk_c3) = sk_c10)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[459, 456])).
% 0.60/0.76 tff(461,plain,
% 0.60/0.76 ((multiply(sk_c9, sk_c8) = sk_c10) | (inverse(sk_c3) = sk_c10)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[460, 456])).
% 0.60/0.76 tff(462,plain,
% 0.60/0.76 ((multiply(sk_c9, sk_c8) = sk_c10) | (inverse(sk_c3) = sk_c10)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[461, 456])).
% 0.60/0.76 tff(463,plain,
% 0.60/0.76 (multiply(sk_c9, sk_c8) = sk_c10),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[462, 439])).
% 0.60/0.76 tff(464,plain,
% 0.60/0.76 (~(multiply(sk_c10, inverse(sk_c10)) = sk_c8)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[424, 417, 463, 455])).
% 0.60/0.76 tff(465,plain,
% 0.60/0.76 (~(multiply(inverse(sk_c9), sk_c9) = sk_c8)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[464, 324])).
% 0.60/0.76 tff(466,plain,
% 0.60/0.76 (multiply(sk_c10, multiply(sk_c9, sk_c8)) = multiply(sk_c10, sk_c10)),
% 0.60/0.76 inference(monotonicity,[status(thm)],[463])).
% 0.60/0.76 tff(467,plain,
% 0.60/0.76 (multiply(sk_c10, sk_c10) = multiply(sk_c10, multiply(sk_c9, sk_c8))),
% 0.60/0.76 inference(symmetry,[status(thm)],[466])).
% 0.60/0.76 tff(468,plain,
% 0.60/0.76 (sk_c10 = sk_c9),
% 0.60/0.76 inference(transitivity,[status(thm)],[108, 209, 66, 454, 445])).
% 0.60/0.76 tff(469,plain,
% 0.60/0.76 (multiply(sk_c10, sk_c10) = multiply(inverse(sk_c1), sk_c9)),
% 0.60/0.76 inference(monotonicity,[status(thm)],[205, 468])).
% 0.60/0.76 tff(470,plain,
% 0.60/0.76 (multiply(inverse(sk_c1), sk_c9) = multiply(sk_c10, sk_c10)),
% 0.60/0.76 inference(symmetry,[status(thm)],[469])).
% 0.60/0.76 tff(471,plain,
% 0.60/0.76 (multiply(inverse(sk_c9), sk_c9) = sk_c8),
% 0.60/0.76 inference(transitivity,[status(thm)],[318, 470, 467, 429, 351, 52])).
% 0.60/0.76 tff(472,plain,
% 0.60/0.76 ($false),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[471, 465])).
% 0.60/0.76 tff(473,plain,(inverse(sk_c3) = sk_c10), inference(lemma,lemma(discharge,[]))).
% 0.60/0.76 tff(474,plain,
% 0.60/0.76 (sk_c10 = inverse(sk_c3)),
% 0.60/0.76 inference(symmetry,[status(thm)],[473])).
% 0.60/0.76 tff(475,plain,
% 0.60/0.76 (multiply(sk_c10, sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.60/0.76 inference(monotonicity,[status(thm)],[474])).
% 0.60/0.76 tff(476,plain,
% 0.60/0.76 (multiply(inverse(sk_c3), sk_c3) = multiply(sk_c10, sk_c3)),
% 0.60/0.76 inference(symmetry,[status(thm)],[475])).
% 0.60/0.76 tff(477,plain,
% 0.60/0.76 (multiply(sk_c10, sk_c9) = multiply(sk_c10, sk_c3)),
% 0.60/0.76 inference(transitivity,[status(thm)],[240, 317, 9, 94, 476])).
% 0.60/0.77 tff(478,plain,
% 0.60/0.77 (multiply(multiply(sk_c10, sk_c9), sk_c10) = multiply(multiply(sk_c10, sk_c3), sk_c10)),
% 0.60/0.77 inference(monotonicity,[status(thm)],[477])).
% 0.60/0.77 tff(479,plain,
% 0.60/0.77 (multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9),
% 0.60/0.77 inference(transitivity,[status(thm)],[245, 478, 43, 438, 276])).
% 0.60/0.77 tff(480,plain,
% 0.60/0.77 (identity = multiply(sk_c10, sk_c3)),
% 0.60/0.77 inference(transitivity,[status(thm)],[94, 476])).
% 0.60/0.77 tff(481,plain,
% 0.60/0.77 (multiply(identity, sk_c10) = multiply(multiply(sk_c10, sk_c3), sk_c10)),
% 0.60/0.77 inference(monotonicity,[status(thm)],[480])).
% 0.60/0.77 tff(482,plain,
% 0.60/0.77 (multiply(multiply(sk_c10, sk_c3), sk_c10) = multiply(identity, sk_c10)),
% 0.60/0.77 inference(symmetry,[status(thm)],[481])).
% 0.60/0.77 tff(483,plain,
% 0.60/0.77 (multiply(sk_c10, sk_c4) = multiply(sk_c10, multiply(sk_c3, sk_c10))),
% 0.60/0.77 inference(symmetry,[status(thm)],[438])).
% 0.60/0.77 tff(484,plain,
% 0.60/0.77 (sk_c9 = sk_c10),
% 0.60/0.77 inference(transitivity,[status(thm)],[277, 483, 44, 482, 21])).
% 0.60/0.77 tff(485,plain,
% 0.60/0.77 (multiply(sk_c9, sk_c8) = multiply(sk_c10, sk_c8)),
% 0.60/0.77 inference(monotonicity,[status(thm)],[484])).
% 0.60/0.77 tff(486,plain,
% 0.60/0.77 (multiply(sk_c9, sk_c8) = sk_c10),
% 0.60/0.77 inference(transitivity,[status(thm)],[485, 414, 277, 483, 44, 482, 21])).
% 0.60/0.77 tff(487,plain,
% 0.60/0.77 (multiply(sk_c10, sk_c10) = multiply(multiply(identity, sk_c10), sk_c10)),
% 0.60/0.77 inference(monotonicity,[status(thm)],[108])).
% 0.60/0.77 tff(488,plain,
% 0.60/0.77 (multiply(multiply(identity, sk_c10), sk_c10) = multiply(sk_c10, sk_c10)),
% 0.60/0.77 inference(symmetry,[status(thm)],[487])).
% 0.60/0.77 tff(489,plain,
% 0.60/0.77 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, sk_c10), sk_c10) = multiply(identity, multiply(sk_c10, sk_c10)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(490,plain,
% 0.60/0.77 (multiply(multiply(identity, sk_c10), sk_c10) = multiply(identity, multiply(sk_c10, sk_c10))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[489, 41])).
% 0.60/0.77 tff(491,plain,
% 0.60/0.77 (multiply(identity, multiply(sk_c10, sk_c10)) = multiply(multiply(identity, sk_c10), sk_c10)),
% 0.60/0.77 inference(symmetry,[status(thm)],[490])).
% 0.60/0.77 tff(492,plain,
% 0.60/0.77 (multiply(identity, multiply(sk_c10, sk_c10)) = multiply(multiply(sk_c10, sk_c3), multiply(sk_c10, sk_c10))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[480])).
% 0.60/0.77 tff(493,plain,
% 0.60/0.77 (multiply(multiply(sk_c10, sk_c3), multiply(sk_c10, sk_c10)) = multiply(identity, multiply(sk_c10, sk_c10))),
% 0.60/0.77 inference(symmetry,[status(thm)],[492])).
% 0.60/0.77 tff(494,plain,
% 0.60/0.77 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c10, sk_c3), multiply(sk_c10, sk_c10)) = multiply(sk_c10, multiply(sk_c3, multiply(sk_c10, sk_c10))))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(495,plain,
% 0.60/0.77 (multiply(multiply(sk_c10, sk_c3), multiply(sk_c10, sk_c10)) = multiply(sk_c10, multiply(sk_c3, multiply(sk_c10, sk_c10)))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[494, 41])).
% 0.60/0.77 tff(496,plain,
% 0.60/0.77 (multiply(sk_c10, multiply(sk_c3, multiply(sk_c10, sk_c10))) = multiply(multiply(sk_c10, sk_c3), multiply(sk_c10, sk_c10))),
% 0.60/0.77 inference(symmetry,[status(thm)],[495])).
% 0.60/0.77 tff(497,plain,
% 0.60/0.77 (sk_c4 = multiply(sk_c3, sk_c10)),
% 0.60/0.77 inference(symmetry,[status(thm)],[437])).
% 0.60/0.77 tff(498,plain,
% 0.60/0.77 (multiply(sk_c4, sk_c10) = multiply(multiply(sk_c3, sk_c10), sk_c10)),
% 0.60/0.77 inference(monotonicity,[status(thm)],[497])).
% 0.60/0.77 tff(499,plain,
% 0.60/0.77 (multiply(multiply(sk_c3, sk_c10), sk_c10) = multiply(sk_c4, sk_c10)),
% 0.60/0.77 inference(symmetry,[status(thm)],[498])).
% 0.60/0.77 tff(500,plain,
% 0.60/0.77 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c3, sk_c10), sk_c10) = multiply(sk_c3, multiply(sk_c10, sk_c10)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(501,plain,
% 0.60/0.77 (multiply(multiply(sk_c3, sk_c10), sk_c10) = multiply(sk_c3, multiply(sk_c10, sk_c10))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[500, 41])).
% 0.60/0.77 tff(502,plain,
% 0.60/0.77 (multiply(sk_c3, multiply(sk_c10, sk_c10)) = multiply(multiply(sk_c3, sk_c10), sk_c10)),
% 0.60/0.77 inference(symmetry,[status(thm)],[501])).
% 0.60/0.77 tff(503,plain,
% 0.60/0.77 (multiply(sk_c3, multiply(sk_c10, sk_c10)) = multiply(sk_c4, sk_c10)),
% 0.60/0.77 inference(transitivity,[status(thm)],[502, 499])).
% 0.60/0.77 tff(504,plain,
% 0.60/0.77 (multiply(sk_c10, multiply(sk_c3, multiply(sk_c10, sk_c10))) = multiply(sk_c10, multiply(sk_c4, sk_c10))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[503])).
% 0.60/0.77 tff(505,plain,
% 0.60/0.77 (multiply(sk_c10, multiply(sk_c4, sk_c10)) = multiply(sk_c10, multiply(sk_c3, multiply(sk_c10, sk_c10)))),
% 0.60/0.77 inference(symmetry,[status(thm)],[504])).
% 0.60/0.77 tff(506,plain,
% 0.60/0.77 ((~![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)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(507,plain,
% 0.60/0.77 (multiply(multiply(sk_c10, sk_c4), sk_c10) = multiply(sk_c10, multiply(sk_c4, sk_c10))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[506, 41])).
% 0.60/0.77 tff(508,plain,
% 0.60/0.77 (multiply(sk_c10, sk_c4) = inverse(sk_c10)),
% 0.60/0.77 inference(transitivity,[status(thm)],[276, 310])).
% 0.60/0.77 tff(509,plain,
% 0.60/0.77 (multiply(multiply(sk_c10, sk_c4), sk_c10) = multiply(inverse(sk_c10), sk_c10)),
% 0.60/0.77 inference(monotonicity,[status(thm)],[508])).
% 0.60/0.77 tff(510,plain,
% 0.60/0.77 (multiply(inverse(sk_c10), sk_c10) = multiply(multiply(sk_c10, sk_c4), sk_c10)),
% 0.60/0.77 inference(symmetry,[status(thm)],[509])).
% 0.60/0.77 tff(511,plain,
% 0.60/0.77 (identity = multiply(inverse(sk_c10), sk_c10)),
% 0.60/0.77 inference(symmetry,[status(thm)],[12])).
% 0.60/0.77 tff(512,plain,
% 0.60/0.77 (identity = multiply(sk_c10, sk_c10)),
% 0.60/0.77 inference(transitivity,[status(thm)],[511, 510, 507, 505, 496, 493, 491, 488])).
% 0.60/0.77 tff(513,plain,
% 0.60/0.77 (multiply(identity, sk_c8) = multiply(multiply(sk_c10, sk_c10), sk_c8)),
% 0.60/0.77 inference(monotonicity,[status(thm)],[512])).
% 0.60/0.77 tff(514,plain,
% 0.60/0.77 (multiply(multiply(sk_c10, sk_c10), sk_c8) = multiply(identity, sk_c8)),
% 0.60/0.77 inference(symmetry,[status(thm)],[513])).
% 0.60/0.77 tff(515,plain,
% 0.60/0.77 (multiply(sk_c10, multiply(sk_c10, sk_c8)) = multiply(inverse(sk_c1), sk_c9)),
% 0.60/0.77 inference(monotonicity,[status(thm)],[205, 414])).
% 0.60/0.77 tff(516,plain,
% 0.60/0.77 (multiply(inverse(sk_c1), sk_c9) = multiply(sk_c10, multiply(sk_c10, sk_c8))),
% 0.60/0.77 inference(symmetry,[status(thm)],[515])).
% 0.60/0.77 tff(517,plain,
% 0.60/0.77 (multiply(inverse(sk_c9), sk_c9) = sk_c8),
% 0.60/0.77 inference(transitivity,[status(thm)],[318, 516, 224, 514, 52])).
% 0.60/0.77 tff(518,plain,
% 0.60/0.77 (((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(inverse(sk_c9), sk_c9) = sk_c8)) | (~(multiply(sk_c9, inverse(sk_c9)) = sk_c8)))) <=> ((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | (~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(inverse(sk_c9), sk_c9) = sk_c8)) | (~(multiply(sk_c9, inverse(sk_c9)) = sk_c8)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(519,plain,
% 0.60/0.77 (((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c9), sk_c9) = sk_c8)) | (~(multiply(sk_c9, inverse(sk_c9)) = sk_c8)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9))) <=> ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(inverse(sk_c9), sk_c9) = sk_c8)) | (~(multiply(sk_c9, inverse(sk_c9)) = sk_c8)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(520,plain,
% 0.60/0.77 (((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c9), sk_c9) = sk_c8)) | (~(multiply(sk_c9, inverse(sk_c9)) = sk_c8)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)))) <=> ((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(inverse(sk_c9), sk_c9) = sk_c8)) | (~(multiply(sk_c9, inverse(sk_c9)) = sk_c8))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[519])).
% 0.60/0.77 tff(521,plain,
% 0.60/0.77 (((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c9), sk_c9) = sk_c8)) | (~(multiply(sk_c9, inverse(sk_c9)) = sk_c8)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)))) <=> ((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | (~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(inverse(sk_c9), sk_c9) = sk_c8)) | (~(multiply(sk_c9, inverse(sk_c9)) = sk_c8)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[520, 518])).
% 0.60/0.77 tff(522,plain,
% 0.60/0.77 ((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(sk_c9) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(inverse(sk_c9), sk_c9) = sk_c8)) | (~(multiply(sk_c9, inverse(sk_c9)) = sk_c8)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(523,plain,
% 0.60/0.77 ((~![X4: $i, X2: $i, X7: $i, X5: $i] : ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(inverse(X2) = sk_c10)) | (~(inverse(X4) = sk_c10)) | (~(multiply(sk_c10, multiply(X4, sk_c10)) = sk_c9)) | (~(multiply(X7, sk_c8) = sk_c10)) | (~(inverse(X7) = sk_c10)) | (~(multiply(inverse(X5), sk_c9) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(sk_c10, multiply(X2, sk_c10)) = sk_c9)))) | (~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(inverse(sk_c9) = sk_c10)) | (~(multiply(sk_c10, sk_c8) = sk_c9)) | (~(inverse(sk_c10) = sk_c9)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(inverse(sk_c9), sk_c9) = sk_c8)) | (~(multiply(sk_c9, inverse(sk_c9)) = sk_c8))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[522, 521])).
% 0.60/0.77 tff(524,plain,
% 0.60/0.77 ((~(multiply(sk_c9, sk_c8) = sk_c10)) | (~(multiply(sk_c10, multiply(sk_c9, sk_c10)) = sk_c9)) | (~(multiply(inverse(sk_c9), sk_c9) = sk_c8)) | (~(multiply(sk_c9, inverse(sk_c9)) = sk_c8))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[523, 304, 309, 414, 194])).
% 0.60/0.77 tff(525,plain,
% 0.60/0.77 (~(multiply(sk_c9, inverse(sk_c9)) = sk_c8)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[524, 517, 486, 479])).
% 0.60/0.77 tff(526,plain,
% 0.60/0.77 (~(multiply(inverse(sk_c9), sk_c9) = sk_c8)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[525, 314])).
% 0.60/0.77 tff(527,plain,
% 0.60/0.77 ($false),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[517, 526])).
% 0.60/0.77 % SZS output end Proof
% 0.60/0.78 % E exiting
%------------------------------------------------------------------------------