%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP213-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:07:28 AM UTC 2025
% Result : Unsatisfiable 0.38s 0.60s
% Output : Proof 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : GRP213-1 : TPTP v9.0.0. Released v2.5.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 19 15:49:09 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.38/0.60 % SZS status Unsatisfiable
% 0.38/0.60 % SZS output start Proof
% 0.38/0.60 tff(sk_c8_type, type, (
% 0.38/0.60 sk_c8: $i)).
% 0.38/0.60 tff(multiply_type, type, (
% 0.38/0.60 multiply: ( $i * $i ) > $i)).
% 0.38/0.60 tff(sk_c7_type, type, (
% 0.38/0.60 sk_c7: $i)).
% 0.38/0.60 tff(identity_type, type, (
% 0.38/0.60 identity: $i)).
% 0.38/0.60 tff(sk_c1_type, type, (
% 0.38/0.60 sk_c1: $i)).
% 0.38/0.60 tff(inverse_type, type, (
% 0.38/0.60 inverse: $i > $i)).
% 0.38/0.60 tff(sk_c4_type, type, (
% 0.38/0.60 sk_c4: $i)).
% 0.38/0.60 tff(sk_c6_type, type, (
% 0.38/0.60 sk_c6: $i)).
% 0.38/0.60 tff(sk_c5_type, type, (
% 0.38/0.60 sk_c5: $i)).
% 0.38/0.60 tff(sk_c3_type, type, (
% 0.38/0.60 sk_c3: $i)).
% 0.38/0.60 tff(sk_c2_type, type, (
% 0.38/0.60 sk_c2: $i)).
% 0.38/0.60 tff(1,plain,
% 0.38/0.60 (^[X: $i] : refl((multiply(identity, X) = X) <=> (multiply(identity, X) = X))),
% 0.38/0.60 inference(bind,[status(th)],[])).
% 0.38/0.60 tff(2,plain,
% 0.38/0.60 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.38/0.60 inference(quant_intro,[status(thm)],[1])).
% 0.38/0.60 tff(3,plain,
% 0.38/0.60 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(4,axiom,(![X: $i] : (multiply(identity, X) = X)), file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax','left_identity')).
% 0.38/0.60 tff(5,plain,
% 0.38/0.60 (![X: $i] : (multiply(identity, X) = X)),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.38/0.60 tff(6,plain,(
% 0.38/0.60 ![X: $i] : (multiply(identity, X) = X)),
% 0.38/0.60 inference(skolemize,[status(sab)],[5])).
% 0.38/0.60 tff(7,plain,
% 0.38/0.60 (![X: $i] : (multiply(identity, X) = X)),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.38/0.60 tff(8,plain,
% 0.38/0.60 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c8) = sk_c8)),
% 0.38/0.60 inference(quant_inst,[status(thm)],[])).
% 0.38/0.60 tff(9,plain,
% 0.38/0.60 (multiply(identity, sk_c8) = sk_c8),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.38/0.60 tff(10,assumption,(~(inverse(sk_c1) = sk_c8)), introduced(assumption)).
% 0.38/0.60 tff(11,plain,
% 0.38/0.60 (((inverse(sk_c1) = sk_c8) | (multiply(sk_c4, sk_c7) = sk_c8)) <=> ((inverse(sk_c1) = sk_c8) | (multiply(sk_c4, sk_c7) = sk_c8))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(12,axiom,((inverse(sk_c1) = sk_c8) | (multiply(sk_c4, sk_c7) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_9')).
% 0.38/0.60 tff(13,plain,
% 0.38/0.60 ((inverse(sk_c1) = sk_c8) | (multiply(sk_c4, sk_c7) = sk_c8)),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.38/0.60 tff(14,plain,
% 0.38/0.60 (multiply(sk_c4, sk_c7) = sk_c8),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[13, 10])).
% 0.38/0.60 tff(15,plain,
% 0.38/0.60 (((inverse(sk_c1) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7)) <=> ((inverse(sk_c1) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(16,axiom,((inverse(sk_c1) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_10')).
% 0.38/0.60 tff(17,plain,
% 0.38/0.60 ((inverse(sk_c1) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7)),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.38/0.60 tff(18,plain,
% 0.38/0.60 (multiply(sk_c8, sk_c6) = sk_c7),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[17, 10])).
% 0.38/0.60 tff(19,plain,
% 0.38/0.60 (((inverse(sk_c1) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6)) <=> ((inverse(sk_c1) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(20,axiom,((inverse(sk_c1) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_11')).
% 0.38/0.60 tff(21,plain,
% 0.38/0.60 ((inverse(sk_c1) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6)),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.38/0.60 tff(22,plain,
% 0.38/0.60 (multiply(sk_c5, sk_c8) = sk_c6),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[21, 10])).
% 0.38/0.60 tff(23,plain,
% 0.38/0.60 (sk_c6 = multiply(sk_c5, sk_c8)),
% 0.38/0.60 inference(symmetry,[status(thm)],[22])).
% 0.38/0.60 tff(24,plain,
% 0.38/0.60 (multiply(sk_c8, sk_c6) = multiply(sk_c8, multiply(sk_c5, sk_c8))),
% 0.38/0.60 inference(monotonicity,[status(thm)],[23])).
% 0.38/0.60 tff(25,plain,
% 0.38/0.60 (multiply(sk_c8, multiply(sk_c5, sk_c8)) = multiply(sk_c8, sk_c6)),
% 0.38/0.60 inference(symmetry,[status(thm)],[24])).
% 0.38/0.60 tff(26,plain,
% 0.38/0.60 (^[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))))),
% 0.38/0.60 inference(bind,[status(th)],[])).
% 0.38/0.60 tff(27,plain,
% 0.38/0.60 (![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)))),
% 0.38/0.60 inference(quant_intro,[status(thm)],[26])).
% 0.38/0.60 tff(28,plain,
% 0.38/0.60 (![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)))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(29,axiom,(![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax','associativity')).
% 0.38/0.60 tff(30,plain,
% 0.38/0.60 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.38/0.60 tff(31,plain,(
% 0.38/0.60 ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.38/0.60 inference(skolemize,[status(sab)],[30])).
% 0.38/0.60 tff(32,plain,
% 0.38/0.60 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.38/0.60 tff(33,plain,
% 0.38/0.60 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c5), sk_c8) = multiply(sk_c8, multiply(sk_c5, sk_c8)))),
% 0.38/0.60 inference(quant_inst,[status(thm)],[])).
% 0.38/0.60 tff(34,plain,
% 0.38/0.60 (multiply(multiply(sk_c8, sk_c5), sk_c8) = multiply(sk_c8, multiply(sk_c5, sk_c8))),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.38/0.60 tff(35,plain,
% 0.38/0.60 (^[X: $i] : refl((multiply(inverse(X), X) = identity) <=> (multiply(inverse(X), X) = identity))),
% 0.38/0.60 inference(bind,[status(th)],[])).
% 0.38/0.60 tff(36,plain,
% 0.38/0.60 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.38/0.60 inference(quant_intro,[status(thm)],[35])).
% 0.38/0.60 tff(37,plain,
% 0.38/0.60 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(38,axiom,(![X: $i] : (multiply(inverse(X), X) = identity)), file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax','left_inverse')).
% 0.38/0.60 tff(39,plain,
% 0.38/0.60 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.38/0.60 tff(40,plain,(
% 0.38/0.60 ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.38/0.60 inference(skolemize,[status(sab)],[39])).
% 0.38/0.60 tff(41,plain,
% 0.38/0.60 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.38/0.60 tff(42,plain,
% 0.38/0.60 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c5), sk_c5) = identity)),
% 0.38/0.60 inference(quant_inst,[status(thm)],[])).
% 0.38/0.60 tff(43,plain,
% 0.38/0.60 (multiply(inverse(sk_c5), sk_c5) = identity),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.38/0.60 tff(44,assumption,(~(inverse(sk_c5) = sk_c8)), introduced(assumption)).
% 0.38/0.60 tff(45,plain,
% 0.38/0.60 (((inverse(sk_c5) = sk_c8) | (multiply(sk_c2, sk_c3) = sk_c8)) <=> ((inverse(sk_c5) = sk_c8) | (multiply(sk_c2, sk_c3) = sk_c8))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(46,plain,
% 0.38/0.60 (((multiply(sk_c2, sk_c3) = sk_c8) | (inverse(sk_c5) = sk_c8)) <=> ((inverse(sk_c5) = sk_c8) | (multiply(sk_c2, sk_c3) = sk_c8))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(47,axiom,((multiply(sk_c2, sk_c3) = sk_c8) | (inverse(sk_c5) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_18')).
% 0.38/0.60 tff(48,plain,
% 0.38/0.60 ((inverse(sk_c5) = sk_c8) | (multiply(sk_c2, sk_c3) = sk_c8)),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.38/0.60 tff(49,plain,
% 0.38/0.60 ((inverse(sk_c5) = sk_c8) | (multiply(sk_c2, sk_c3) = sk_c8)),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[48, 45])).
% 0.38/0.60 tff(50,plain,
% 0.38/0.60 (multiply(sk_c2, sk_c3) = sk_c8),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[49, 44])).
% 0.38/0.60 tff(51,plain,
% 0.38/0.60 (sk_c8 = multiply(sk_c2, sk_c3)),
% 0.38/0.60 inference(symmetry,[status(thm)],[50])).
% 0.38/0.60 tff(52,plain,
% 0.38/0.60 (multiply(sk_c3, sk_c8) = multiply(sk_c3, multiply(sk_c2, sk_c3))),
% 0.38/0.60 inference(monotonicity,[status(thm)],[51])).
% 0.38/0.60 tff(53,plain,
% 0.38/0.60 (multiply(sk_c3, multiply(sk_c2, sk_c3)) = multiply(sk_c3, sk_c8)),
% 0.38/0.60 inference(symmetry,[status(thm)],[52])).
% 0.38/0.60 tff(54,plain,
% 0.38/0.60 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c3, sk_c2), sk_c3) = multiply(sk_c3, multiply(sk_c2, sk_c3)))),
% 0.38/0.60 inference(quant_inst,[status(thm)],[])).
% 0.38/0.60 tff(55,plain,
% 0.38/0.60 (multiply(multiply(sk_c3, sk_c2), sk_c3) = multiply(sk_c3, multiply(sk_c2, sk_c3))),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[54, 32])).
% 0.38/0.60 tff(56,plain,
% 0.38/0.60 (((inverse(sk_c2) = sk_c3) | (inverse(sk_c5) = sk_c8)) <=> ((inverse(sk_c2) = sk_c3) | (inverse(sk_c5) = sk_c8))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(57,axiom,((inverse(sk_c2) = sk_c3) | (inverse(sk_c5) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_24')).
% 0.38/0.60 tff(58,plain,
% 0.38/0.60 ((inverse(sk_c2) = sk_c3) | (inverse(sk_c5) = sk_c8)),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.38/0.60 tff(59,plain,
% 0.38/0.60 (inverse(sk_c2) = sk_c3),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[58, 44])).
% 0.38/0.60 tff(60,plain,
% 0.38/0.60 (sk_c3 = inverse(sk_c2)),
% 0.38/0.60 inference(symmetry,[status(thm)],[59])).
% 0.38/0.60 tff(61,plain,
% 0.38/0.60 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, sk_c3), sk_c1) = multiply(sk_c2, multiply(sk_c3, sk_c1)))),
% 0.38/0.60 inference(quant_inst,[status(thm)],[])).
% 0.38/0.60 tff(62,plain,
% 0.38/0.60 (multiply(multiply(sk_c2, sk_c3), sk_c1) = multiply(sk_c2, multiply(sk_c3, sk_c1))),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[61, 32])).
% 0.38/0.60 tff(63,plain,
% 0.38/0.60 (((inverse(sk_c1) = sk_c8) | (inverse(sk_c5) = sk_c8)) <=> ((inverse(sk_c1) = sk_c8) | (inverse(sk_c5) = sk_c8))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(64,axiom,((inverse(sk_c1) = sk_c8) | (inverse(sk_c5) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_12')).
% 0.38/0.60 tff(65,plain,
% 0.38/0.60 ((inverse(sk_c1) = sk_c8) | (inverse(sk_c5) = sk_c8)),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.38/0.60 tff(66,plain,
% 0.38/0.60 (inverse(sk_c1) = sk_c8),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[65, 44])).
% 0.38/0.60 tff(67,plain,
% 0.38/0.60 (sk_c8 = inverse(sk_c1)),
% 0.38/0.60 inference(symmetry,[status(thm)],[66])).
% 0.38/0.60 tff(68,plain,
% 0.38/0.60 (multiply(sk_c2, sk_c3) = inverse(sk_c1)),
% 0.38/0.60 inference(transitivity,[status(thm)],[50, 67])).
% 0.38/0.60 tff(69,plain,
% 0.38/0.60 (multiply(multiply(sk_c2, sk_c3), sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.38/0.60 inference(monotonicity,[status(thm)],[68])).
% 0.38/0.60 tff(70,plain,
% 0.38/0.60 (multiply(inverse(sk_c1), sk_c1) = multiply(multiply(sk_c2, sk_c3), sk_c1)),
% 0.38/0.60 inference(symmetry,[status(thm)],[69])).
% 0.38/0.60 tff(71,plain,
% 0.38/0.60 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c1), sk_c1) = identity)),
% 0.38/0.60 inference(quant_inst,[status(thm)],[])).
% 0.38/0.60 tff(72,plain,
% 0.38/0.60 (multiply(inverse(sk_c1), sk_c1) = identity),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[71, 41])).
% 0.38/0.60 tff(73,plain,
% 0.38/0.60 (identity = multiply(inverse(sk_c1), sk_c1)),
% 0.38/0.60 inference(symmetry,[status(thm)],[72])).
% 0.38/0.60 tff(74,plain,
% 0.38/0.60 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c2), sk_c2) = identity)),
% 0.38/0.60 inference(quant_inst,[status(thm)],[])).
% 0.38/0.60 tff(75,plain,
% 0.38/0.60 (multiply(inverse(sk_c2), sk_c2) = identity),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[74, 41])).
% 0.38/0.60 tff(76,plain,
% 0.38/0.60 (multiply(sk_c3, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.38/0.60 inference(monotonicity,[status(thm)],[60])).
% 0.38/0.60 tff(77,plain,
% 0.38/0.60 (multiply(sk_c3, sk_c2) = multiply(sk_c2, multiply(sk_c3, sk_c1))),
% 0.38/0.60 inference(transitivity,[status(thm)],[76, 75, 73, 70, 62])).
% 0.38/0.60 tff(78,plain,
% 0.38/0.60 (multiply(multiply(sk_c3, sk_c2), sk_c3) = multiply(multiply(sk_c2, multiply(sk_c3, sk_c1)), inverse(sk_c2))),
% 0.38/0.60 inference(monotonicity,[status(thm)],[77, 60])).
% 0.38/0.60 tff(79,plain,
% 0.38/0.60 (multiply(multiply(sk_c2, multiply(sk_c3, sk_c1)), inverse(sk_c2)) = multiply(multiply(sk_c3, sk_c2), sk_c3)),
% 0.38/0.60 inference(symmetry,[status(thm)],[78])).
% 0.38/0.60 tff(80,plain,
% 0.38/0.60 (identity = multiply(sk_c2, multiply(sk_c3, sk_c1))),
% 0.38/0.60 inference(transitivity,[status(thm)],[73, 70, 62])).
% 0.38/0.60 tff(81,plain,
% 0.38/0.60 (multiply(identity, sk_c3) = multiply(multiply(sk_c2, multiply(sk_c3, sk_c1)), inverse(sk_c2))),
% 0.38/0.60 inference(monotonicity,[status(thm)],[80, 60])).
% 0.38/0.60 tff(82,plain,
% 0.38/0.60 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c3) = sk_c3)),
% 0.38/0.60 inference(quant_inst,[status(thm)],[])).
% 0.38/0.60 tff(83,plain,
% 0.38/0.60 (multiply(identity, sk_c3) = sk_c3),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[82, 7])).
% 0.38/0.60 tff(84,plain,
% 0.38/0.60 (sk_c3 = multiply(identity, sk_c3)),
% 0.38/0.60 inference(symmetry,[status(thm)],[83])).
% 0.38/0.60 tff(85,plain,
% 0.38/0.60 (sk_c3 = multiply(sk_c3, sk_c8)),
% 0.38/0.60 inference(transitivity,[status(thm)],[84, 81, 79, 55, 53])).
% 0.38/0.60 tff(86,plain,
% 0.38/0.60 (multiply(sk_c2, sk_c3) = multiply(sk_c2, multiply(sk_c3, sk_c8))),
% 0.38/0.60 inference(monotonicity,[status(thm)],[85])).
% 0.38/0.60 tff(87,plain,
% 0.38/0.60 (multiply(sk_c2, multiply(sk_c3, sk_c8)) = multiply(sk_c2, sk_c3)),
% 0.38/0.60 inference(symmetry,[status(thm)],[86])).
% 0.38/0.60 tff(88,plain,
% 0.38/0.60 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, sk_c3), sk_c8) = multiply(sk_c2, multiply(sk_c3, sk_c8)))),
% 0.38/0.60 inference(quant_inst,[status(thm)],[])).
% 0.38/0.60 tff(89,plain,
% 0.38/0.60 (multiply(multiply(sk_c2, sk_c3), sk_c8) = multiply(sk_c2, multiply(sk_c3, sk_c8))),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[88, 32])).
% 0.38/0.60 tff(90,plain,
% 0.38/0.60 (multiply(multiply(sk_c2, sk_c3), sk_c8) = multiply(sk_c8, sk_c8)),
% 0.38/0.60 inference(monotonicity,[status(thm)],[50])).
% 0.38/0.60 tff(91,plain,
% 0.38/0.60 (multiply(sk_c8, sk_c8) = multiply(multiply(sk_c2, sk_c3), sk_c8)),
% 0.38/0.60 inference(symmetry,[status(thm)],[90])).
% 0.38/0.60 tff(92,plain,
% 0.38/0.60 (multiply(sk_c8, sk_c8) = multiply(sk_c8, multiply(sk_c2, sk_c3))),
% 0.38/0.60 inference(monotonicity,[status(thm)],[51])).
% 0.38/0.60 tff(93,plain,
% 0.38/0.60 (multiply(sk_c8, multiply(sk_c2, sk_c3)) = multiply(sk_c8, sk_c8)),
% 0.38/0.60 inference(symmetry,[status(thm)],[92])).
% 0.38/0.60 tff(94,plain,
% 0.38/0.60 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, multiply(sk_c8, multiply(sk_c2, sk_c3))) = multiply(sk_c8, multiply(sk_c2, sk_c3)))),
% 0.38/0.60 inference(quant_inst,[status(thm)],[])).
% 0.38/0.60 tff(95,plain,
% 0.38/0.60 (multiply(identity, multiply(sk_c8, multiply(sk_c2, sk_c3))) = multiply(sk_c8, multiply(sk_c2, sk_c3))),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[94, 7])).
% 0.38/0.60 tff(96,plain,
% 0.38/0.60 (multiply(sk_c8, multiply(sk_c2, sk_c3)) = sk_c8),
% 0.38/0.60 inference(transitivity,[status(thm)],[93, 91, 89, 87, 50])).
% 0.38/0.60 tff(97,assumption,(~(inverse(sk_c8) = sk_c7)), introduced(assumption)).
% 0.38/0.60 tff(98,plain,
% 0.38/0.60 (((multiply(sk_c1, sk_c8) = sk_c7) | (inverse(sk_c8) = sk_c7)) <=> ((multiply(sk_c1, sk_c8) = sk_c7) | (inverse(sk_c8) = sk_c7))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(99,axiom,((multiply(sk_c1, sk_c8) = sk_c7) | (inverse(sk_c8) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_1')).
% 0.38/0.60 tff(100,plain,
% 0.38/0.60 ((multiply(sk_c1, sk_c8) = sk_c7) | (inverse(sk_c8) = sk_c7)),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.38/0.60 tff(101,plain,
% 0.38/0.60 ((multiply(sk_c1, sk_c8) = sk_c7) | (inverse(sk_c8) = sk_c7)),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[100, 98])).
% 0.38/0.60 tff(102,plain,
% 0.38/0.60 ((multiply(sk_c1, sk_c8) = sk_c7) | (inverse(sk_c8) = sk_c7)),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[101, 98])).
% 0.38/0.60 tff(103,plain,
% 0.38/0.60 ((multiply(sk_c1, sk_c8) = sk_c7) | (inverse(sk_c8) = sk_c7)),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.38/0.60 tff(104,plain,
% 0.38/0.60 ((multiply(sk_c1, sk_c8) = sk_c7) | (inverse(sk_c8) = sk_c7)),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[103, 98])).
% 0.38/0.60 tff(105,plain,
% 0.38/0.60 (multiply(sk_c1, sk_c8) = sk_c7),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[104, 97])).
% 0.38/0.60 tff(106,plain,
% 0.38/0.60 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c8), sk_c8) = identity)),
% 0.38/0.60 inference(quant_inst,[status(thm)],[])).
% 0.38/0.60 tff(107,plain,
% 0.38/0.60 (multiply(inverse(sk_c8), sk_c8) = identity),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[106, 41])).
% 0.38/0.60 tff(108,plain,
% 0.38/0.60 (((inverse(sk_c8) = sk_c7) | (multiply(sk_c2, sk_c3) = sk_c8)) <=> ((inverse(sk_c8) = sk_c7) | (multiply(sk_c2, sk_c3) = sk_c8))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(109,plain,
% 0.38/0.60 (((multiply(sk_c2, sk_c3) = sk_c8) | (inverse(sk_c8) = sk_c7)) <=> ((inverse(sk_c8) = sk_c7) | (multiply(sk_c2, sk_c3) = sk_c8))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(110,axiom,((multiply(sk_c2, sk_c3) = sk_c8) | (inverse(sk_c8) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_13')).
% 0.38/0.60 tff(111,plain,
% 0.38/0.60 ((inverse(sk_c8) = sk_c7) | (multiply(sk_c2, sk_c3) = sk_c8)),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.38/0.60 tff(112,plain,
% 0.38/0.60 ((inverse(sk_c8) = sk_c7) | (multiply(sk_c2, sk_c3) = sk_c8)),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[111, 108])).
% 0.38/0.60 tff(113,plain,
% 0.38/0.60 (multiply(sk_c2, sk_c3) = sk_c8),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[112, 97])).
% 0.38/0.60 tff(114,plain,
% 0.38/0.60 (multiply(inverse(sk_c8), multiply(sk_c2, sk_c3)) = multiply(inverse(sk_c8), sk_c8)),
% 0.38/0.60 inference(monotonicity,[status(thm)],[113])).
% 0.38/0.60 tff(115,plain,
% 0.38/0.60 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(inverse(sk_c8), sk_c2), sk_c3) = multiply(inverse(sk_c8), multiply(sk_c2, sk_c3)))),
% 0.38/0.60 inference(quant_inst,[status(thm)],[])).
% 0.38/0.60 tff(116,plain,
% 0.38/0.60 (multiply(multiply(inverse(sk_c8), sk_c2), sk_c3) = multiply(inverse(sk_c8), multiply(sk_c2, sk_c3))),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[115, 32])).
% 0.38/0.60 tff(117,plain,
% 0.38/0.60 (((inverse(sk_c2) = sk_c3) | (inverse(sk_c8) = sk_c7)) <=> ((inverse(sk_c2) = sk_c3) | (inverse(sk_c8) = sk_c7))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(118,axiom,((inverse(sk_c2) = sk_c3) | (inverse(sk_c8) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_19')).
% 0.38/0.60 tff(119,plain,
% 0.38/0.60 ((inverse(sk_c2) = sk_c3) | (inverse(sk_c8) = sk_c7)),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.38/0.60 tff(120,plain,
% 0.38/0.60 (inverse(sk_c2) = sk_c3),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[119, 97])).
% 0.38/0.60 tff(121,plain,
% 0.38/0.60 (sk_c3 = inverse(sk_c2)),
% 0.38/0.60 inference(symmetry,[status(thm)],[120])).
% 0.38/0.60 tff(122,plain,
% 0.38/0.60 (((inverse(sk_c1) = sk_c8) | (inverse(sk_c8) = sk_c7)) <=> ((inverse(sk_c1) = sk_c8) | (inverse(sk_c8) = sk_c7))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(123,axiom,((inverse(sk_c1) = sk_c8) | (inverse(sk_c8) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_7')).
% 0.38/0.60 tff(124,plain,
% 0.38/0.60 ((inverse(sk_c1) = sk_c8) | (inverse(sk_c8) = sk_c7)),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.38/0.60 tff(125,plain,
% 0.38/0.60 (inverse(sk_c1) = sk_c8),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[124, 97])).
% 0.38/0.60 tff(126,plain,
% 0.38/0.60 (sk_c8 = inverse(sk_c1)),
% 0.38/0.60 inference(symmetry,[status(thm)],[125])).
% 0.38/0.60 tff(127,plain,
% 0.38/0.60 (multiply(sk_c2, sk_c3) = inverse(sk_c1)),
% 0.38/0.60 inference(transitivity,[status(thm)],[113, 126])).
% 0.38/0.60 tff(128,plain,
% 0.38/0.60 (multiply(multiply(sk_c2, sk_c3), sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.38/0.60 inference(monotonicity,[status(thm)],[127])).
% 0.38/0.60 tff(129,plain,
% 0.38/0.60 (multiply(inverse(sk_c1), sk_c1) = multiply(multiply(sk_c2, sk_c3), sk_c1)),
% 0.38/0.60 inference(symmetry,[status(thm)],[128])).
% 0.38/0.60 tff(130,plain,
% 0.38/0.60 (identity = multiply(sk_c2, multiply(sk_c3, sk_c1))),
% 0.38/0.60 inference(transitivity,[status(thm)],[73, 129, 62])).
% 0.38/0.60 tff(131,plain,
% 0.38/0.60 (multiply(identity, sk_c3) = multiply(multiply(sk_c2, multiply(sk_c3, sk_c1)), inverse(sk_c2))),
% 0.38/0.60 inference(monotonicity,[status(thm)],[130, 121])).
% 0.38/0.60 tff(132,plain,
% 0.38/0.60 (multiply(multiply(sk_c2, multiply(sk_c3, sk_c1)), inverse(sk_c2)) = multiply(identity, sk_c3)),
% 0.38/0.60 inference(symmetry,[status(thm)],[131])).
% 0.38/0.60 tff(133,plain,
% 0.38/0.60 (multiply(sk_c3, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.38/0.60 inference(monotonicity,[status(thm)],[121])).
% 0.38/0.60 tff(134,plain,
% 0.38/0.60 (multiply(sk_c3, sk_c2) = multiply(sk_c2, multiply(sk_c3, sk_c1))),
% 0.38/0.60 inference(transitivity,[status(thm)],[133, 75, 73, 129, 62])).
% 0.38/0.60 tff(135,plain,
% 0.38/0.60 (multiply(multiply(sk_c3, sk_c2), sk_c3) = multiply(multiply(sk_c2, multiply(sk_c3, sk_c1)), inverse(sk_c2))),
% 0.38/0.60 inference(monotonicity,[status(thm)],[134, 121])).
% 0.38/0.60 tff(136,plain,
% 0.38/0.60 (multiply(sk_c3, multiply(sk_c2, sk_c3)) = multiply(multiply(sk_c3, sk_c2), sk_c3)),
% 0.38/0.60 inference(symmetry,[status(thm)],[55])).
% 0.38/0.60 tff(137,plain,
% 0.38/0.60 (sk_c8 = multiply(sk_c2, sk_c3)),
% 0.38/0.60 inference(symmetry,[status(thm)],[113])).
% 0.38/0.60 tff(138,plain,
% 0.38/0.60 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, multiply(sk_c3, sk_c1)), inverse(sk_c2)) = multiply(sk_c2, multiply(multiply(sk_c3, sk_c1), inverse(sk_c2))))),
% 0.38/0.61 inference(quant_inst,[status(thm)],[])).
% 0.38/0.61 tff(139,plain,
% 0.38/0.61 (multiply(multiply(sk_c2, multiply(sk_c3, sk_c1)), inverse(sk_c2)) = multiply(sk_c2, multiply(multiply(sk_c3, sk_c1), inverse(sk_c2)))),
% 0.38/0.61 inference(unit_resolution,[status(thm)],[138, 32])).
% 0.38/0.61 tff(140,plain,
% 0.38/0.61 (multiply(sk_c2, multiply(multiply(sk_c3, sk_c1), inverse(sk_c2))) = multiply(multiply(sk_c2, multiply(sk_c3, sk_c1)), inverse(sk_c2))),
% 0.38/0.61 inference(symmetry,[status(thm)],[139])).
% 0.38/0.61 tff(141,plain,
% 0.38/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c3, sk_c1), inverse(sk_c2)) = multiply(sk_c3, multiply(sk_c1, inverse(sk_c2))))),
% 0.38/0.61 inference(quant_inst,[status(thm)],[])).
% 0.38/0.61 tff(142,plain,
% 0.38/0.61 (multiply(multiply(sk_c3, sk_c1), inverse(sk_c2)) = multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))),
% 0.38/0.61 inference(unit_resolution,[status(thm)],[141, 32])).
% 0.38/0.61 tff(143,plain,
% 0.38/0.61 (multiply(sk_c2, multiply(multiply(sk_c3, sk_c1), inverse(sk_c2))) = multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2))))),
% 0.38/0.61 inference(monotonicity,[status(thm)],[142])).
% 0.38/0.61 tff(144,plain,
% 0.38/0.61 (multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))) = multiply(sk_c2, multiply(multiply(sk_c3, sk_c1), inverse(sk_c2)))),
% 0.38/0.61 inference(symmetry,[status(thm)],[143])).
% 0.38/0.61 tff(145,plain,
% 0.38/0.61 (multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))) = sk_c3),
% 0.38/0.61 inference(transitivity,[status(thm)],[144, 140, 132, 83])).
% 0.38/0.61 tff(146,plain,
% 0.38/0.61 (multiply(multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))), sk_c8) = multiply(sk_c3, multiply(sk_c2, sk_c3))),
% 0.38/0.61 inference(monotonicity,[status(thm)],[145, 137])).
% 0.38/0.61 tff(147,plain,
% 0.38/0.61 (multiply(multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))), sk_c8) = sk_c3),
% 0.38/0.61 inference(transitivity,[status(thm)],[146, 136, 135, 132, 83])).
% 0.38/0.61 tff(148,plain,
% 0.38/0.61 (multiply(multiply(inverse(sk_c8), sk_c2), multiply(multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))), sk_c8)) = multiply(multiply(inverse(sk_c8), sk_c2), sk_c3)),
% 0.38/0.61 inference(monotonicity,[status(thm)],[147])).
% 0.38/0.61 tff(149,plain,
% 0.38/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(inverse(sk_c8), sk_c2), multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2))))), sk_c8) = multiply(multiply(inverse(sk_c8), sk_c2), multiply(multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))), sk_c8)))),
% 0.38/0.61 inference(quant_inst,[status(thm)],[])).
% 0.38/0.61 tff(150,plain,
% 0.38/0.61 (multiply(multiply(multiply(inverse(sk_c8), sk_c2), multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2))))), sk_c8) = multiply(multiply(inverse(sk_c8), sk_c2), multiply(multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))), sk_c8))),
% 0.38/0.61 inference(unit_resolution,[status(thm)],[149, 32])).
% 0.38/0.61 tff(151,plain,
% 0.38/0.61 (multiply(multiply(inverse(sk_c8), sk_c2), multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2))))) = multiply(multiply(inverse(sk_c8), sk_c2), sk_c3)),
% 0.38/0.61 inference(monotonicity,[status(thm)],[145])).
% 0.38/0.61 tff(152,plain,
% 0.38/0.61 (multiply(multiply(inverse(sk_c8), sk_c2), sk_c3) = multiply(multiply(inverse(sk_c8), sk_c2), multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))))),
% 0.38/0.61 inference(symmetry,[status(thm)],[151])).
% 0.38/0.61 tff(153,plain,
% 0.38/0.61 (multiply(inverse(sk_c8), multiply(sk_c2, sk_c3)) = multiply(multiply(inverse(sk_c8), sk_c2), sk_c3)),
% 0.38/0.61 inference(symmetry,[status(thm)],[116])).
% 0.38/0.61 tff(154,plain,
% 0.38/0.61 (multiply(inverse(sk_c8), sk_c8) = multiply(inverse(sk_c8), multiply(sk_c2, sk_c3))),
% 0.38/0.61 inference(symmetry,[status(thm)],[114])).
% 0.38/0.61 tff(155,plain,
% 0.38/0.61 (identity = multiply(inverse(sk_c8), sk_c8)),
% 0.38/0.61 inference(symmetry,[status(thm)],[107])).
% 0.38/0.61 tff(156,plain,
% 0.38/0.61 (identity = multiply(multiply(inverse(sk_c8), sk_c2), multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))))),
% 0.38/0.61 inference(transitivity,[status(thm)],[155, 154, 153, 152])).
% 0.38/0.61 tff(157,plain,
% 0.38/0.61 (multiply(identity, sk_c8) = multiply(multiply(multiply(inverse(sk_c8), sk_c2), multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2))))), sk_c8)),
% 0.38/0.61 inference(monotonicity,[status(thm)],[156])).
% 0.38/0.61 tff(158,plain,
% 0.38/0.61 (sk_c8 = multiply(identity, sk_c8)),
% 0.38/0.61 inference(symmetry,[status(thm)],[9])).
% 0.38/0.61 tff(159,plain,
% 0.38/0.61 (sk_c8 = identity),
% 0.38/0.61 inference(transitivity,[status(thm)],[158, 157, 150, 148, 116, 114, 107])).
% 0.38/0.61 tff(160,plain,
% 0.38/0.61 (multiply(sk_c1, sk_c8) = multiply(sk_c1, identity)),
% 0.38/0.61 inference(monotonicity,[status(thm)],[159])).
% 0.38/0.61 tff(161,plain,
% 0.38/0.61 (multiply(sk_c1, identity) = multiply(sk_c1, sk_c8)),
% 0.38/0.61 inference(symmetry,[status(thm)],[160])).
% 0.38/0.61 tff(162,plain,
% 0.38/0.61 (multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))) = inverse(sk_c2)),
% 0.38/0.61 inference(transitivity,[status(thm)],[144, 140, 132, 83, 121])).
% 0.38/0.61 tff(163,plain,
% 0.38/0.61 (multiply(multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))), sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.38/0.61 inference(monotonicity,[status(thm)],[162])).
% 0.38/0.61 tff(164,plain,
% 0.38/0.61 (multiply(inverse(sk_c2), sk_c2) = multiply(multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))), sk_c2)),
% 0.38/0.61 inference(symmetry,[status(thm)],[163])).
% 0.38/0.61 tff(165,plain,
% 0.38/0.61 (identity = multiply(inverse(sk_c2), sk_c2)),
% 0.38/0.61 inference(symmetry,[status(thm)],[75])).
% 0.38/0.61 tff(166,plain,
% 0.38/0.61 (identity = multiply(multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))), sk_c2)),
% 0.38/0.61 inference(transitivity,[status(thm)],[165, 164])).
% 0.38/0.61 tff(167,plain,
% 0.38/0.61 (multiply(sk_c1, identity) = multiply(sk_c1, multiply(multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))), sk_c2))),
% 0.38/0.61 inference(monotonicity,[status(thm)],[166])).
% 0.38/0.61 tff(168,plain,
% 0.38/0.61 (multiply(sk_c1, multiply(multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))), sk_c2)) = multiply(sk_c1, identity)),
% 0.38/0.61 inference(symmetry,[status(thm)],[167])).
% 0.38/0.61 tff(169,plain,
% 0.38/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2))))), sk_c2) = multiply(sk_c1, multiply(multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))), sk_c2)))),
% 0.38/0.61 inference(quant_inst,[status(thm)],[])).
% 0.38/0.61 tff(170,plain,
% 0.38/0.61 (multiply(multiply(sk_c1, multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2))))), sk_c2) = multiply(sk_c1, multiply(multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))), sk_c2))),
% 0.38/0.61 inference(unit_resolution,[status(thm)],[169, 32])).
% 0.38/0.61 tff(171,plain,
% 0.38/0.61 (multiply(sk_c1, multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2))))) = multiply(sk_c1, inverse(sk_c2))),
% 0.38/0.61 inference(monotonicity,[status(thm)],[162])).
% 0.38/0.61 tff(172,plain,
% 0.38/0.61 (multiply(multiply(sk_c1, multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2))))), sk_c2) = multiply(multiply(sk_c1, inverse(sk_c2)), sk_c2)),
% 0.38/0.61 inference(monotonicity,[status(thm)],[171])).
% 0.38/0.61 tff(173,plain,
% 0.38/0.61 (multiply(multiply(sk_c1, inverse(sk_c2)), sk_c2) = multiply(multiply(sk_c1, multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2))))), sk_c2)),
% 0.38/0.61 inference(symmetry,[status(thm)],[172])).
% 0.38/0.61 tff(174,plain,
% 0.38/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, sk_c3), multiply(sk_c1, inverse(sk_c2))) = multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))))),
% 0.38/0.61 inference(quant_inst,[status(thm)],[])).
% 0.38/0.61 tff(175,plain,
% 0.38/0.61 (multiply(multiply(sk_c2, sk_c3), multiply(sk_c1, inverse(sk_c2))) = multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2))))),
% 0.38/0.61 inference(unit_resolution,[status(thm)],[174, 32])).
% 0.38/0.61 tff(176,plain,
% 0.38/0.61 (multiply(sk_c8, multiply(sk_c1, inverse(sk_c2))) = multiply(multiply(sk_c2, sk_c3), multiply(sk_c1, inverse(sk_c2)))),
% 0.38/0.61 inference(monotonicity,[status(thm)],[137])).
% 0.38/0.61 tff(177,plain,
% 0.38/0.61 (multiply(sk_c8, multiply(sk_c1, inverse(sk_c2))) = inverse(sk_c2)),
% 0.38/0.61 inference(transitivity,[status(thm)],[176, 175, 144, 140, 132, 83, 121])).
% 0.38/0.61 tff(178,plain,
% 0.38/0.61 (multiply(identity, multiply(sk_c8, multiply(sk_c1, inverse(sk_c2)))) = multiply(multiply(sk_c2, multiply(sk_c3, sk_c1)), inverse(sk_c2))),
% 0.38/0.61 inference(monotonicity,[status(thm)],[130, 177])).
% 0.38/0.61 tff(179,plain,
% 0.38/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, sk_c8), multiply(sk_c1, inverse(sk_c2))) = multiply(identity, multiply(sk_c8, multiply(sk_c1, inverse(sk_c2)))))),
% 0.38/0.61 inference(quant_inst,[status(thm)],[])).
% 0.38/0.61 tff(180,plain,
% 0.38/0.61 (multiply(multiply(identity, sk_c8), multiply(sk_c1, inverse(sk_c2))) = multiply(identity, multiply(sk_c8, multiply(sk_c1, inverse(sk_c2))))),
% 0.38/0.61 inference(unit_resolution,[status(thm)],[179, 32])).
% 0.38/0.61 tff(181,plain,
% 0.38/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(inverse(sk_c8), sk_c8), sk_c3) = multiply(inverse(sk_c8), multiply(sk_c8, sk_c3)))),
% 0.38/0.61 inference(quant_inst,[status(thm)],[])).
% 0.38/0.61 tff(182,plain,
% 0.38/0.61 (multiply(multiply(inverse(sk_c8), sk_c8), sk_c3) = multiply(inverse(sk_c8), multiply(sk_c8, sk_c3))),
% 0.38/0.61 inference(unit_resolution,[status(thm)],[181, 32])).
% 0.38/0.61 tff(183,plain,
% 0.38/0.61 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c2, multiply(sk_c3, sk_c1))),
% 0.38/0.61 inference(transitivity,[status(thm)],[107, 73, 129, 62])).
% 0.38/0.61 tff(184,plain,
% 0.38/0.61 (multiply(multiply(inverse(sk_c8), sk_c8), sk_c3) = multiply(multiply(sk_c2, multiply(sk_c3, sk_c1)), inverse(sk_c2))),
% 0.38/0.61 inference(monotonicity,[status(thm)],[183, 121])).
% 0.38/0.61 tff(185,plain,
% 0.38/0.61 (multiply(multiply(sk_c2, multiply(sk_c3, sk_c1)), inverse(sk_c2)) = multiply(multiply(inverse(sk_c8), sk_c8), sk_c3)),
% 0.38/0.61 inference(symmetry,[status(thm)],[184])).
% 0.38/0.61 tff(186,plain,
% 0.38/0.61 (inverse(sk_c2) = multiply(inverse(sk_c8), multiply(sk_c8, sk_c3))),
% 0.38/0.61 inference(transitivity,[status(thm)],[120, 84, 131, 185, 182])).
% 0.38/0.61 tff(187,plain,
% 0.38/0.61 (multiply(sk_c1, inverse(sk_c2)) = multiply(sk_c1, multiply(inverse(sk_c8), multiply(sk_c8, sk_c3)))),
% 0.38/0.61 inference(monotonicity,[status(thm)],[186])).
% 0.38/0.61 tff(188,plain,
% 0.38/0.61 (multiply(sk_c1, multiply(inverse(sk_c8), multiply(sk_c8, sk_c3))) = multiply(sk_c1, inverse(sk_c2))),
% 0.38/0.61 inference(symmetry,[status(thm)],[187])).
% 0.38/0.61 tff(189,plain,
% 0.38/0.61 (multiply(multiply(multiply(inverse(sk_c8), sk_c2), multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2))))), sk_c8) = multiply(identity, sk_c8)),
% 0.38/0.61 inference(symmetry,[status(thm)],[157])).
% 0.38/0.61 tff(190,plain,
% 0.38/0.61 (multiply(multiply(inverse(sk_c8), sk_c2), multiply(multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))), sk_c8)) = multiply(multiply(multiply(inverse(sk_c8), sk_c2), multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2))))), sk_c8)),
% 0.38/0.61 inference(symmetry,[status(thm)],[150])).
% 0.38/0.61 tff(191,plain,
% 0.38/0.61 (multiply(multiply(inverse(sk_c8), sk_c2), sk_c3) = multiply(multiply(inverse(sk_c8), sk_c2), multiply(multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))), sk_c8))),
% 0.38/0.61 inference(symmetry,[status(thm)],[148])).
% 0.38/0.61 tff(192,plain,
% 0.38/0.61 (identity = multiply(identity, sk_c8)),
% 0.38/0.61 inference(transitivity,[status(thm)],[155, 154, 153, 191, 190, 189])).
% 0.38/0.61 tff(193,plain,
% 0.38/0.61 (multiply(identity, multiply(sk_c1, multiply(inverse(sk_c8), multiply(sk_c8, sk_c3)))) = multiply(multiply(identity, sk_c8), multiply(sk_c1, inverse(sk_c2)))),
% 0.38/0.61 inference(monotonicity,[status(thm)],[192, 188])).
% 0.38/0.61 tff(194,plain,
% 0.38/0.61 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, multiply(sk_c1, multiply(inverse(sk_c8), multiply(sk_c8, sk_c3)))) = multiply(sk_c1, multiply(inverse(sk_c8), multiply(sk_c8, sk_c3))))),
% 0.38/0.61 inference(quant_inst,[status(thm)],[])).
% 0.38/0.61 tff(195,plain,
% 0.38/0.61 (multiply(identity, multiply(sk_c1, multiply(inverse(sk_c8), multiply(sk_c8, sk_c3)))) = multiply(sk_c1, multiply(inverse(sk_c8), multiply(sk_c8, sk_c3)))),
% 0.38/0.61 inference(unit_resolution,[status(thm)],[194, 7])).
% 0.38/0.61 tff(196,plain,
% 0.38/0.61 (multiply(sk_c1, multiply(inverse(sk_c8), multiply(sk_c8, sk_c3))) = multiply(identity, multiply(sk_c1, multiply(inverse(sk_c8), multiply(sk_c8, sk_c3))))),
% 0.38/0.61 inference(symmetry,[status(thm)],[195])).
% 0.38/0.61 tff(197,plain,
% 0.38/0.61 (multiply(sk_c1, inverse(sk_c2)) = inverse(sk_c2)),
% 0.38/0.61 inference(transitivity,[status(thm)],[187, 196, 193, 180, 178, 132, 83, 121])).
% 0.38/0.61 tff(198,plain,
% 0.38/0.61 (multiply(multiply(sk_c1, inverse(sk_c2)), sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.38/0.61 inference(monotonicity,[status(thm)],[197])).
% 0.38/0.61 tff(199,plain,
% 0.38/0.61 (multiply(inverse(sk_c2), sk_c2) = multiply(multiply(sk_c1, inverse(sk_c2)), sk_c2)),
% 0.38/0.61 inference(symmetry,[status(thm)],[198])).
% 0.38/0.61 tff(200,plain,
% 0.38/0.61 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c1) = sk_c1)),
% 0.38/0.61 inference(quant_inst,[status(thm)],[])).
% 0.38/0.61 tff(201,plain,
% 0.38/0.61 (multiply(identity, sk_c1) = sk_c1),
% 0.38/0.61 inference(unit_resolution,[status(thm)],[200, 7])).
% 0.38/0.61 tff(202,plain,
% 0.38/0.61 (multiply(identity, sk_c1) = multiply(multiply(identity, sk_c8), sk_c1)),
% 0.38/0.61 inference(monotonicity,[status(thm)],[192])).
% 0.38/0.61 tff(203,plain,
% 0.38/0.61 (multiply(multiply(identity, sk_c8), sk_c1) = multiply(identity, sk_c1)),
% 0.38/0.61 inference(symmetry,[status(thm)],[202])).
% 0.38/0.61 tff(204,plain,
% 0.38/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, sk_c8), sk_c1) = multiply(identity, multiply(sk_c8, sk_c1)))),
% 0.38/0.61 inference(quant_inst,[status(thm)],[])).
% 0.38/0.61 tff(205,plain,
% 0.38/0.61 (multiply(multiply(identity, sk_c8), sk_c1) = multiply(identity, multiply(sk_c8, sk_c1))),
% 0.38/0.61 inference(unit_resolution,[status(thm)],[204, 32])).
% 0.38/0.61 tff(206,plain,
% 0.38/0.61 (multiply(identity, multiply(sk_c8, sk_c1)) = multiply(multiply(identity, sk_c8), sk_c1)),
% 0.38/0.61 inference(symmetry,[status(thm)],[205])).
% 0.38/0.61 tff(207,plain,
% 0.38/0.61 (multiply(sk_c8, sk_c1) = multiply(multiply(sk_c2, sk_c3), sk_c1)),
% 0.38/0.61 inference(monotonicity,[status(thm)],[137])).
% 0.38/0.61 tff(208,plain,
% 0.38/0.61 (multiply(sk_c8, sk_c1) = identity),
% 0.38/0.61 inference(transitivity,[status(thm)],[207, 128, 72])).
% 0.38/0.61 tff(209,plain,
% 0.38/0.61 (multiply(identity, multiply(sk_c8, sk_c1)) = multiply(identity, identity)),
% 0.38/0.61 inference(monotonicity,[status(thm)],[208])).
% 0.38/0.61 tff(210,plain,
% 0.38/0.61 (multiply(identity, identity) = multiply(identity, multiply(sk_c8, sk_c1))),
% 0.38/0.61 inference(symmetry,[status(thm)],[209])).
% 0.38/0.61 tff(211,plain,
% 0.38/0.61 (multiply(identity, identity) = multiply(identity, multiply(multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))), sk_c2))),
% 0.38/0.61 inference(monotonicity,[status(thm)],[166])).
% 0.38/0.61 tff(212,plain,
% 0.38/0.61 (multiply(identity, multiply(multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))), sk_c2)) = multiply(identity, identity)),
% 0.38/0.61 inference(symmetry,[status(thm)],[211])).
% 0.38/0.61 tff(213,plain,
% 0.38/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2))))), sk_c2) = multiply(identity, multiply(multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))), sk_c2)))),
% 0.38/0.61 inference(quant_inst,[status(thm)],[])).
% 0.38/0.61 tff(214,plain,
% 0.38/0.61 (multiply(multiply(identity, multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2))))), sk_c2) = multiply(identity, multiply(multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))), sk_c2))),
% 0.38/0.61 inference(unit_resolution,[status(thm)],[213, 32])).
% 0.38/0.61 tff(215,plain,
% 0.38/0.61 (multiply(identity, multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2))))) = multiply(multiply(sk_c2, multiply(sk_c3, sk_c1)), inverse(sk_c2))),
% 0.38/0.61 inference(monotonicity,[status(thm)],[130, 162])).
% 0.38/0.61 tff(216,plain,
% 0.38/0.61 (multiply(identity, multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2))))) = inverse(sk_c2)),
% 0.38/0.61 inference(transitivity,[status(thm)],[215, 132, 83, 121])).
% 0.38/0.61 tff(217,plain,
% 0.38/0.61 (multiply(multiply(identity, multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2))))), sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.38/0.61 inference(monotonicity,[status(thm)],[216])).
% 0.38/0.61 tff(218,plain,
% 0.38/0.61 (multiply(inverse(sk_c2), sk_c2) = multiply(multiply(identity, multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2))))), sk_c2)),
% 0.38/0.61 inference(symmetry,[status(thm)],[217])).
% 0.38/0.61 tff(219,plain,
% 0.38/0.61 (sk_c8 = sk_c1),
% 0.38/0.61 inference(transitivity,[status(thm)],[158, 157, 150, 148, 116, 114, 107, 165, 218, 214, 212, 210, 206, 203, 201])).
% 0.38/0.61 tff(220,plain,
% 0.38/0.61 (inverse(sk_c8) = inverse(sk_c1)),
% 0.38/0.61 inference(monotonicity,[status(thm)],[219])).
% 0.38/0.61 tff(221,plain,
% 0.38/0.61 (inverse(sk_c8) = sk_c7),
% 0.38/0.61 inference(transitivity,[status(thm)],[220, 125, 158, 157, 150, 148, 116, 114, 107, 165, 199, 173, 170, 168, 161, 105])).
% 0.38/0.61 tff(222,plain,
% 0.38/0.61 ($false),
% 0.38/0.61 inference(unit_resolution,[status(thm)],[97, 221])).
% 0.38/0.61 tff(223,plain,(inverse(sk_c8) = sk_c7), inference(lemma,lemma(discharge,[]))).
% 0.38/0.61 tff(224,plain,
% 0.38/0.61 (sk_c7 = inverse(sk_c8)),
% 0.38/0.61 inference(symmetry,[status(thm)],[223])).
% 0.38/0.61 tff(225,assumption,(~(multiply(sk_c1, sk_c8) = sk_c7)), introduced(assumption)).
% 0.38/0.61 tff(226,plain,
% 0.38/0.61 (((multiply(sk_c1, sk_c8) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7)) <=> ((multiply(sk_c1, sk_c8) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7))),
% 0.38/0.61 inference(rewrite,[status(thm)],[])).
% 0.38/0.61 tff(227,axiom,((multiply(sk_c1, sk_c8) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_4')).
% 0.38/0.61 tff(228,plain,
% 0.38/0.61 ((multiply(sk_c1, sk_c8) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7)),
% 0.38/0.61 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.38/0.61 tff(229,plain,
% 0.38/0.61 (multiply(sk_c8, sk_c6) = sk_c7),
% 0.38/0.61 inference(unit_resolution,[status(thm)],[228, 225])).
% 0.38/0.61 tff(230,plain,
% 0.38/0.61 (((multiply(sk_c1, sk_c8) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6)) <=> ((multiply(sk_c1, sk_c8) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6))),
% 0.38/0.61 inference(rewrite,[status(thm)],[])).
% 0.38/0.61 tff(231,axiom,((multiply(sk_c1, sk_c8) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_5')).
% 0.38/0.61 tff(232,plain,
% 0.38/0.61 ((multiply(sk_c1, sk_c8) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6)),
% 0.38/0.61 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.38/0.61 tff(233,plain,
% 0.38/0.61 (multiply(sk_c5, sk_c8) = sk_c6),
% 0.38/0.61 inference(unit_resolution,[status(thm)],[232, 225])).
% 0.38/0.61 tff(234,plain,
% 0.38/0.61 (multiply(sk_c8, multiply(sk_c5, sk_c8)) = multiply(sk_c8, sk_c6)),
% 0.38/0.61 inference(monotonicity,[status(thm)],[233])).
% 0.38/0.61 tff(235,plain,
% 0.38/0.61 (((multiply(sk_c1, sk_c8) = sk_c7) | (inverse(sk_c5) = sk_c8)) <=> ((multiply(sk_c1, sk_c8) = sk_c7) | (inverse(sk_c5) = sk_c8))),
% 0.38/0.61 inference(rewrite,[status(thm)],[])).
% 0.38/0.61 tff(236,axiom,((multiply(sk_c1, sk_c8) = sk_c7) | (inverse(sk_c5) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_6')).
% 0.38/0.61 tff(237,plain,
% 0.38/0.61 ((multiply(sk_c1, sk_c8) = sk_c7) | (inverse(sk_c5) = sk_c8)),
% 0.38/0.61 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.38/0.61 tff(238,plain,
% 0.38/0.61 ((multiply(sk_c1, sk_c8) = sk_c7) | (inverse(sk_c5) = sk_c8)),
% 0.38/0.61 inference(modus_ponens,[status(thm)],[237, 235])).
% 0.38/0.61 tff(239,plain,
% 0.38/0.61 ((multiply(sk_c1, sk_c8) = sk_c7) | (inverse(sk_c5) = sk_c8)),
% 0.38/0.61 inference(modus_ponens,[status(thm)],[238, 235])).
% 0.38/0.61 tff(240,plain,
% 0.38/0.61 ((multiply(sk_c1, sk_c8) = sk_c7) | (inverse(sk_c5) = sk_c8)),
% 0.38/0.61 inference(modus_ponens,[status(thm)],[239, 235])).
% 0.38/0.61 tff(241,plain,
% 0.38/0.61 ((multiply(sk_c1, sk_c8) = sk_c7) | (inverse(sk_c5) = sk_c8)),
% 0.38/0.61 inference(modus_ponens,[status(thm)],[240, 235])).
% 0.38/0.61 tff(242,plain,
% 0.38/0.61 (inverse(sk_c5) = sk_c8),
% 0.38/0.61 inference(unit_resolution,[status(thm)],[241, 225])).
% 0.38/0.61 tff(243,plain,
% 0.38/0.61 (sk_c8 = inverse(sk_c5)),
% 0.38/0.61 inference(symmetry,[status(thm)],[242])).
% 0.38/0.61 tff(244,plain,
% 0.38/0.61 (multiply(sk_c8, sk_c5) = multiply(inverse(sk_c5), sk_c5)),
% 0.38/0.61 inference(monotonicity,[status(thm)],[243])).
% 0.38/0.61 tff(245,plain,
% 0.38/0.61 (multiply(inverse(sk_c5), sk_c5) = multiply(sk_c8, sk_c5)),
% 0.38/0.61 inference(symmetry,[status(thm)],[244])).
% 0.38/0.61 tff(246,plain,
% 0.38/0.61 (identity = multiply(inverse(sk_c5), sk_c5)),
% 0.38/0.61 inference(symmetry,[status(thm)],[43])).
% 0.38/0.61 tff(247,plain,
% 0.38/0.61 (identity = multiply(sk_c8, sk_c5)),
% 0.38/0.61 inference(transitivity,[status(thm)],[246, 245])).
% 0.38/0.61 tff(248,plain,
% 0.38/0.61 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c5), sk_c8)),
% 0.38/0.61 inference(monotonicity,[status(thm)],[247])).
% 0.38/0.61 tff(249,plain,
% 0.38/0.61 (sk_c8 = sk_c7),
% 0.38/0.61 inference(transitivity,[status(thm)],[158, 248, 34, 234, 229])).
% 0.38/0.61 tff(250,plain,
% 0.38/0.61 (((multiply(sk_c1, sk_c8) = sk_c7) | (inverse(sk_c4) = sk_c8)) <=> ((multiply(sk_c1, sk_c8) = sk_c7) | (inverse(sk_c4) = sk_c8))),
% 0.38/0.61 inference(rewrite,[status(thm)],[])).
% 0.38/0.61 tff(251,axiom,((multiply(sk_c1, sk_c8) = sk_c7) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_2')).
% 0.38/0.61 tff(252,plain,
% 0.38/0.61 ((multiply(sk_c1, sk_c8) = sk_c7) | (inverse(sk_c4) = sk_c8)),
% 0.38/0.61 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.38/0.61 tff(253,plain,
% 0.38/0.61 ((multiply(sk_c1, sk_c8) = sk_c7) | (inverse(sk_c4) = sk_c8)),
% 0.38/0.61 inference(modus_ponens,[status(thm)],[252, 250])).
% 0.38/0.61 tff(254,plain,
% 0.38/0.61 ((multiply(sk_c1, sk_c8) = sk_c7) | (inverse(sk_c4) = sk_c8)),
% 0.38/0.61 inference(modus_ponens,[status(thm)],[253, 250])).
% 0.38/0.61 tff(255,plain,
% 0.38/0.61 ((multiply(sk_c1, sk_c8) = sk_c7) | (inverse(sk_c4) = sk_c8)),
% 0.38/0.61 inference(modus_ponens,[status(thm)],[254, 250])).
% 0.38/0.61 tff(256,plain,
% 0.38/0.61 ((multiply(sk_c1, sk_c8) = sk_c7) | (inverse(sk_c4) = sk_c8)),
% 0.38/0.61 inference(modus_ponens,[status(thm)],[255, 250])).
% 0.38/0.61 tff(257,plain,
% 0.38/0.61 (inverse(sk_c4) = sk_c8),
% 0.38/0.61 inference(unit_resolution,[status(thm)],[256, 225])).
% 0.38/0.61 tff(258,plain,
% 0.38/0.61 (multiply(sk_c4, inverse(sk_c4)) = multiply(sk_c4, sk_c8)),
% 0.38/0.62 inference(monotonicity,[status(thm)],[257])).
% 0.38/0.62 tff(259,plain,
% 0.38/0.62 ((multiply(sk_c4, inverse(sk_c4)) = sk_c8) <=> (multiply(sk_c4, sk_c8) = sk_c7)),
% 0.38/0.62 inference(monotonicity,[status(thm)],[258, 249])).
% 0.38/0.62 tff(260,plain,
% 0.38/0.62 ((multiply(sk_c4, sk_c8) = sk_c7) <=> (multiply(sk_c4, inverse(sk_c4)) = sk_c8)),
% 0.38/0.62 inference(symmetry,[status(thm)],[259])).
% 0.38/0.62 tff(261,plain,
% 0.38/0.62 (((multiply(sk_c1, sk_c8) = sk_c7) | (multiply(sk_c4, sk_c7) = sk_c8)) <=> ((multiply(sk_c1, sk_c8) = sk_c7) | (multiply(sk_c4, sk_c7) = sk_c8))),
% 0.38/0.62 inference(rewrite,[status(thm)],[])).
% 0.38/0.62 tff(262,axiom,((multiply(sk_c1, sk_c8) = sk_c7) | (multiply(sk_c4, sk_c7) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_3')).
% 0.38/0.62 tff(263,plain,
% 0.38/0.62 ((multiply(sk_c1, sk_c8) = sk_c7) | (multiply(sk_c4, sk_c7) = sk_c8)),
% 0.38/0.62 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.38/0.62 tff(264,plain,
% 0.38/0.62 (multiply(sk_c4, sk_c7) = sk_c8),
% 0.38/0.62 inference(unit_resolution,[status(thm)],[263, 225])).
% 0.38/0.62 tff(265,plain,
% 0.38/0.62 (multiply(sk_c4, sk_c8) = multiply(sk_c4, sk_c7)),
% 0.38/0.62 inference(monotonicity,[status(thm)],[249])).
% 0.38/0.62 tff(266,plain,
% 0.38/0.62 (multiply(sk_c4, sk_c8) = sk_c7),
% 0.38/0.62 inference(transitivity,[status(thm)],[265, 264, 158, 248, 34, 234, 229])).
% 0.38/0.62 tff(267,plain,
% 0.38/0.62 (multiply(sk_c4, inverse(sk_c4)) = sk_c8),
% 0.38/0.62 inference(modus_ponens,[status(thm)],[266, 260])).
% 0.38/0.62 tff(268,plain,
% 0.38/0.62 (multiply(multiply(identity, sk_c8), sk_c6) = multiply(sk_c8, sk_c6)),
% 0.38/0.62 inference(monotonicity,[status(thm)],[9])).
% 0.38/0.62 tff(269,plain,
% 0.38/0.62 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, sk_c8), sk_c6) = multiply(identity, multiply(sk_c8, sk_c6)))),
% 0.38/0.62 inference(quant_inst,[status(thm)],[])).
% 0.38/0.62 tff(270,plain,
% 0.38/0.62 (multiply(multiply(identity, sk_c8), sk_c6) = multiply(identity, multiply(sk_c8, sk_c6))),
% 0.38/0.62 inference(unit_resolution,[status(thm)],[269, 32])).
% 0.38/0.62 tff(271,plain,
% 0.38/0.62 (multiply(identity, multiply(sk_c8, sk_c6)) = multiply(multiply(identity, sk_c8), sk_c6)),
% 0.38/0.62 inference(symmetry,[status(thm)],[270])).
% 0.38/0.62 tff(272,plain,
% 0.38/0.62 (sk_c8 = multiply(sk_c8, sk_c6)),
% 0.38/0.62 inference(transitivity,[status(thm)],[158, 248, 34, 234])).
% 0.38/0.62 tff(273,plain,
% 0.38/0.62 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c4), sk_c4) = identity)),
% 0.38/0.62 inference(quant_inst,[status(thm)],[])).
% 0.38/0.62 tff(274,plain,
% 0.38/0.62 (multiply(inverse(sk_c4), sk_c4) = identity),
% 0.38/0.62 inference(unit_resolution,[status(thm)],[273, 41])).
% 0.38/0.62 tff(275,plain,
% 0.38/0.62 (sk_c8 = inverse(sk_c4)),
% 0.38/0.62 inference(symmetry,[status(thm)],[257])).
% 0.38/0.62 tff(276,plain,
% 0.38/0.62 (multiply(sk_c8, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.38/0.62 inference(monotonicity,[status(thm)],[275])).
% 0.38/0.62 tff(277,plain,
% 0.38/0.62 (multiply(sk_c8, sk_c4) = identity),
% 0.38/0.62 inference(transitivity,[status(thm)],[276, 274])).
% 0.38/0.62 tff(278,plain,
% 0.38/0.62 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(identity, multiply(sk_c8, sk_c6))),
% 0.38/0.62 inference(monotonicity,[status(thm)],[277, 272])).
% 0.38/0.62 tff(279,plain,
% 0.38/0.62 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(sk_c8, multiply(sk_c4, sk_c8)))),
% 0.38/0.62 inference(quant_inst,[status(thm)],[])).
% 0.38/0.62 tff(280,plain,
% 0.38/0.62 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.38/0.62 inference(unit_resolution,[status(thm)],[279, 32])).
% 0.38/0.62 tff(281,plain,
% 0.38/0.62 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.38/0.62 inference(symmetry,[status(thm)],[280])).
% 0.38/0.62 tff(282,plain,
% 0.38/0.62 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7),
% 0.38/0.62 inference(transitivity,[status(thm)],[281, 278, 271, 268, 229])).
% 0.38/0.62 tff(283,plain,
% 0.38/0.62 (multiply(multiply(sk_c8, sk_c5), sk_c8) = multiply(identity, sk_c8)),
% 0.38/0.62 inference(symmetry,[status(thm)],[248])).
% 0.38/0.62 tff(284,plain,
% 0.38/0.62 (multiply(sk_c8, multiply(sk_c5, sk_c8)) = multiply(multiply(sk_c8, sk_c5), sk_c8)),
% 0.38/0.62 inference(symmetry,[status(thm)],[34])).
% 0.38/0.62 tff(285,plain,
% 0.38/0.62 (multiply(sk_c8, sk_c6) = multiply(sk_c8, multiply(sk_c5, sk_c8))),
% 0.38/0.62 inference(symmetry,[status(thm)],[234])).
% 0.38/0.62 tff(286,plain,
% 0.38/0.62 (sk_c7 = multiply(sk_c8, sk_c6)),
% 0.38/0.62 inference(symmetry,[status(thm)],[229])).
% 0.38/0.62 tff(287,plain,
% 0.38/0.62 (inverse(sk_c8) = sk_c8),
% 0.38/0.62 inference(transitivity,[status(thm)],[223, 286, 285, 284, 283, 9])).
% 0.38/0.62 tff(288,plain,
% 0.38/0.62 (sk_c7 = sk_c8),
% 0.38/0.62 inference(transitivity,[status(thm)],[286, 285, 284, 283, 9])).
% 0.38/0.62 tff(289,plain,
% 0.38/0.62 (multiply(sk_c7, multiply(sk_c4, sk_c8)) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.38/0.62 inference(monotonicity,[status(thm)],[288])).
% 0.38/0.62 tff(290,plain,
% 0.38/0.62 (multiply(sk_c4, sk_c7) = multiply(sk_c4, sk_c8)),
% 0.38/0.62 inference(symmetry,[status(thm)],[265])).
% 0.38/0.62 tff(291,plain,
% 0.38/0.62 (sk_c8 = multiply(sk_c4, sk_c7)),
% 0.38/0.62 inference(symmetry,[status(thm)],[264])).
% 0.38/0.62 tff(292,plain,
% 0.38/0.62 (sk_c7 = multiply(sk_c4, sk_c8)),
% 0.38/0.62 inference(transitivity,[status(thm)],[286, 285, 284, 283, 9, 291, 290])).
% 0.38/0.62 tff(293,plain,
% 0.38/0.62 (multiply(sk_c8, sk_c7) = multiply(sk_c7, multiply(sk_c4, sk_c8))),
% 0.38/0.62 inference(monotonicity,[status(thm)],[249, 292])).
% 0.38/0.62 tff(294,plain,
% 0.38/0.62 (multiply(sk_c8, sk_c8) = multiply(sk_c8, sk_c7)),
% 0.38/0.62 inference(monotonicity,[status(thm)],[249])).
% 0.38/0.62 tff(295,plain,
% 0.38/0.62 (multiply(sk_c8, sk_c8) = sk_c7),
% 0.38/0.62 inference(transitivity,[status(thm)],[294, 293, 289, 281, 278, 271, 268, 229])).
% 0.38/0.62 tff(296,plain,
% 0.38/0.62 (^[X4: $i, X3: $i, X5: $i, X1: $i] : refl(((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7))))),
% 0.38/0.62 inference(bind,[status(th)],[])).
% 0.38/0.62 tff(297,plain,
% 0.38/0.62 (![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7))) <=> ![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))),
% 0.38/0.62 inference(quant_intro,[status(thm)],[296])).
% 0.38/0.62 tff(298,plain,
% 0.38/0.62 (![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7))) <=> ![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))),
% 0.38/0.62 inference(rewrite,[status(thm)],[])).
% 0.38/0.62 tff(299,plain,
% 0.38/0.62 (^[X4: $i, X3: $i, X5: $i, X1: $i] : rewrite(((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(inverse(X4) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7))))),
% 0.38/0.62 inference(bind,[status(th)],[])).
% 0.38/0.62 tff(300,plain,
% 0.38/0.62 (![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(inverse(X4) = sk_c8))) <=> ![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))),
% 0.38/0.62 inference(quant_intro,[status(thm)],[299])).
% 0.38/0.62 tff(301,plain,
% 0.38/0.62 (![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(inverse(X4) = sk_c8))) <=> ![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(inverse(X4) = sk_c8)))),
% 0.38/0.62 inference(elim_unused_vars,[status(thm)],[])).
% 0.38/0.62 tff(302,plain,
% 0.38/0.62 (![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) <=> ![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(inverse(X4) = sk_c8)))),
% 0.38/0.62 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.38/0.62 tff(303,plain,
% 0.38/0.62 (![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) <=> ![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(inverse(X4) = sk_c8)))),
% 0.38/0.62 inference(transitivity,[status(thm)],[302, 301])).
% 0.38/0.62 tff(304,plain,
% 0.38/0.62 (![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) <=> ![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))),
% 0.38/0.62 inference(transitivity,[status(thm)],[303, 300])).
% 0.38/0.62 tff(305,plain,
% 0.38/0.62 (^[X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) <=> ((~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)))), ((((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X5, X6) = sk_c8))) <=> (((~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(multiply(X5, X6) = sk_c8))))), rewrite((((~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(multiply(X5, X6) = sk_c8))) <=> ((~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)))), ((((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X5, X6) = sk_c8))) <=> ((~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))))), (((((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X5, X6) = sk_c8))) | (~(inverse(X5) = X6))) <=> (((~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X5) = X6))))), rewrite((((~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X5) = X6))) <=> ((~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)))), (((((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X5, X6) = sk_c8))) | (~(inverse(X5) = X6))) <=> ((~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))))), ((((((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X5, X6) = sk_c8))) | (~(inverse(X5) = X6))) | (~(inverse(sk_c8) = sk_c7))) <=> (((~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(sk_c8) = sk_c7))))), rewrite((((~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(sk_c8) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)))), ((((((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X5, X6) = sk_c8))) | (~(inverse(X5) = X6))) | (~(inverse(sk_c8) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))))), (((((((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X5, X6) = sk_c8))) | (~(inverse(X5) = X6))) | (~(inverse(sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)))), (((((((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X5, X6) = sk_c8))) | (~(inverse(X5) = X6))) | (~(inverse(sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))))), ((((((((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X5, X6) = sk_c8))) | (~(inverse(X5) = X6))) | (~(inverse(sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(multiply(X1, sk_c7) = sk_c8))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(multiply(X1, sk_c7) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)))), ((((((((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X5, X6) = sk_c8))) | (~(inverse(X5) = X6))) | (~(inverse(sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))))), (((((((((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X5, X6) = sk_c8))) | (~(inverse(X5) = X6))) | (~(inverse(sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(multiply(sk_c8, X2) = sk_c7))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(multiply(sk_c8, X2) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)))), (((((((((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X5, X6) = sk_c8))) | (~(inverse(X5) = X6))) | (~(inverse(sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))))), ((((((((((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X5, X6) = sk_c8))) | (~(inverse(X5) = X6))) | (~(inverse(sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)))), ((((((((((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X5, X6) = sk_c8))) | (~(inverse(X5) = X6))) | (~(inverse(sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))))), (((((((((((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X5, X6) = sk_c8))) | (~(inverse(X5) = X6))) | (~(inverse(sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))) | (~(inverse(X3) = sk_c8))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X3) = sk_c8))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7))) | (~(inverse(X3) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)))), (((((((((((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X5, X6) = sk_c8))) | (~(inverse(X5) = X6))) | (~(inverse(sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))) | (~(inverse(X3) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)))))),
% 0.38/0.62 inference(bind,[status(th)],[])).
% 0.38/0.62 tff(306,plain,
% 0.38/0.62 (![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((((((((((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X5, X6) = sk_c8))) | (~(inverse(X5) = X6))) | (~(inverse(sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))) | (~(inverse(X3) = sk_c8))) <=> ![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c8)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)))),
% 0.38/0.62 inference(quant_intro,[status(thm)],[305])).
% 0.38/0.62 tff(307,plain,
% 0.38/0.62 (![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((((((((((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X5, X6) = sk_c8))) | (~(inverse(X5) = X6))) | (~(inverse(sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))) | (~(inverse(X3) = sk_c8))) <=> ![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))),
% 0.38/0.62 inference(transitivity,[status(thm)],[306, 304])).
% 0.38/0.62 tff(308,axiom,(![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((((((((((~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X5, X6) = sk_c8))) | (~(inverse(X5) = X6))) | (~(inverse(sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))) | (~(inverse(X3) = sk_c8)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_25')).
% 0.38/0.63 tff(309,plain,
% 0.38/0.63 (![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))),
% 0.38/0.63 inference(modus_ponens,[status(thm)],[308, 307])).
% 0.38/0.63 tff(310,plain,
% 0.38/0.63 (![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))),
% 0.38/0.63 inference(modus_ponens,[status(thm)],[309, 298])).
% 0.38/0.63 tff(311,plain,(
% 0.38/0.63 ![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))),
% 0.38/0.63 inference(skolemize,[status(sab)],[310])).
% 0.38/0.63 tff(312,plain,
% 0.38/0.63 (![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))),
% 0.38/0.63 inference(modus_ponens,[status(thm)],[311, 297])).
% 0.38/0.63 tff(313,plain,
% 0.38/0.63 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)))),
% 0.38/0.63 inference(rewrite,[status(thm)],[])).
% 0.38/0.63 tff(314,plain,
% 0.38/0.63 (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)))),
% 0.38/0.63 inference(rewrite,[status(thm)],[])).
% 0.38/0.63 tff(315,plain,
% 0.38/0.63 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8))))),
% 0.38/0.63 inference(monotonicity,[status(thm)],[314])).
% 0.38/0.63 tff(316,plain,
% 0.38/0.63 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)))),
% 0.38/0.63 inference(transitivity,[status(thm)],[315, 313])).
% 0.38/0.63 tff(317,plain,
% 0.38/0.63 ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)))),
% 0.38/0.63 inference(quant_inst,[status(thm)],[])).
% 0.38/0.63 tff(318,plain,
% 0.38/0.63 ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8))),
% 0.38/0.63 inference(modus_ponens,[status(thm)],[317, 316])).
% 0.38/0.63 tff(319,plain,
% 0.38/0.63 ((~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7))),
% 0.38/0.63 inference(unit_resolution,[status(thm)],[318, 223, 257, 264, 312])).
% 0.38/0.63 tff(320,plain,
% 0.38/0.63 ($false),
% 0.38/0.63 inference(unit_resolution,[status(thm)],[319, 295, 287, 282, 267])).
% 0.38/0.63 tff(321,plain,(multiply(sk_c1, sk_c8) = sk_c7), inference(lemma,lemma(discharge,[]))).
% 0.38/0.63 tff(322,plain,
% 0.38/0.63 (multiply(sk_c1, sk_c8) = multiply(sk_c1, multiply(sk_c2, sk_c3))),
% 0.38/0.63 inference(monotonicity,[status(thm)],[51])).
% 0.38/0.63 tff(323,plain,
% 0.38/0.63 (multiply(sk_c1, multiply(sk_c2, sk_c3)) = multiply(sk_c1, sk_c8)),
% 0.38/0.63 inference(symmetry,[status(thm)],[322])).
% 0.38/0.63 tff(324,plain,
% 0.38/0.63 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c2), sk_c3) = multiply(sk_c1, multiply(sk_c2, sk_c3)))),
% 0.38/0.63 inference(quant_inst,[status(thm)],[])).
% 0.38/0.63 tff(325,plain,
% 0.38/0.63 (multiply(multiply(sk_c1, sk_c2), sk_c3) = multiply(sk_c1, multiply(sk_c2, sk_c3))),
% 0.38/0.63 inference(unit_resolution,[status(thm)],[324, 32])).
% 0.38/0.63 tff(326,plain,
% 0.38/0.63 (multiply(multiply(sk_c1, sk_c2), sk_c3) = multiply(multiply(sk_c1, sk_c2), multiply(sk_c3, sk_c8))),
% 0.38/0.63 inference(monotonicity,[status(thm)],[85])).
% 0.38/0.63 tff(327,plain,
% 0.38/0.63 (multiply(multiply(sk_c1, sk_c2), multiply(sk_c3, sk_c8)) = multiply(multiply(sk_c1, sk_c2), sk_c3)),
% 0.38/0.63 inference(symmetry,[status(thm)],[326])).
% 0.38/0.63 tff(328,plain,
% 0.38/0.63 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c1, sk_c2), sk_c3), sk_c8) = multiply(multiply(sk_c1, sk_c2), multiply(sk_c3, sk_c8)))),
% 0.38/0.63 inference(quant_inst,[status(thm)],[])).
% 0.38/0.63 tff(329,plain,
% 0.38/0.63 (multiply(multiply(multiply(sk_c1, sk_c2), sk_c3), sk_c8) = multiply(multiply(sk_c1, sk_c2), multiply(sk_c3, sk_c8))),
% 0.38/0.63 inference(unit_resolution,[status(thm)],[328, 32])).
% 0.38/0.63 tff(330,plain,
% 0.38/0.63 (multiply(multiply(sk_c1, sk_c2), sk_c3) = inverse(sk_c8)),
% 0.38/0.63 inference(transitivity,[status(thm)],[325, 323, 321, 224])).
% 0.38/0.63 tff(331,plain,
% 0.38/0.63 (multiply(multiply(multiply(sk_c1, sk_c2), sk_c3), sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.38/0.63 inference(monotonicity,[status(thm)],[330])).
% 0.38/0.63 tff(332,plain,
% 0.38/0.63 (multiply(inverse(sk_c8), sk_c8) = multiply(multiply(multiply(sk_c1, sk_c2), sk_c3), sk_c8)),
% 0.38/0.63 inference(symmetry,[status(thm)],[331])).
% 0.38/0.63 tff(333,plain,
% 0.38/0.63 (identity = inverse(sk_c8)),
% 0.38/0.63 inference(transitivity,[status(thm)],[155, 332, 329, 327, 325, 323, 321, 224])).
% 0.38/0.63 tff(334,plain,
% 0.38/0.63 (multiply(identity, multiply(sk_c8, multiply(sk_c2, sk_c3))) = multiply(inverse(sk_c8), sk_c8)),
% 0.38/0.63 inference(monotonicity,[status(thm)],[333, 96])).
% 0.38/0.63 tff(335,plain,
% 0.38/0.63 (multiply(inverse(sk_c8), sk_c8) = multiply(identity, multiply(sk_c8, multiply(sk_c2, sk_c3)))),
% 0.38/0.63 inference(symmetry,[status(thm)],[334])).
% 0.38/0.63 tff(336,plain,
% 0.38/0.63 (multiply(sk_c1, sk_c8) = inverse(sk_c8)),
% 0.38/0.63 inference(transitivity,[status(thm)],[321, 224])).
% 0.38/0.63 tff(337,plain,
% 0.38/0.63 (multiply(multiply(sk_c1, sk_c8), sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.38/0.63 inference(monotonicity,[status(thm)],[336])).
% 0.38/0.63 tff(338,plain,
% 0.38/0.63 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c8), sk_c8) = multiply(sk_c1, multiply(sk_c8, sk_c8)))),
% 0.38/0.63 inference(quant_inst,[status(thm)],[])).
% 0.38/0.63 tff(339,plain,
% 0.38/0.63 (multiply(multiply(sk_c1, sk_c8), sk_c8) = multiply(sk_c1, multiply(sk_c8, sk_c8))),
% 0.38/0.63 inference(unit_resolution,[status(thm)],[338, 32])).
% 0.38/0.63 tff(340,plain,
% 0.38/0.63 (multiply(sk_c1, multiply(sk_c8, sk_c8)) = multiply(multiply(sk_c1, sk_c8), sk_c8)),
% 0.38/0.63 inference(symmetry,[status(thm)],[339])).
% 0.38/0.63 tff(341,plain,
% 0.38/0.63 (multiply(multiply(sk_c1, sk_c2), multiply(sk_c3, sk_c8)) = multiply(multiply(multiply(sk_c1, sk_c2), sk_c3), sk_c8)),
% 0.38/0.63 inference(symmetry,[status(thm)],[329])).
% 0.38/0.63 tff(342,plain,
% 0.38/0.63 (multiply(sk_c1, multiply(sk_c2, sk_c3)) = multiply(multiply(sk_c1, sk_c2), sk_c3)),
% 0.38/0.63 inference(symmetry,[status(thm)],[325])).
% 0.38/0.63 tff(343,plain,
% 0.38/0.63 (sk_c7 = multiply(sk_c1, sk_c8)),
% 0.38/0.63 inference(symmetry,[status(thm)],[321])).
% 0.38/0.63 tff(344,plain,
% 0.38/0.63 (sk_c7 = multiply(sk_c8, sk_c8)),
% 0.38/0.63 inference(transitivity,[status(thm)],[343, 322, 342, 326, 341, 331, 335, 95, 93])).
% 0.38/0.63 tff(345,plain,
% 0.38/0.63 (multiply(sk_c1, sk_c7) = multiply(sk_c1, multiply(sk_c8, sk_c8))),
% 0.38/0.63 inference(monotonicity,[status(thm)],[344])).
% 0.38/0.63 tff(346,plain,
% 0.38/0.63 (multiply(sk_c1, sk_c7) = sk_c8),
% 0.38/0.63 inference(transitivity,[status(thm)],[345, 340, 337, 335, 95, 93, 91, 89, 87, 50])).
% 0.38/0.63 tff(347,plain,
% 0.38/0.63 (multiply(sk_c8, multiply(sk_c2, sk_c3)) = multiply(sk_c2, sk_c3)),
% 0.47/0.63 inference(transitivity,[status(thm)],[93, 91, 89, 87])).
% 0.47/0.63 tff(348,plain,
% 0.47/0.63 (multiply(multiply(sk_c8, multiply(sk_c2, sk_c3)), sk_c1) = multiply(multiply(sk_c2, sk_c3), sk_c1)),
% 0.47/0.63 inference(monotonicity,[status(thm)],[347])).
% 0.47/0.63 tff(349,plain,
% 0.47/0.63 (multiply(multiply(sk_c8, multiply(sk_c2, sk_c3)), sk_c1) = inverse(sk_c8)),
% 0.47/0.63 inference(transitivity,[status(thm)],[348, 69, 72, 155, 332, 329, 327, 325, 323, 321, 224])).
% 0.47/0.63 tff(350,plain,
% 0.47/0.63 (multiply(multiply(multiply(sk_c8, multiply(sk_c2, sk_c3)), sk_c1), multiply(sk_c8, multiply(sk_c2, sk_c3))) = multiply(inverse(sk_c8), sk_c8)),
% 0.47/0.63 inference(monotonicity,[status(thm)],[349, 96])).
% 0.47/0.63 tff(351,plain,
% 0.47/0.63 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c8, multiply(sk_c2, sk_c3)), sk_c1), multiply(sk_c8, multiply(sk_c2, sk_c3))) = multiply(multiply(sk_c8, multiply(sk_c2, sk_c3)), multiply(sk_c1, multiply(sk_c8, multiply(sk_c2, sk_c3)))))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(352,plain,
% 0.47/0.63 (multiply(multiply(multiply(sk_c8, multiply(sk_c2, sk_c3)), sk_c1), multiply(sk_c8, multiply(sk_c2, sk_c3))) = multiply(multiply(sk_c8, multiply(sk_c2, sk_c3)), multiply(sk_c1, multiply(sk_c8, multiply(sk_c2, sk_c3))))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[351, 32])).
% 0.47/0.63 tff(353,plain,
% 0.47/0.63 (multiply(multiply(sk_c8, multiply(sk_c2, sk_c3)), multiply(sk_c1, multiply(sk_c8, multiply(sk_c2, sk_c3)))) = multiply(multiply(multiply(sk_c8, multiply(sk_c2, sk_c3)), sk_c1), multiply(sk_c8, multiply(sk_c2, sk_c3)))),
% 0.47/0.63 inference(symmetry,[status(thm)],[352])).
% 0.47/0.63 tff(354,plain,
% 0.47/0.63 (multiply(sk_c1, multiply(sk_c8, multiply(sk_c2, sk_c3))) = multiply(sk_c1, multiply(sk_c8, sk_c8))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[93])).
% 0.47/0.63 tff(355,plain,
% 0.47/0.63 (multiply(sk_c1, multiply(sk_c8, sk_c8)) = multiply(sk_c1, multiply(sk_c8, multiply(sk_c2, sk_c3)))),
% 0.47/0.63 inference(symmetry,[status(thm)],[354])).
% 0.47/0.63 tff(356,plain,
% 0.47/0.63 (multiply(inverse(sk_c8), sk_c8) = multiply(multiply(sk_c1, sk_c8), sk_c8)),
% 0.47/0.63 inference(symmetry,[status(thm)],[337])).
% 0.47/0.63 tff(357,plain,
% 0.47/0.63 (sk_c7 = multiply(sk_c1, multiply(sk_c8, multiply(sk_c2, sk_c3)))),
% 0.47/0.63 inference(transitivity,[status(thm)],[343, 322, 342, 326, 341, 331, 356, 339, 355])).
% 0.47/0.63 tff(358,plain,
% 0.47/0.63 (multiply(sk_c2, multiply(sk_c3, sk_c8)) = multiply(multiply(sk_c2, sk_c3), sk_c8)),
% 0.47/0.63 inference(symmetry,[status(thm)],[89])).
% 0.47/0.63 tff(359,plain,
% 0.47/0.63 (sk_c8 = multiply(sk_c8, multiply(sk_c2, sk_c3))),
% 0.47/0.63 inference(transitivity,[status(thm)],[51, 86, 358, 90, 92])).
% 0.47/0.63 tff(360,plain,
% 0.47/0.63 (multiply(sk_c8, sk_c7) = multiply(multiply(sk_c8, multiply(sk_c2, sk_c3)), multiply(sk_c1, multiply(sk_c8, multiply(sk_c2, sk_c3))))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[359, 357])).
% 0.47/0.63 tff(361,plain,
% 0.47/0.63 (multiply(sk_c8, multiply(sk_c1, sk_c8)) = multiply(sk_c8, sk_c7)),
% 0.47/0.63 inference(monotonicity,[status(thm)],[321])).
% 0.47/0.63 tff(362,plain,
% 0.47/0.63 (multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7),
% 0.47/0.63 inference(transitivity,[status(thm)],[361, 360, 353, 350, 332, 329, 327, 325, 323, 321])).
% 0.47/0.63 tff(363,plain,
% 0.47/0.63 (multiply(sk_c8, inverse(sk_c8)) = multiply(sk_c8, sk_c7)),
% 0.47/0.63 inference(monotonicity,[status(thm)],[223])).
% 0.47/0.63 tff(364,plain,
% 0.47/0.63 ((multiply(sk_c8, inverse(sk_c8)) = sk_c8) <=> (multiply(sk_c8, sk_c7) = sk_c8)),
% 0.47/0.63 inference(monotonicity,[status(thm)],[363])).
% 0.47/0.63 tff(365,plain,
% 0.47/0.63 ((multiply(sk_c8, sk_c7) = sk_c8) <=> (multiply(sk_c8, inverse(sk_c8)) = sk_c8)),
% 0.47/0.63 inference(symmetry,[status(thm)],[364])).
% 0.47/0.63 tff(366,plain,
% 0.47/0.63 (sk_c7 = sk_c8),
% 0.47/0.63 inference(transitivity,[status(thm)],[343, 322, 342, 326, 341, 331, 335, 95, 93, 91, 89, 87, 50])).
% 0.47/0.63 tff(367,plain,
% 0.47/0.63 ((multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7) <=> (multiply(sk_c8, sk_c7) = sk_c8)),
% 0.47/0.63 inference(monotonicity,[status(thm)],[361, 366])).
% 0.47/0.63 tff(368,plain,
% 0.47/0.63 ((multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7) <=> (multiply(sk_c8, inverse(sk_c8)) = sk_c8)),
% 0.47/0.63 inference(transitivity,[status(thm)],[367, 365])).
% 0.47/0.63 tff(369,plain,
% 0.47/0.63 (multiply(sk_c8, inverse(sk_c8)) = sk_c8),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[362, 368])).
% 0.47/0.63 tff(370,plain,
% 0.47/0.64 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c8)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(371,plain,
% 0.47/0.64 (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c8)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(372,plain,
% 0.47/0.64 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c8))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[371])).
% 0.47/0.64 tff(373,plain,
% 0.47/0.64 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c8)))),
% 0.47/0.64 inference(transitivity,[status(thm)],[372, 370])).
% 0.47/0.64 tff(374,plain,
% 0.47/0.64 ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(375,plain,
% 0.47/0.64 ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c8))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[374, 373])).
% 0.47/0.64 tff(376,plain,
% 0.47/0.64 ((~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c8))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[375, 321, 223, 66, 312])).
% 0.47/0.64 tff(377,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[376, 369, 362, 346])).
% 0.47/0.64 tff(378,plain,(inverse(sk_c5) = sk_c8), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(379,plain,
% 0.47/0.64 (sk_c8 = inverse(sk_c5)),
% 0.47/0.64 inference(symmetry,[status(thm)],[378])).
% 0.47/0.64 tff(380,plain,
% 0.47/0.64 (multiply(sk_c8, sk_c5) = multiply(inverse(sk_c5), sk_c5)),
% 0.47/0.64 inference(monotonicity,[status(thm)],[379])).
% 0.47/0.64 tff(381,plain,
% 0.47/0.64 (multiply(sk_c8, sk_c5) = identity),
% 0.47/0.64 inference(transitivity,[status(thm)],[380, 43])).
% 0.47/0.64 tff(382,plain,
% 0.47/0.64 (multiply(multiply(sk_c8, sk_c5), sk_c8) = multiply(identity, sk_c8)),
% 0.47/0.64 inference(monotonicity,[status(thm)],[381])).
% 0.47/0.64 tff(383,plain,
% 0.47/0.64 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c5), sk_c8)),
% 0.47/0.64 inference(symmetry,[status(thm)],[382])).
% 0.47/0.64 tff(384,plain,
% 0.47/0.64 (sk_c8 = sk_c7),
% 0.47/0.64 inference(transitivity,[status(thm)],[158, 383, 34, 25, 18])).
% 0.47/0.64 tff(385,plain,
% 0.47/0.64 (multiply(sk_c4, sk_c8) = multiply(sk_c4, sk_c7)),
% 0.47/0.64 inference(monotonicity,[status(thm)],[384])).
% 0.47/0.64 tff(386,plain,
% 0.47/0.64 (((inverse(sk_c1) = sk_c8) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c1) = sk_c8) | (inverse(sk_c4) = sk_c8))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(387,axiom,((inverse(sk_c1) = sk_c8) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_8')).
% 0.47/0.64 tff(388,plain,
% 0.47/0.64 ((inverse(sk_c1) = sk_c8) | (inverse(sk_c4) = sk_c8)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[387, 386])).
% 0.47/0.64 tff(389,plain,
% 0.47/0.64 (inverse(sk_c4) = sk_c8),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[388, 10])).
% 0.47/0.64 tff(390,plain,
% 0.47/0.64 (multiply(sk_c4, inverse(sk_c4)) = multiply(sk_c4, sk_c8)),
% 0.47/0.64 inference(monotonicity,[status(thm)],[389])).
% 0.47/0.64 tff(391,plain,
% 0.47/0.64 (multiply(sk_c4, inverse(sk_c4)) = sk_c8),
% 0.47/0.64 inference(transitivity,[status(thm)],[390, 385, 14])).
% 0.47/0.64 tff(392,plain,
% 0.47/0.64 (multiply(inverse(sk_c5), sk_c5) = multiply(sk_c8, sk_c5)),
% 0.47/0.64 inference(symmetry,[status(thm)],[380])).
% 0.47/0.64 tff(393,plain,
% 0.47/0.64 (sk_c8 = inverse(sk_c4)),
% 0.47/0.64 inference(symmetry,[status(thm)],[389])).
% 0.47/0.64 tff(394,plain,
% 0.47/0.64 (multiply(sk_c8, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.47/0.64 inference(monotonicity,[status(thm)],[393])).
% 0.47/0.64 tff(395,plain,
% 0.47/0.64 (multiply(sk_c8, sk_c4) = multiply(sk_c8, sk_c5)),
% 0.47/0.64 inference(transitivity,[status(thm)],[394, 274, 246, 392])).
% 0.47/0.64 tff(396,plain,
% 0.47/0.64 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(multiply(sk_c8, sk_c5), sk_c8)),
% 0.47/0.64 inference(monotonicity,[status(thm)],[395])).
% 0.47/0.64 tff(397,plain,
% 0.47/0.64 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7),
% 0.47/0.64 inference(transitivity,[status(thm)],[281, 396, 34, 25, 18])).
% 0.47/0.64 tff(398,plain,
% 0.47/0.64 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c7) = sk_c7)),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(399,plain,
% 0.47/0.64 (multiply(identity, sk_c7) = sk_c7),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[398, 7])).
% 0.47/0.64 tff(400,plain,
% 0.47/0.64 (multiply(sk_c8, sk_c4) = identity),
% 0.47/0.64 inference(transitivity,[status(thm)],[394, 274])).
% 0.47/0.64 tff(401,plain,
% 0.47/0.64 (multiply(multiply(sk_c8, sk_c4), sk_c7) = multiply(identity, sk_c7)),
% 0.47/0.64 inference(monotonicity,[status(thm)],[400])).
% 0.47/0.64 tff(402,plain,
% 0.47/0.64 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c4), sk_c7) = multiply(sk_c8, multiply(sk_c4, sk_c7)))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(403,plain,
% 0.47/0.64 (multiply(multiply(sk_c8, sk_c4), sk_c7) = multiply(sk_c8, multiply(sk_c4, sk_c7))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[402, 32])).
% 0.47/0.64 tff(404,plain,
% 0.47/0.64 (multiply(sk_c8, multiply(sk_c4, sk_c7)) = multiply(multiply(sk_c8, sk_c4), sk_c7)),
% 0.47/0.64 inference(symmetry,[status(thm)],[403])).
% 0.47/0.64 tff(405,plain,
% 0.47/0.64 (sk_c8 = multiply(sk_c4, sk_c7)),
% 0.47/0.64 inference(symmetry,[status(thm)],[14])).
% 0.47/0.64 tff(406,plain,
% 0.47/0.64 (multiply(sk_c8, sk_c8) = multiply(sk_c8, multiply(sk_c4, sk_c7))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[405])).
% 0.47/0.64 tff(407,plain,
% 0.47/0.64 (multiply(sk_c8, sk_c8) = sk_c7),
% 0.47/0.64 inference(transitivity,[status(thm)],[406, 404, 401, 399])).
% 0.47/0.64 tff(408,plain,
% 0.47/0.64 (sk_c7 = multiply(sk_c8, sk_c6)),
% 0.47/0.64 inference(symmetry,[status(thm)],[18])).
% 0.47/0.64 tff(409,plain,
% 0.47/0.64 (inverse(sk_c8) = sk_c8),
% 0.47/0.64 inference(transitivity,[status(thm)],[223, 408, 24, 284, 382, 9])).
% 0.47/0.64 tff(410,plain,
% 0.47/0.64 (sk_c7 = sk_c8),
% 0.47/0.64 inference(transitivity,[status(thm)],[408, 24, 284, 382, 9])).
% 0.47/0.64 tff(411,plain,
% 0.47/0.64 (multiply(sk_c8, sk_c7) = multiply(sk_c8, sk_c8)),
% 0.47/0.64 inference(monotonicity,[status(thm)],[410])).
% 0.47/0.64 tff(412,plain,
% 0.47/0.64 (multiply(sk_c8, sk_c7) = sk_c8),
% 0.47/0.64 inference(transitivity,[status(thm)],[411, 406, 404, 401, 399, 408, 24, 284, 382, 9])).
% 0.47/0.64 tff(413,plain,
% 0.47/0.64 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(414,plain,
% 0.47/0.64 (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(415,plain,
% 0.47/0.64 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[414])).
% 0.47/0.64 tff(416,plain,
% 0.47/0.64 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)))),
% 0.47/0.64 inference(transitivity,[status(thm)],[415, 413])).
% 0.47/0.64 tff(417,plain,
% 0.47/0.64 ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(418,plain,
% 0.47/0.64 ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[417, 416])).
% 0.47/0.64 tff(419,plain,
% 0.47/0.64 ((~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(multiply(sk_c8, sk_c8) = sk_c7)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[418, 223, 389, 312])).
% 0.47/0.64 tff(420,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[419, 412, 409, 407, 397, 391])).
% 0.47/0.64 tff(421,plain,(inverse(sk_c1) = sk_c8), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(422,plain,
% 0.47/0.64 (sk_c8 = inverse(sk_c1)),
% 0.47/0.64 inference(symmetry,[status(thm)],[421])).
% 0.47/0.64 tff(423,plain,
% 0.47/0.64 (multiply(sk_c8, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.47/0.64 inference(monotonicity,[status(thm)],[422])).
% 0.47/0.64 tff(424,plain,
% 0.47/0.64 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c8, sk_c1)),
% 0.47/0.64 inference(symmetry,[status(thm)],[423])).
% 0.47/0.64 tff(425,plain,
% 0.47/0.64 (identity = multiply(sk_c8, sk_c1)),
% 0.47/0.64 inference(transitivity,[status(thm)],[73, 424])).
% 0.47/0.64 tff(426,plain,
% 0.47/0.64 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c1), sk_c8)),
% 0.47/0.64 inference(monotonicity,[status(thm)],[425])).
% 0.47/0.64 tff(427,plain,
% 0.47/0.64 (multiply(multiply(sk_c8, sk_c1), sk_c8) = multiply(identity, sk_c8)),
% 0.47/0.64 inference(symmetry,[status(thm)],[426])).
% 0.47/0.64 tff(428,plain,
% 0.47/0.64 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c1), sk_c8) = multiply(sk_c8, multiply(sk_c1, sk_c8)))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(429,plain,
% 0.47/0.64 (multiply(multiply(sk_c8, sk_c1), sk_c8) = multiply(sk_c8, multiply(sk_c1, sk_c8))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[428, 32])).
% 0.47/0.64 tff(430,plain,
% 0.47/0.64 (multiply(sk_c8, multiply(sk_c1, sk_c8)) = multiply(multiply(sk_c8, sk_c1), sk_c8)),
% 0.47/0.64 inference(symmetry,[status(thm)],[429])).
% 0.47/0.64 tff(431,plain,
% 0.47/0.64 (multiply(sk_c8, sk_c7) = multiply(sk_c8, multiply(sk_c1, sk_c8))),
% 0.47/0.64 inference(symmetry,[status(thm)],[361])).
% 0.47/0.64 tff(432,plain,
% 0.47/0.64 (multiply(sk_c8, sk_c7) = sk_c8),
% 0.47/0.64 inference(transitivity,[status(thm)],[431, 430, 427, 9])).
% 0.47/0.64 tff(433,plain,
% 0.47/0.64 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, multiply(sk_c8, inverse(sk_c2))), sk_c2) = multiply(sk_c7, multiply(multiply(sk_c8, inverse(sk_c2)), sk_c2)))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(434,plain,
% 0.47/0.64 (multiply(multiply(sk_c7, multiply(sk_c8, inverse(sk_c2))), sk_c2) = multiply(sk_c7, multiply(multiply(sk_c8, inverse(sk_c2)), sk_c2))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[433, 32])).
% 0.47/0.64 tff(435,plain,
% 0.47/0.64 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, inverse(sk_c2)) = inverse(sk_c2))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(436,plain,
% 0.47/0.64 (multiply(identity, inverse(sk_c2)) = inverse(sk_c2)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[435, 7])).
% 0.47/0.64 tff(437,assumption,(~(inverse(sk_c8) = sk_c8)), introduced(assumption)).
% 0.47/0.64 tff(438,assumption,(~(multiply(sk_c2, sk_c3) = sk_c8)), introduced(assumption)).
% 0.47/0.64 tff(439,plain,
% 0.47/0.64 (((multiply(sk_c2, sk_c3) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6)) <=> ((multiply(sk_c2, sk_c3) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(440,axiom,((multiply(sk_c2, sk_c3) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_17')).
% 0.47/0.64 tff(441,plain,
% 0.47/0.64 ((multiply(sk_c2, sk_c3) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[440, 439])).
% 0.47/0.64 tff(442,plain,
% 0.47/0.64 (multiply(sk_c5, sk_c8) = sk_c6),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[441, 438])).
% 0.47/0.64 tff(443,plain,
% 0.47/0.64 (sk_c6 = multiply(sk_c5, sk_c8)),
% 0.47/0.64 inference(symmetry,[status(thm)],[442])).
% 0.47/0.64 tff(444,plain,
% 0.47/0.64 (multiply(sk_c8, sk_c6) = multiply(sk_c8, multiply(sk_c5, sk_c8))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[443])).
% 0.47/0.64 tff(445,plain,
% 0.47/0.64 (((multiply(sk_c2, sk_c3) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7)) <=> ((multiply(sk_c2, sk_c3) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(446,axiom,((multiply(sk_c2, sk_c3) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_16')).
% 0.47/0.64 tff(447,plain,
% 0.47/0.64 ((multiply(sk_c2, sk_c3) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[446, 445])).
% 0.47/0.65 tff(448,plain,
% 0.47/0.65 (multiply(sk_c8, sk_c6) = sk_c7),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[447, 438])).
% 0.47/0.65 tff(449,plain,
% 0.47/0.65 (sk_c7 = multiply(sk_c8, sk_c6)),
% 0.47/0.65 inference(symmetry,[status(thm)],[448])).
% 0.47/0.65 tff(450,plain,
% 0.47/0.65 (inverse(sk_c8) = sk_c8),
% 0.47/0.65 inference(transitivity,[status(thm)],[223, 449, 444, 284, 382, 9])).
% 0.47/0.65 tff(451,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[437, 450])).
% 0.47/0.65 tff(452,plain,((multiply(sk_c2, sk_c3) = sk_c8) | (inverse(sk_c8) = sk_c8)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.65 tff(453,plain,
% 0.47/0.65 (multiply(sk_c2, sk_c3) = sk_c8),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[452, 437])).
% 0.47/0.65 tff(454,plain,
% 0.47/0.65 (multiply(sk_c2, sk_c3) = inverse(sk_c1)),
% 0.47/0.65 inference(transitivity,[status(thm)],[453, 422])).
% 0.47/0.65 tff(455,plain,
% 0.47/0.65 (multiply(multiply(sk_c2, sk_c3), sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.47/0.65 inference(monotonicity,[status(thm)],[454])).
% 0.47/0.65 tff(456,plain,
% 0.47/0.65 (multiply(inverse(sk_c1), sk_c1) = multiply(multiply(sk_c2, sk_c3), sk_c1)),
% 0.47/0.65 inference(symmetry,[status(thm)],[455])).
% 0.47/0.65 tff(457,plain,
% 0.47/0.65 (identity = multiply(sk_c2, multiply(sk_c3, sk_c1))),
% 0.47/0.65 inference(transitivity,[status(thm)],[73, 456, 62])).
% 0.47/0.65 tff(458,plain,
% 0.47/0.65 (multiply(identity, inverse(sk_c2)) = multiply(multiply(sk_c2, multiply(sk_c3, sk_c1)), inverse(sk_c2))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[457])).
% 0.47/0.65 tff(459,plain,
% 0.47/0.65 (multiply(multiply(sk_c2, multiply(sk_c3, sk_c1)), inverse(sk_c2)) = multiply(identity, inverse(sk_c2))),
% 0.47/0.65 inference(symmetry,[status(thm)],[458])).
% 0.47/0.65 tff(460,plain,
% 0.47/0.65 (multiply(sk_c7, sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.47/0.65 inference(monotonicity,[status(thm)],[224])).
% 0.47/0.65 tff(461,plain,
% 0.47/0.65 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c7, sk_c8)),
% 0.47/0.65 inference(symmetry,[status(thm)],[460])).
% 0.47/0.65 tff(462,plain,
% 0.47/0.65 (multiply(sk_c2, multiply(sk_c3, sk_c1)) = multiply(multiply(sk_c2, sk_c3), sk_c1)),
% 0.47/0.65 inference(symmetry,[status(thm)],[62])).
% 0.47/0.65 tff(463,plain,
% 0.47/0.65 (multiply(sk_c2, multiply(sk_c3, sk_c1)) = multiply(sk_c7, sk_c8)),
% 0.47/0.65 inference(transitivity,[status(thm)],[462, 455, 72, 155, 461])).
% 0.47/0.65 tff(464,plain,
% 0.47/0.65 (multiply(multiply(sk_c2, multiply(sk_c3, sk_c1)), inverse(sk_c2)) = multiply(multiply(sk_c7, sk_c8), inverse(sk_c2))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[463])).
% 0.47/0.65 tff(465,plain,
% 0.47/0.65 (multiply(multiply(sk_c7, sk_c8), inverse(sk_c2)) = multiply(multiply(sk_c2, multiply(sk_c3, sk_c1)), inverse(sk_c2))),
% 0.47/0.65 inference(symmetry,[status(thm)],[464])).
% 0.47/0.65 tff(466,plain,
% 0.47/0.65 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c8), inverse(sk_c2)) = multiply(sk_c7, multiply(sk_c8, inverse(sk_c2))))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(467,plain,
% 0.47/0.65 (multiply(multiply(sk_c7, sk_c8), inverse(sk_c2)) = multiply(sk_c7, multiply(sk_c8, inverse(sk_c2)))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[466, 32])).
% 0.47/0.65 tff(468,plain,
% 0.47/0.65 (multiply(sk_c7, multiply(sk_c8, inverse(sk_c2))) = multiply(multiply(sk_c7, sk_c8), inverse(sk_c2))),
% 0.47/0.65 inference(symmetry,[status(thm)],[467])).
% 0.47/0.65 tff(469,plain,
% 0.47/0.65 (multiply(sk_c7, multiply(sk_c8, inverse(sk_c2))) = inverse(sk_c2)),
% 0.47/0.65 inference(transitivity,[status(thm)],[468, 465, 459, 436])).
% 0.47/0.65 tff(470,plain,
% 0.47/0.65 (multiply(multiply(sk_c7, multiply(sk_c8, inverse(sk_c2))), sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.47/0.65 inference(monotonicity,[status(thm)],[469])).
% 0.47/0.65 tff(471,plain,
% 0.47/0.65 (multiply(inverse(sk_c2), sk_c2) = multiply(multiply(sk_c7, multiply(sk_c8, inverse(sk_c2))), sk_c2)),
% 0.47/0.65 inference(symmetry,[status(thm)],[470])).
% 0.47/0.65 tff(472,plain,
% 0.47/0.65 (identity = multiply(sk_c7, multiply(multiply(sk_c8, inverse(sk_c2)), sk_c2))),
% 0.47/0.65 inference(transitivity,[status(thm)],[165, 471, 434])).
% 0.47/0.65 tff(473,plain,
% 0.47/0.65 (multiply(identity, sk_c8) = multiply(multiply(sk_c7, multiply(multiply(sk_c8, inverse(sk_c2)), sk_c2)), sk_c8)),
% 0.47/0.65 inference(monotonicity,[status(thm)],[472])).
% 0.47/0.65 tff(474,plain,
% 0.47/0.65 (multiply(multiply(sk_c7, multiply(multiply(sk_c8, inverse(sk_c2)), sk_c2)), sk_c8) = multiply(identity, sk_c8)),
% 0.47/0.65 inference(symmetry,[status(thm)],[473])).
% 0.47/0.65 tff(475,plain,
% 0.47/0.65 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, multiply(multiply(sk_c8, inverse(sk_c2)), sk_c2)), sk_c8) = multiply(sk_c7, multiply(multiply(multiply(sk_c8, inverse(sk_c2)), sk_c2), sk_c8)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(476,plain,
% 0.47/0.65 (multiply(multiply(sk_c7, multiply(multiply(sk_c8, inverse(sk_c2)), sk_c2)), sk_c8) = multiply(sk_c7, multiply(multiply(multiply(sk_c8, inverse(sk_c2)), sk_c2), sk_c8))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[475, 32])).
% 0.47/0.65 tff(477,plain,
% 0.47/0.65 (multiply(sk_c7, multiply(multiply(multiply(sk_c8, inverse(sk_c2)), sk_c2), sk_c8)) = multiply(multiply(sk_c7, multiply(multiply(sk_c8, inverse(sk_c2)), sk_c2)), sk_c8)),
% 0.47/0.65 inference(symmetry,[status(thm)],[476])).
% 0.47/0.65 tff(478,plain,
% 0.47/0.65 (multiply(sk_c7, sk_c8) = identity),
% 0.47/0.65 inference(transitivity,[status(thm)],[460, 107])).
% 0.47/0.65 tff(479,plain,
% 0.47/0.65 (multiply(sk_c8, multiply(sk_c7, sk_c8)) = multiply(sk_c8, identity)),
% 0.47/0.65 inference(monotonicity,[status(thm)],[478])).
% 0.47/0.65 tff(480,plain,
% 0.47/0.65 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c7), sk_c8) = multiply(sk_c8, multiply(sk_c7, sk_c8)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(481,plain,
% 0.47/0.65 (multiply(multiply(sk_c8, sk_c7), sk_c8) = multiply(sk_c8, multiply(sk_c7, sk_c8))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[480, 32])).
% 0.47/0.65 tff(482,plain,
% 0.47/0.65 (multiply(sk_c8, sk_c7) = multiply(sk_c8, multiply(sk_c1, sk_c8))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[343])).
% 0.47/0.65 tff(483,plain,
% 0.47/0.65 (multiply(sk_c8, multiply(sk_c1, sk_c8)) = multiply(sk_c8, sk_c7)),
% 0.47/0.65 inference(symmetry,[status(thm)],[482])).
% 0.47/0.65 tff(484,plain,
% 0.47/0.65 (multiply(sk_c8, sk_c1) = identity),
% 0.47/0.65 inference(transitivity,[status(thm)],[423, 72])).
% 0.47/0.65 tff(485,plain,
% 0.47/0.65 (multiply(multiply(sk_c8, sk_c1), sk_c8) = multiply(identity, sk_c8)),
% 0.47/0.65 inference(monotonicity,[status(thm)],[484])).
% 0.47/0.65 tff(486,plain,
% 0.47/0.65 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c1), sk_c8)),
% 0.47/0.65 inference(symmetry,[status(thm)],[485])).
% 0.47/0.65 tff(487,plain,
% 0.47/0.65 (sk_c8 = multiply(sk_c8, sk_c7)),
% 0.47/0.65 inference(transitivity,[status(thm)],[158, 486, 429, 483])).
% 0.47/0.65 tff(488,plain,
% 0.47/0.65 (multiply(sk_c8, sk_c8) = multiply(multiply(sk_c8, sk_c7), sk_c8)),
% 0.47/0.65 inference(monotonicity,[status(thm)],[487])).
% 0.47/0.65 tff(489,plain,
% 0.47/0.65 (multiply(sk_c8, sk_c7) = sk_c8),
% 0.47/0.65 inference(transitivity,[status(thm)],[482, 430, 485, 9])).
% 0.47/0.65 tff(490,plain,
% 0.47/0.65 (multiply(sk_c8, multiply(sk_c8, sk_c7)) = multiply(sk_c8, sk_c8)),
% 0.47/0.65 inference(monotonicity,[status(thm)],[489])).
% 0.47/0.65 tff(491,plain,
% 0.47/0.65 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c8), sk_c7) = multiply(sk_c8, multiply(sk_c8, sk_c7)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(492,plain,
% 0.47/0.65 (multiply(multiply(sk_c8, sk_c8), sk_c7) = multiply(sk_c8, multiply(sk_c8, sk_c7))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[491, 32])).
% 0.47/0.65 tff(493,plain,
% 0.47/0.65 (multiply(sk_c8, multiply(sk_c2, sk_c3)) = multiply(sk_c8, sk_c8)),
% 0.47/0.65 inference(monotonicity,[status(thm)],[453])).
% 0.47/0.65 tff(494,plain,
% 0.47/0.65 (multiply(multiply(sk_c8, multiply(sk_c2, sk_c3)), sk_c7) = multiply(multiply(sk_c8, sk_c8), sk_c7)),
% 0.47/0.65 inference(monotonicity,[status(thm)],[493])).
% 0.47/0.65 tff(495,plain,
% 0.47/0.65 (multiply(multiply(sk_c8, multiply(sk_c2, sk_c3)), multiply(sk_c1, sk_c8)) = multiply(multiply(sk_c8, multiply(sk_c2, sk_c3)), sk_c7)),
% 0.47/0.65 inference(monotonicity,[status(thm)],[321])).
% 0.47/0.65 tff(496,plain,
% 0.47/0.65 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c8, multiply(sk_c2, sk_c3)), sk_c1), sk_c8) = multiply(multiply(sk_c8, multiply(sk_c2, sk_c3)), multiply(sk_c1, sk_c8)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(497,plain,
% 0.47/0.65 (multiply(multiply(multiply(sk_c8, multiply(sk_c2, sk_c3)), sk_c1), sk_c8) = multiply(multiply(sk_c8, multiply(sk_c2, sk_c3)), multiply(sk_c1, sk_c8))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[496, 32])).
% 0.47/0.65 tff(498,plain,
% 0.47/0.65 (multiply(multiply(sk_c8, multiply(sk_c2, sk_c3)), sk_c1) = multiply(multiply(sk_c8, sk_c8), sk_c1)),
% 0.47/0.65 inference(monotonicity,[status(thm)],[493])).
% 0.47/0.65 tff(499,plain,
% 0.47/0.65 (multiply(multiply(sk_c8, sk_c8), sk_c1) = multiply(multiply(sk_c8, multiply(sk_c2, sk_c3)), sk_c1)),
% 0.47/0.65 inference(symmetry,[status(thm)],[498])).
% 0.47/0.65 tff(500,plain,
% 0.47/0.65 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c8), sk_c1) = multiply(sk_c8, multiply(sk_c8, sk_c1)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(501,plain,
% 0.47/0.65 (multiply(multiply(sk_c8, sk_c8), sk_c1) = multiply(sk_c8, multiply(sk_c8, sk_c1))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[500, 32])).
% 0.47/0.65 tff(502,plain,
% 0.47/0.65 (multiply(sk_c8, multiply(sk_c8, sk_c1)) = multiply(multiply(sk_c8, sk_c8), sk_c1)),
% 0.47/0.65 inference(symmetry,[status(thm)],[501])).
% 0.47/0.65 tff(503,plain,
% 0.47/0.65 (multiply(sk_c8, multiply(sk_c8, sk_c1)) = multiply(sk_c8, identity)),
% 0.47/0.65 inference(monotonicity,[status(thm)],[484])).
% 0.47/0.65 tff(504,plain,
% 0.47/0.65 (multiply(sk_c8, identity) = multiply(sk_c8, multiply(sk_c8, sk_c1))),
% 0.47/0.65 inference(symmetry,[status(thm)],[503])).
% 0.47/0.65 tff(505,plain,
% 0.47/0.65 (multiply(sk_c3, multiply(sk_c1, inverse(sk_c2))) = multiply(multiply(sk_c3, sk_c1), inverse(sk_c2))),
% 0.47/0.65 inference(symmetry,[status(thm)],[142])).
% 0.47/0.65 tff(506,plain,
% 0.47/0.65 (multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))) = multiply(sk_c2, multiply(multiply(sk_c3, sk_c1), inverse(sk_c2)))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[505])).
% 0.47/0.65 tff(507,plain,
% 0.47/0.65 (multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))) = inverse(sk_c2)),
% 0.47/0.65 inference(transitivity,[status(thm)],[506, 140, 459, 436])).
% 0.47/0.65 tff(508,plain,
% 0.47/0.65 (multiply(multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))), sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.47/0.65 inference(monotonicity,[status(thm)],[507])).
% 0.47/0.65 tff(509,plain,
% 0.47/0.65 (multiply(inverse(sk_c2), sk_c2) = multiply(multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))), sk_c2)),
% 0.47/0.65 inference(symmetry,[status(thm)],[508])).
% 0.47/0.65 tff(510,plain,
% 0.47/0.65 (identity = multiply(multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))), sk_c2)),
% 0.47/0.65 inference(transitivity,[status(thm)],[165, 509])).
% 0.47/0.65 tff(511,plain,
% 0.47/0.65 (multiply(sk_c8, identity) = multiply(sk_c8, multiply(multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))), sk_c2))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[510])).
% 0.47/0.65 tff(512,plain,
% 0.47/0.65 (multiply(sk_c8, multiply(multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))), sk_c2)) = multiply(sk_c8, identity)),
% 0.47/0.65 inference(symmetry,[status(thm)],[511])).
% 0.47/0.65 tff(513,plain,
% 0.47/0.65 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2))))), sk_c2) = multiply(sk_c8, multiply(multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))), sk_c2)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(514,plain,
% 0.47/0.65 (multiply(multiply(sk_c8, multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2))))), sk_c2) = multiply(sk_c8, multiply(multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))), sk_c2))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[513, 32])).
% 0.47/0.65 tff(515,plain,
% 0.47/0.65 (multiply(sk_c8, multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2))))) = multiply(sk_c8, inverse(sk_c2))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[507])).
% 0.47/0.65 tff(516,plain,
% 0.47/0.65 (multiply(multiply(sk_c8, multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2))))), sk_c2) = multiply(multiply(sk_c8, inverse(sk_c2)), sk_c2)),
% 0.47/0.65 inference(monotonicity,[status(thm)],[515])).
% 0.47/0.65 tff(517,plain,
% 0.47/0.65 (multiply(multiply(sk_c8, inverse(sk_c2)), sk_c2) = multiply(multiply(sk_c8, multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2))))), sk_c2)),
% 0.47/0.65 inference(symmetry,[status(thm)],[516])).
% 0.47/0.65 tff(518,plain,
% 0.47/0.65 (multiply(multiply(sk_c8, inverse(sk_c2)), sk_c2) = multiply(multiply(sk_c8, multiply(sk_c2, sk_c3)), sk_c1)),
% 0.47/0.65 inference(transitivity,[status(thm)],[517, 514, 512, 504, 502, 499])).
% 0.47/0.65 tff(519,plain,
% 0.47/0.65 (multiply(multiply(multiply(sk_c8, inverse(sk_c2)), sk_c2), sk_c8) = multiply(multiply(multiply(sk_c8, multiply(sk_c2, sk_c3)), sk_c1), sk_c8)),
% 0.47/0.65 inference(monotonicity,[status(thm)],[518])).
% 0.47/0.65 tff(520,plain,
% 0.47/0.65 (multiply(multiply(multiply(sk_c8, inverse(sk_c2)), sk_c2), sk_c8) = multiply(sk_c8, identity)),
% 0.47/0.65 inference(transitivity,[status(thm)],[519, 497, 495, 494, 492, 490, 488, 481, 479])).
% 0.47/0.65 tff(521,plain,
% 0.47/0.65 (multiply(sk_c7, multiply(multiply(multiply(sk_c8, inverse(sk_c2)), sk_c2), sk_c8)) = multiply(sk_c7, multiply(sk_c8, identity))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[520])).
% 0.47/0.65 tff(522,plain,
% 0.47/0.65 (multiply(sk_c7, multiply(sk_c8, identity)) = multiply(sk_c7, multiply(multiply(multiply(sk_c8, inverse(sk_c2)), sk_c2), sk_c8))),
% 0.47/0.65 inference(symmetry,[status(thm)],[521])).
% 0.47/0.65 tff(523,plain,
% 0.47/0.65 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c8), identity) = multiply(sk_c7, multiply(sk_c8, identity)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(524,plain,
% 0.47/0.65 (multiply(multiply(sk_c7, sk_c8), identity) = multiply(sk_c7, multiply(sk_c8, identity))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[523, 32])).
% 0.47/0.65 tff(525,plain,
% 0.47/0.65 (multiply(multiply(sk_c7, sk_c8), identity) = multiply(identity, identity)),
% 0.47/0.65 inference(monotonicity,[status(thm)],[478])).
% 0.47/0.65 tff(526,plain,
% 0.47/0.65 (multiply(identity, identity) = multiply(multiply(sk_c7, sk_c8), identity)),
% 0.47/0.65 inference(symmetry,[status(thm)],[525])).
% 0.47/0.65 tff(527,plain,
% 0.47/0.65 (multiply(identity, identity) = multiply(identity, multiply(multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))), sk_c2))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[510])).
% 0.47/0.65 tff(528,plain,
% 0.47/0.65 (multiply(identity, multiply(multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2)))), sk_c2)) = multiply(identity, identity)),
% 0.47/0.65 inference(symmetry,[status(thm)],[527])).
% 0.47/0.65 tff(529,plain,
% 0.47/0.65 (multiply(identity, multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2))))) = multiply(multiply(sk_c2, multiply(sk_c3, sk_c1)), inverse(sk_c2))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[457, 507])).
% 0.47/0.65 tff(530,plain,
% 0.47/0.65 (multiply(identity, multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2))))) = inverse(sk_c2)),
% 0.47/0.65 inference(transitivity,[status(thm)],[529, 459, 436])).
% 0.47/0.65 tff(531,plain,
% 0.47/0.65 (multiply(multiply(identity, multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2))))), sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.47/0.65 inference(monotonicity,[status(thm)],[530])).
% 0.47/0.65 tff(532,plain,
% 0.47/0.65 (multiply(inverse(sk_c2), sk_c2) = multiply(multiply(identity, multiply(sk_c2, multiply(sk_c3, multiply(sk_c1, inverse(sk_c2))))), sk_c2)),
% 0.47/0.65 inference(symmetry,[status(thm)],[531])).
% 0.47/0.65 tff(533,plain,
% 0.47/0.65 (multiply(sk_c7, multiply(sk_c8, sk_c7)) = multiply(inverse(sk_c8), sk_c8)),
% 0.47/0.65 inference(monotonicity,[status(thm)],[224, 489])).
% 0.47/0.65 tff(534,plain,
% 0.47/0.65 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c8), sk_c7) = multiply(sk_c7, multiply(sk_c8, sk_c7)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(535,plain,
% 0.47/0.65 (multiply(multiply(sk_c7, sk_c8), sk_c7) = multiply(sk_c7, multiply(sk_c8, sk_c7))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[534, 32])).
% 0.47/0.65 tff(536,plain,
% 0.47/0.65 (identity = multiply(sk_c7, sk_c8)),
% 0.47/0.65 inference(transitivity,[status(thm)],[155, 461])).
% 0.47/0.65 tff(537,plain,
% 0.47/0.65 (multiply(identity, sk_c7) = multiply(multiply(sk_c7, sk_c8), sk_c7)),
% 0.47/0.65 inference(monotonicity,[status(thm)],[536])).
% 0.47/0.65 tff(538,plain,
% 0.47/0.65 (sk_c7 = multiply(identity, sk_c7)),
% 0.47/0.65 inference(symmetry,[status(thm)],[399])).
% 0.47/0.65 tff(539,plain,
% 0.47/0.65 (inverse(sk_c8) = sk_c8),
% 0.47/0.65 inference(transitivity,[status(thm)],[223, 538, 537, 535, 533, 107, 165, 532, 214, 528, 526, 524, 522, 477, 474, 9])).
% 0.47/0.65 tff(540,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[437, 539])).
% 0.47/0.65 tff(541,plain,(inverse(sk_c8) = sk_c8), inference(lemma,lemma(discharge,[]))).
% 0.47/0.65 tff(542,plain,
% 0.47/0.65 (sk_c7 = sk_c8),
% 0.47/0.65 inference(transitivity,[status(thm)],[224, 541])).
% 0.47/0.65 tff(543,plain,
% 0.47/0.65 ((multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7) <=> (multiply(sk_c8, sk_c7) = sk_c8)),
% 0.47/0.65 inference(monotonicity,[status(thm)],[361, 542])).
% 0.47/0.65 tff(544,plain,
% 0.47/0.65 ((~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) <=> (~(multiply(sk_c8, sk_c7) = sk_c8))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[543])).
% 0.47/0.65 tff(545,plain,
% 0.47/0.65 (multiply(sk_c1, sk_c7) = multiply(sk_c1, sk_c8)),
% 0.47/0.65 inference(monotonicity,[status(thm)],[542])).
% 0.47/0.65 tff(546,plain,
% 0.47/0.65 (multiply(sk_c1, sk_c7) = sk_c8),
% 0.47/0.65 inference(transitivity,[status(thm)],[545, 321, 224, 541])).
% 0.47/0.65 tff(547,plain,
% 0.47/0.65 (multiply(sk_c1, inverse(sk_c1)) = multiply(sk_c1, sk_c8)),
% 0.47/0.65 inference(monotonicity,[status(thm)],[421])).
% 0.47/0.65 tff(548,plain,
% 0.47/0.65 (multiply(sk_c1, inverse(sk_c1)) = inverse(sk_c8)),
% 0.47/0.65 inference(transitivity,[status(thm)],[547, 321, 224])).
% 0.47/0.65 tff(549,plain,
% 0.47/0.65 ((multiply(sk_c1, inverse(sk_c1)) = sk_c8) <=> (inverse(sk_c8) = sk_c8)),
% 0.47/0.65 inference(monotonicity,[status(thm)],[548])).
% 0.47/0.65 tff(550,plain,
% 0.47/0.65 ((inverse(sk_c8) = sk_c8) <=> (multiply(sk_c1, inverse(sk_c1)) = sk_c8)),
% 0.47/0.65 inference(symmetry,[status(thm)],[549])).
% 0.47/0.65 tff(551,plain,
% 0.47/0.65 (multiply(sk_c1, inverse(sk_c1)) = sk_c8),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[541, 550])).
% 0.47/0.65 tff(552,plain,
% 0.47/0.65 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(553,plain,
% 0.47/0.65 (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(554,plain,
% 0.47/0.65 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7))))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[553])).
% 0.47/0.66 tff(555,plain,
% 0.47/0.66 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)))),
% 0.47/0.66 inference(transitivity,[status(thm)],[554, 552])).
% 0.47/0.66 tff(556,plain,
% 0.47/0.66 ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(557,plain,
% 0.47/0.66 ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X5, inverse(X5)) = sk_c8)) | (~(multiply(X4, sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[556, 555])).
% 0.47/0.66 tff(558,plain,
% 0.47/0.66 ((~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(multiply(sk_c1, inverse(sk_c1)) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[557, 321, 223, 421, 312])).
% 0.47/0.66 tff(559,plain,
% 0.47/0.66 (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[558, 551, 546])).
% 0.47/0.66 tff(560,plain,
% 0.47/0.66 (~(multiply(sk_c8, sk_c7) = sk_c8)),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[559, 544])).
% 0.47/0.66 tff(561,plain,
% 0.47/0.66 ($false),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[560, 432])).
% 0.47/0.66 % SZS output end Proof
% 0.47/0.66 % E exiting
%------------------------------------------------------------------------------