%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP335-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:07:38 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP335-1 : TPTP v9.0.0. Released v2.5.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 16:00:33 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.41 % SZS status Unsatisfiable
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 tff(sk_c8_type, type, (
% 0.21/0.41 sk_c8: $i)).
% 0.21/0.41 tff(multiply_type, type, (
% 0.21/0.41 multiply: ( $i * $i ) > $i)).
% 0.21/0.41 tff(sk_c7_type, type, (
% 0.21/0.41 sk_c7: $i)).
% 0.21/0.41 tff(sk_c1_type, type, (
% 0.21/0.41 sk_c1: $i)).
% 0.21/0.41 tff(identity_type, type, (
% 0.21/0.41 identity: $i)).
% 0.21/0.41 tff(sk_c4_type, type, (
% 0.21/0.41 sk_c4: $i)).
% 0.21/0.41 tff(inverse_type, type, (
% 0.21/0.41 inverse: $i > $i)).
% 0.21/0.41 tff(sk_c2_type, type, (
% 0.21/0.41 sk_c2: $i)).
% 0.21/0.41 tff(sk_c3_type, type, (
% 0.21/0.41 sk_c3: $i)).
% 0.21/0.41 tff(sk_c6_type, type, (
% 0.21/0.41 sk_c6: $i)).
% 0.21/0.41 tff(sk_c5_type, type, (
% 0.21/0.41 sk_c5: $i)).
% 0.21/0.41 tff(1,plain,
% 0.21/0.41 (^[X: $i] : refl((multiply(identity, X) = X) <=> (multiply(identity, X) = X))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(2,plain,
% 0.21/0.41 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.21/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.41 tff(3,plain,
% 0.21/0.41 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(4,axiom,(![X: $i] : (multiply(identity, X) = X)), file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax','left_identity')).
% 0.21/0.41 tff(5,plain,
% 0.21/0.41 (![X: $i] : (multiply(identity, X) = X)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.41 tff(6,plain,(
% 0.21/0.41 ![X: $i] : (multiply(identity, X) = X)),
% 0.21/0.41 inference(skolemize,[status(sab)],[5])).
% 0.21/0.41 tff(7,plain,
% 0.21/0.41 (![X: $i] : (multiply(identity, X) = X)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.41 tff(8,plain,
% 0.21/0.41 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c8) = sk_c8)),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(9,plain,
% 0.21/0.41 (multiply(identity, sk_c8) = sk_c8),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.41 tff(10,plain,
% 0.21/0.41 ((sk_c7 = inverse(sk_c3)) <=> (inverse(sk_c3) = sk_c7)),
% 0.21/0.41 inference(commutativity,[status(thm)],[])).
% 0.21/0.41 tff(11,assumption,(~(inverse(sk_c3) = sk_c8)), introduced(assumption)).
% 0.21/0.41 tff(12,plain,
% 0.21/0.41 (((inverse(sk_c1) = sk_c7) | (inverse(sk_c3) = sk_c8)) <=> ((inverse(sk_c1) = sk_c7) | (inverse(sk_c3) = sk_c8))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(13,axiom,((inverse(sk_c1) = sk_c7) | (inverse(sk_c3) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_15')).
% 0.21/0.41 tff(14,plain,
% 0.21/0.41 ((inverse(sk_c1) = sk_c7) | (inverse(sk_c3) = sk_c8)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.21/0.41 tff(15,plain,
% 0.21/0.41 (inverse(sk_c1) = sk_c7),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[14, 11])).
% 0.21/0.41 tff(16,plain,
% 0.21/0.41 (sk_c7 = inverse(sk_c1)),
% 0.21/0.41 inference(symmetry,[status(thm)],[15])).
% 0.21/0.41 tff(17,plain,
% 0.21/0.41 (((inverse(sk_c2) = sk_c7) | (inverse(sk_c3) = sk_c8)) <=> ((inverse(sk_c2) = sk_c7) | (inverse(sk_c3) = sk_c8))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(18,axiom,((inverse(sk_c2) = sk_c7) | (inverse(sk_c3) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_27')).
% 0.21/0.41 tff(19,plain,
% 0.21/0.41 ((inverse(sk_c2) = sk_c7) | (inverse(sk_c3) = sk_c8)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.21/0.41 tff(20,plain,
% 0.21/0.41 (inverse(sk_c2) = sk_c7),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[19, 11])).
% 0.21/0.41 tff(21,plain,
% 0.21/0.41 (inverse(sk_c2) = inverse(sk_c1)),
% 0.21/0.41 inference(transitivity,[status(thm)],[20, 16])).
% 0.21/0.41 tff(22,plain,
% 0.21/0.41 ((inverse(sk_c2) = sk_c8) <=> (inverse(sk_c1) = sk_c8)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[21])).
% 0.21/0.41 tff(23,plain,
% 0.21/0.41 ((inverse(sk_c1) = sk_c8) <=> (inverse(sk_c2) = sk_c8)),
% 0.21/0.41 inference(symmetry,[status(thm)],[22])).
% 0.21/0.41 tff(24,plain,
% 0.21/0.41 (((inverse(sk_c3) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c6)) <=> ((inverse(sk_c3) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c6))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 (((multiply(sk_c1, sk_c7) = sk_c6) | (inverse(sk_c3) = sk_c8)) <=> ((inverse(sk_c3) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c6))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(26,axiom,((multiply(sk_c1, sk_c7) = sk_c6) | (inverse(sk_c3) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_9')).
% 0.21/0.41 tff(27,plain,
% 0.21/0.41 ((inverse(sk_c3) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c6)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.21/0.41 tff(28,plain,
% 0.21/0.41 ((inverse(sk_c3) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c6)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.21/0.42 tff(29,plain,
% 0.21/0.42 (multiply(sk_c1, sk_c7) = sk_c6),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[28, 11])).
% 0.21/0.42 tff(30,plain,
% 0.21/0.42 (sk_c6 = multiply(sk_c1, sk_c7)),
% 0.21/0.42 inference(symmetry,[status(thm)],[29])).
% 0.21/0.42 tff(31,plain,
% 0.21/0.42 (((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c3) = sk_c8)) <=> ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c3) = sk_c8))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(32,axiom,((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c3) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_3')).
% 0.21/0.42 tff(33,plain,
% 0.21/0.42 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c3) = sk_c8)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.21/0.42 tff(34,plain,
% 0.21/0.42 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c3) = sk_c8)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[33, 31])).
% 0.21/0.42 tff(35,plain,
% 0.21/0.42 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c3) = sk_c8)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[34, 31])).
% 0.21/0.42 tff(36,plain,
% 0.21/0.42 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c3) = sk_c8)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.21/0.42 tff(37,plain,
% 0.21/0.42 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c3) = sk_c8)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[36, 31])).
% 0.21/0.42 tff(38,plain,
% 0.21/0.42 (multiply(sk_c7, sk_c8) = sk_c6),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[37, 11])).
% 0.21/0.42 tff(39,plain,
% 0.21/0.42 (((inverse(sk_c3) = sk_c8) | (multiply(sk_c2, sk_c7) = sk_c8)) <=> ((inverse(sk_c3) = sk_c8) | (multiply(sk_c2, sk_c7) = sk_c8))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(40,plain,
% 0.21/0.42 (((multiply(sk_c2, sk_c7) = sk_c8) | (inverse(sk_c3) = sk_c8)) <=> ((inverse(sk_c3) = sk_c8) | (multiply(sk_c2, sk_c7) = sk_c8))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(41,axiom,((multiply(sk_c2, sk_c7) = sk_c8) | (inverse(sk_c3) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_21')).
% 0.21/0.42 tff(42,plain,
% 0.21/0.42 ((inverse(sk_c3) = sk_c8) | (multiply(sk_c2, sk_c7) = sk_c8)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.21/0.42 tff(43,plain,
% 0.21/0.42 ((inverse(sk_c3) = sk_c8) | (multiply(sk_c2, sk_c7) = sk_c8)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[42, 39])).
% 0.21/0.42 tff(44,plain,
% 0.21/0.42 (multiply(sk_c2, sk_c7) = sk_c8),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[43, 11])).
% 0.21/0.42 tff(45,plain,
% 0.21/0.42 (multiply(sk_c7, multiply(sk_c2, sk_c7)) = multiply(sk_c7, sk_c8)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[44])).
% 0.21/0.42 tff(46,plain,
% 0.21/0.42 (^[Z: $i, Y: $i, X: $i] : refl((multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))) <=> (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(47,plain,
% 0.21/0.42 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[46])).
% 0.21/0.42 tff(48,plain,
% 0.21/0.42 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(49,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')).
% 0.21/0.42 tff(50,plain,
% 0.21/0.42 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.21/0.42 tff(51,plain,(
% 0.21/0.42 ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[50])).
% 0.21/0.42 tff(52,plain,
% 0.21/0.42 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.21/0.42 tff(53,plain,
% 0.21/0.42 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c2), sk_c7) = multiply(sk_c7, multiply(sk_c2, sk_c7)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(54,plain,
% 0.21/0.42 (multiply(multiply(sk_c7, sk_c2), sk_c7) = multiply(sk_c7, multiply(sk_c2, sk_c7))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.21/0.42 tff(55,plain,
% 0.21/0.42 (sk_c7 = inverse(sk_c2)),
% 0.21/0.42 inference(symmetry,[status(thm)],[20])).
% 0.21/0.42 tff(56,plain,
% 0.21/0.42 (multiply(sk_c7, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[55])).
% 0.21/0.42 tff(57,plain,
% 0.21/0.42 (multiply(inverse(sk_c2), sk_c2) = multiply(sk_c7, sk_c2)),
% 0.21/0.42 inference(symmetry,[status(thm)],[56])).
% 0.21/0.42 tff(58,plain,
% 0.21/0.42 (^[X: $i] : refl((multiply(inverse(X), X) = identity) <=> (multiply(inverse(X), X) = identity))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(59,plain,
% 0.21/0.42 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.21/0.42 inference(quant_intro,[status(thm)],[58])).
% 0.21/0.42 tff(60,plain,
% 0.21/0.42 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(61,axiom,(![X: $i] : (multiply(inverse(X), X) = identity)), file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax','left_inverse')).
% 0.21/0.42 tff(62,plain,
% 0.21/0.42 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.21/0.42 tff(63,plain,(
% 0.21/0.42 ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.21/0.42 inference(skolemize,[status(sab)],[62])).
% 0.21/0.42 tff(64,plain,
% 0.21/0.42 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.21/0.42 tff(65,plain,
% 0.21/0.42 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c2), sk_c2) = identity)),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(66,plain,
% 0.21/0.42 (multiply(inverse(sk_c2), sk_c2) = identity),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.21/0.42 tff(67,plain,
% 0.21/0.42 (identity = multiply(inverse(sk_c2), sk_c2)),
% 0.21/0.42 inference(symmetry,[status(thm)],[66])).
% 0.21/0.42 tff(68,plain,
% 0.21/0.42 (identity = multiply(sk_c7, sk_c2)),
% 0.21/0.42 inference(transitivity,[status(thm)],[67, 57])).
% 0.21/0.42 tff(69,plain,
% 0.21/0.42 (multiply(identity, sk_c7) = multiply(multiply(sk_c7, sk_c2), sk_c7)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[68])).
% 0.21/0.42 tff(70,plain,
% 0.21/0.42 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c7) = sk_c7)),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(71,plain,
% 0.21/0.42 (multiply(identity, sk_c7) = sk_c7),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[70, 7])).
% 0.21/0.42 tff(72,plain,
% 0.21/0.42 (sk_c7 = multiply(identity, sk_c7)),
% 0.21/0.42 inference(symmetry,[status(thm)],[71])).
% 0.21/0.42 tff(73,plain,
% 0.21/0.42 (inverse(sk_c1) = multiply(sk_c1, sk_c7)),
% 0.21/0.42 inference(transitivity,[status(thm)],[15, 72, 69, 54, 45, 38, 30])).
% 0.21/0.42 tff(74,plain,
% 0.21/0.42 ((inverse(sk_c1) = sk_c8) <=> (multiply(sk_c1, sk_c7) = sk_c8)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[73])).
% 0.21/0.42 tff(75,plain,
% 0.21/0.42 ((multiply(sk_c1, sk_c7) = sk_c8) <=> (inverse(sk_c1) = sk_c8)),
% 0.21/0.42 inference(symmetry,[status(thm)],[74])).
% 0.21/0.42 tff(76,plain,
% 0.21/0.42 ((multiply(sk_c1, sk_c7) = sk_c8) <=> (inverse(sk_c2) = sk_c8)),
% 0.21/0.42 inference(transitivity,[status(thm)],[75, 23])).
% 0.21/0.42 tff(77,plain,
% 0.21/0.42 (multiply(multiply(sk_c7, sk_c2), sk_c7) = multiply(identity, sk_c7)),
% 0.21/0.42 inference(symmetry,[status(thm)],[69])).
% 0.21/0.42 tff(78,plain,
% 0.21/0.42 (multiply(sk_c7, multiply(sk_c2, sk_c7)) = multiply(multiply(sk_c7, sk_c2), sk_c7)),
% 0.21/0.42 inference(symmetry,[status(thm)],[54])).
% 0.21/0.42 tff(79,plain,
% 0.21/0.42 (multiply(sk_c7, sk_c8) = multiply(sk_c7, multiply(sk_c2, sk_c7))),
% 0.21/0.42 inference(symmetry,[status(thm)],[45])).
% 0.21/0.42 tff(80,plain,
% 0.21/0.42 (sk_c6 = multiply(sk_c7, sk_c8)),
% 0.21/0.42 inference(symmetry,[status(thm)],[38])).
% 0.21/0.42 tff(81,plain,
% 0.21/0.42 (sk_c6 = sk_c7),
% 0.21/0.42 inference(transitivity,[status(thm)],[80, 79, 78, 77, 71])).
% 0.21/0.42 tff(82,plain,
% 0.21/0.42 (multiply(sk_c6, sk_c6) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[81, 30])).
% 0.21/0.42 tff(83,plain,
% 0.21/0.42 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(sk_c6, sk_c6)),
% 0.21/0.42 inference(symmetry,[status(thm)],[82])).
% 0.21/0.42 tff(84,plain,
% 0.21/0.42 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(sk_c7, multiply(sk_c1, sk_c7)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(85,plain,
% 0.21/0.42 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[84, 52])).
% 0.21/0.42 tff(86,plain,
% 0.21/0.42 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c1), sk_c1) = identity)),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(87,plain,
% 0.21/0.42 (multiply(inverse(sk_c1), sk_c1) = identity),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[86, 64])).
% 0.21/0.42 tff(88,plain,
% 0.21/0.42 (multiply(sk_c7, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[16])).
% 0.21/0.42 tff(89,plain,
% 0.21/0.42 (multiply(sk_c7, sk_c1) = multiply(sk_c7, sk_c2)),
% 0.21/0.42 inference(transitivity,[status(thm)],[88, 87, 67, 57])).
% 0.21/0.42 tff(90,plain,
% 0.21/0.42 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(multiply(sk_c7, sk_c2), sk_c7)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[89])).
% 0.21/0.42 tff(91,plain,
% 0.21/0.42 (multiply(multiply(sk_c7, sk_c2), sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.21/0.42 inference(symmetry,[status(thm)],[90])).
% 0.21/0.42 tff(92,plain,
% 0.21/0.42 (sk_c7 = multiply(sk_c6, sk_c6)),
% 0.21/0.42 inference(transitivity,[status(thm)],[72, 69, 91, 85, 83])).
% 0.21/0.42 tff(93,plain,
% 0.21/0.42 (multiply(sk_c2, sk_c7) = multiply(sk_c2, multiply(sk_c6, sk_c6))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[92])).
% 0.21/0.42 tff(94,plain,
% 0.21/0.42 (multiply(sk_c2, multiply(sk_c6, sk_c6)) = multiply(sk_c2, sk_c7)),
% 0.21/0.42 inference(symmetry,[status(thm)],[93])).
% 0.21/0.42 tff(95,plain,
% 0.21/0.42 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, sk_c6), sk_c6) = multiply(sk_c2, multiply(sk_c6, sk_c6)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(96,plain,
% 0.21/0.42 (multiply(multiply(sk_c2, sk_c6), sk_c6) = multiply(sk_c2, multiply(sk_c6, sk_c6))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[95, 52])).
% 0.21/0.42 tff(97,plain,
% 0.21/0.42 (multiply(sk_c2, sk_c6) = multiply(sk_c2, sk_c7)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[81])).
% 0.21/0.42 tff(98,plain,
% 0.21/0.42 (multiply(sk_c2, sk_c6) = sk_c8),
% 0.21/0.42 inference(transitivity,[status(thm)],[97, 44])).
% 0.21/0.42 tff(99,plain,
% 0.21/0.42 (multiply(multiply(sk_c2, sk_c6), sk_c6) = multiply(sk_c8, sk_c7)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[98, 81])).
% 0.21/0.42 tff(100,plain,
% 0.21/0.42 (multiply(sk_c8, sk_c7) = multiply(multiply(sk_c2, sk_c6), sk_c6)),
% 0.21/0.42 inference(symmetry,[status(thm)],[99])).
% 0.21/0.42 tff(101,plain,
% 0.21/0.42 ((sk_c8 = multiply(sk_c1, sk_c7)) <=> (multiply(sk_c1, sk_c7) = sk_c8)),
% 0.21/0.42 inference(commutativity,[status(thm)],[])).
% 0.21/0.42 tff(102,assumption,(multiply(sk_c1, sk_c7) = sk_c6), introduced(assumption)).
% 0.21/0.42 tff(103,plain,
% 0.21/0.42 (sk_c6 = multiply(sk_c1, sk_c7)),
% 0.21/0.42 inference(symmetry,[status(thm)],[102])).
% 0.21/0.42 tff(104,assumption,(multiply(sk_c7, sk_c8) = sk_c6), introduced(assumption)).
% 0.21/0.42 tff(105,assumption,(multiply(sk_c2, sk_c7) = sk_c8), introduced(assumption)).
% 0.21/0.42 tff(106,plain,
% 0.21/0.42 (multiply(sk_c7, multiply(sk_c2, sk_c7)) = multiply(sk_c7, sk_c8)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[105])).
% 0.21/0.42 tff(107,assumption,(inverse(sk_c2) = sk_c7), introduced(assumption)).
% 0.21/0.42 tff(108,plain,
% 0.21/0.42 (sk_c7 = inverse(sk_c2)),
% 0.21/0.42 inference(symmetry,[status(thm)],[107])).
% 0.21/0.42 tff(109,plain,
% 0.21/0.42 (multiply(sk_c7, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[108])).
% 0.21/0.42 tff(110,plain,
% 0.21/0.42 (multiply(inverse(sk_c2), sk_c2) = multiply(sk_c7, sk_c2)),
% 0.21/0.42 inference(symmetry,[status(thm)],[109])).
% 0.21/0.42 tff(111,plain,
% 0.21/0.42 (identity = multiply(sk_c7, sk_c2)),
% 0.21/0.42 inference(transitivity,[status(thm)],[67, 110])).
% 0.21/0.42 tff(112,plain,
% 0.21/0.42 (multiply(identity, sk_c7) = multiply(multiply(sk_c7, sk_c2), sk_c7)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[111])).
% 0.21/0.42 tff(113,plain,
% 0.21/0.42 (sk_c7 = multiply(sk_c1, sk_c7)),
% 0.21/0.42 inference(transitivity,[status(thm)],[72, 112, 54, 106, 104, 103])).
% 0.21/0.42 tff(114,plain,
% 0.21/0.42 (multiply(multiply(sk_c7, sk_c2), sk_c7) = multiply(identity, sk_c7)),
% 0.21/0.42 inference(symmetry,[status(thm)],[112])).
% 0.21/0.42 tff(115,plain,
% 0.21/0.42 (multiply(sk_c7, sk_c8) = multiply(sk_c7, multiply(sk_c2, sk_c7))),
% 0.21/0.42 inference(symmetry,[status(thm)],[106])).
% 0.21/0.42 tff(116,plain,
% 0.21/0.42 (sk_c6 = multiply(sk_c7, sk_c8)),
% 0.21/0.42 inference(symmetry,[status(thm)],[104])).
% 0.21/0.42 tff(117,plain,
% 0.21/0.42 (sk_c6 = sk_c7),
% 0.21/0.42 inference(transitivity,[status(thm)],[116, 115, 78, 114, 71])).
% 0.21/0.42 tff(118,plain,
% 0.21/0.42 (multiply(sk_c6, sk_c8) = multiply(sk_c7, sk_c8)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[117])).
% 0.21/0.42 tff(119,plain,
% 0.21/0.42 (multiply(sk_c6, sk_c8) = sk_c7),
% 0.21/0.42 inference(transitivity,[status(thm)],[118, 115, 78, 114, 71])).
% 0.21/0.42 tff(120,plain,
% 0.21/0.42 (multiply(sk_c2, multiply(sk_c6, sk_c8)) = multiply(sk_c2, sk_c7)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[119])).
% 0.21/0.42 tff(121,plain,
% 0.21/0.42 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, sk_c6), sk_c8) = multiply(sk_c2, multiply(sk_c6, sk_c8)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(122,plain,
% 0.21/0.42 (multiply(multiply(sk_c2, sk_c6), sk_c8) = multiply(sk_c2, multiply(sk_c6, sk_c8))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[121, 52])).
% 0.21/0.42 tff(123,plain,
% 0.21/0.42 (multiply(sk_c2, sk_c6) = multiply(sk_c2, sk_c7)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[117])).
% 0.21/0.42 tff(124,plain,
% 0.21/0.42 (multiply(sk_c2, sk_c7) = multiply(sk_c2, sk_c6)),
% 0.21/0.42 inference(symmetry,[status(thm)],[123])).
% 0.21/0.42 tff(125,plain,
% 0.21/0.42 (sk_c8 = multiply(sk_c2, sk_c7)),
% 0.21/0.42 inference(symmetry,[status(thm)],[105])).
% 0.21/0.42 tff(126,plain,
% 0.21/0.42 (sk_c8 = multiply(sk_c2, sk_c6)),
% 0.21/0.42 inference(transitivity,[status(thm)],[125, 124])).
% 0.21/0.42 tff(127,plain,
% 0.21/0.42 (multiply(sk_c8, sk_c8) = multiply(multiply(sk_c2, sk_c6), sk_c8)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[126])).
% 0.21/0.42 tff(128,plain,
% 0.21/0.42 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c1) = sk_c1)),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(129,plain,
% 0.21/0.42 (multiply(identity, sk_c1) = sk_c1),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[128, 7])).
% 0.21/0.42 tff(130,assumption,(inverse(sk_c1) = sk_c7), introduced(assumption)).
% 0.21/0.42 tff(131,plain,
% 0.21/0.42 (sk_c7 = inverse(sk_c1)),
% 0.21/0.42 inference(symmetry,[status(thm)],[130])).
% 0.21/0.42 tff(132,plain,
% 0.21/0.42 (sk_c6 = inverse(sk_c1)),
% 0.21/0.42 inference(transitivity,[status(thm)],[116, 115, 78, 114, 71, 131])).
% 0.21/0.42 tff(133,plain,
% 0.21/0.42 (multiply(sk_c6, multiply(identity, sk_c1)) = multiply(inverse(sk_c1), sk_c1)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[132, 129])).
% 0.21/0.42 tff(134,plain,
% 0.21/0.42 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, identity), sk_c1) = multiply(sk_c6, multiply(identity, sk_c1)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(135,plain,
% 0.21/0.42 (multiply(multiply(sk_c6, identity), sk_c1) = multiply(sk_c6, multiply(identity, sk_c1))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[134, 52])).
% 0.21/0.42 tff(136,plain,
% 0.21/0.42 (multiply(sk_c6, sk_c2) = multiply(sk_c7, sk_c2)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[117])).
% 0.21/0.42 tff(137,plain,
% 0.21/0.42 (multiply(sk_c7, sk_c2) = multiply(sk_c6, sk_c2)),
% 0.21/0.42 inference(symmetry,[status(thm)],[136])).
% 0.21/0.42 tff(138,plain,
% 0.21/0.42 (identity = multiply(sk_c6, sk_c2)),
% 0.21/0.42 inference(transitivity,[status(thm)],[67, 110, 137])).
% 0.21/0.42 tff(139,plain,
% 0.21/0.42 (multiply(sk_c6, identity) = multiply(sk_c6, multiply(sk_c6, sk_c2))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[138])).
% 0.21/0.42 tff(140,plain,
% 0.21/0.42 (multiply(sk_c6, multiply(sk_c6, sk_c2)) = multiply(sk_c6, identity)),
% 0.21/0.42 inference(symmetry,[status(thm)],[139])).
% 0.21/0.42 tff(141,plain,
% 0.21/0.42 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c6), sk_c2) = multiply(sk_c6, multiply(sk_c6, sk_c2)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(142,plain,
% 0.21/0.42 (multiply(multiply(sk_c6, sk_c6), sk_c2) = multiply(sk_c6, multiply(sk_c6, sk_c2))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[141, 52])).
% 0.21/0.42 tff(143,plain,
% 0.21/0.42 (multiply(sk_c7, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[131])).
% 0.21/0.42 tff(144,plain,
% 0.21/0.42 (multiply(sk_c7, sk_c1) = multiply(sk_c7, sk_c2)),
% 0.21/0.42 inference(transitivity,[status(thm)],[143, 87, 67, 110])).
% 0.21/0.42 tff(145,plain,
% 0.21/0.42 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(multiply(sk_c7, sk_c2), sk_c7)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[144])).
% 0.21/0.42 tff(146,plain,
% 0.21/0.42 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.21/0.42 inference(symmetry,[status(thm)],[85])).
% 0.21/0.43 tff(147,plain,
% 0.21/0.43 (multiply(sk_c6, sk_c6) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[117, 103])).
% 0.21/0.43 tff(148,plain,
% 0.21/0.43 (multiply(sk_c6, sk_c6) = sk_c7),
% 0.21/0.43 inference(transitivity,[status(thm)],[147, 146, 145, 114, 71])).
% 0.21/0.43 tff(149,plain,
% 0.21/0.43 (multiply(multiply(sk_c6, sk_c6), sk_c2) = multiply(sk_c7, sk_c2)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[148])).
% 0.21/0.43 tff(150,plain,
% 0.21/0.43 (multiply(sk_c7, sk_c2) = multiply(multiply(sk_c6, sk_c6), sk_c2)),
% 0.21/0.43 inference(symmetry,[status(thm)],[149])).
% 0.21/0.43 tff(151,plain,
% 0.21/0.43 (identity = multiply(sk_c6, identity)),
% 0.21/0.43 inference(transitivity,[status(thm)],[67, 110, 150, 142, 140])).
% 0.21/0.43 tff(152,plain,
% 0.21/0.43 (multiply(identity, sk_c1) = multiply(multiply(sk_c6, identity), sk_c1)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[151])).
% 0.21/0.43 tff(153,plain,
% 0.21/0.43 (sk_c1 = multiply(identity, sk_c1)),
% 0.21/0.43 inference(symmetry,[status(thm)],[129])).
% 0.21/0.43 tff(154,plain,
% 0.21/0.43 (sk_c1 = identity),
% 0.21/0.43 inference(transitivity,[status(thm)],[153, 152, 135, 133, 87])).
% 0.21/0.43 tff(155,plain,
% 0.21/0.43 (multiply(sk_c1, sk_c8) = multiply(identity, sk_c8)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[154])).
% 0.21/0.43 tff(156,plain,
% 0.21/0.43 (multiply(sk_c1, sk_c8) = sk_c8),
% 0.21/0.43 inference(transitivity,[status(thm)],[155, 9])).
% 0.21/0.43 tff(157,plain,
% 0.21/0.43 (multiply(sk_c8, multiply(sk_c1, sk_c8)) = multiply(sk_c8, sk_c8)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[156])).
% 0.21/0.43 tff(158,plain,
% 0.21/0.43 (multiply(identity, sk_c8) = multiply(sk_c1, sk_c8)),
% 0.21/0.43 inference(symmetry,[status(thm)],[155])).
% 0.21/0.43 tff(159,plain,
% 0.21/0.43 (multiply(sk_c8, multiply(identity, sk_c8)) = multiply(sk_c8, multiply(sk_c1, sk_c8))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[158])).
% 0.21/0.43 tff(160,plain,
% 0.21/0.43 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, identity), sk_c8) = multiply(sk_c8, multiply(identity, sk_c8)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(161,plain,
% 0.21/0.43 (multiply(multiply(sk_c8, identity), sk_c8) = multiply(sk_c8, multiply(identity, sk_c8))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[160, 52])).
% 0.21/0.43 tff(162,plain,
% 0.21/0.43 (multiply(sk_c8, identity) = multiply(sk_c8, multiply(sk_c6, sk_c2))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[138])).
% 0.21/0.43 tff(163,plain,
% 0.21/0.43 (multiply(sk_c8, multiply(sk_c6, sk_c2)) = multiply(sk_c8, identity)),
% 0.21/0.43 inference(symmetry,[status(thm)],[162])).
% 0.21/0.43 tff(164,plain,
% 0.21/0.43 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c6), sk_c2) = multiply(sk_c8, multiply(sk_c6, sk_c2)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(165,plain,
% 0.21/0.43 (multiply(multiply(sk_c8, sk_c6), sk_c2) = multiply(sk_c8, multiply(sk_c6, sk_c2))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[164, 52])).
% 0.21/0.43 tff(166,plain,
% 0.21/0.43 (multiply(sk_c8, sk_c6) = multiply(sk_c8, sk_c7)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[117])).
% 0.21/0.43 tff(167,plain,
% 0.21/0.43 (multiply(sk_c8, sk_c7) = multiply(sk_c8, sk_c6)),
% 0.21/0.43 inference(symmetry,[status(thm)],[166])).
% 0.21/0.43 tff(168,plain,
% 0.21/0.43 (sk_c7 = sk_c6),
% 0.21/0.43 inference(transitivity,[status(thm)],[72, 112, 54, 106, 104])).
% 0.21/0.43 tff(169,plain,
% 0.21/0.43 (multiply(sk_c8, sk_c7) = multiply(multiply(sk_c2, sk_c6), sk_c6)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[126, 168])).
% 0.21/0.43 tff(170,plain,
% 0.21/0.43 (multiply(multiply(sk_c2, sk_c6), sk_c6) = multiply(sk_c8, sk_c7)),
% 0.21/0.43 inference(symmetry,[status(thm)],[169])).
% 0.21/0.43 tff(171,plain,
% 0.21/0.43 (multiply(sk_c2, multiply(sk_c6, sk_c6)) = multiply(multiply(sk_c2, sk_c6), sk_c6)),
% 0.21/0.43 inference(symmetry,[status(thm)],[96])).
% 0.21/0.43 tff(172,plain,
% 0.21/0.43 (multiply(sk_c2, multiply(sk_c6, sk_c6)) = multiply(sk_c2, sk_c7)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[148])).
% 0.21/0.43 tff(173,plain,
% 0.21/0.43 (multiply(sk_c2, sk_c7) = multiply(sk_c2, multiply(sk_c6, sk_c6))),
% 0.21/0.43 inference(symmetry,[status(thm)],[172])).
% 0.21/0.43 tff(174,plain,
% 0.21/0.43 (sk_c8 = multiply(sk_c8, sk_c6)),
% 0.21/0.43 inference(transitivity,[status(thm)],[125, 173, 171, 170, 167])).
% 0.21/0.43 tff(175,plain,
% 0.21/0.43 (multiply(sk_c8, sk_c2) = multiply(multiply(sk_c8, sk_c6), sk_c2)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[174])).
% 0.21/0.43 tff(176,plain,
% 0.21/0.43 (multiply(sk_c8, sk_c2) = multiply(sk_c8, identity)),
% 0.21/0.43 inference(transitivity,[status(thm)],[175, 165, 163])).
% 0.21/0.43 tff(177,plain,
% 0.21/0.43 (multiply(multiply(sk_c8, sk_c2), sk_c8) = multiply(multiply(sk_c8, identity), sk_c8)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[176])).
% 0.21/0.43 tff(178,plain,
% 0.21/0.43 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c2), sk_c8) = multiply(sk_c8, multiply(sk_c2, sk_c8)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(179,plain,
% 0.21/0.43 (multiply(multiply(sk_c8, sk_c2), sk_c8) = multiply(sk_c8, multiply(sk_c2, sk_c8))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[178, 52])).
% 0.21/0.43 tff(180,plain,
% 0.21/0.43 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = multiply(multiply(sk_c8, sk_c2), sk_c8)),
% 0.21/0.43 inference(symmetry,[status(thm)],[179])).
% 0.21/0.43 tff(181,plain,
% 0.21/0.43 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c8),
% 0.21/0.43 inference(transitivity,[status(thm)],[180, 177, 161, 159, 157, 127, 122, 120, 105])).
% 0.21/0.43 tff(182,plain,
% 0.21/0.43 ((multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7) <=> (sk_c8 = multiply(sk_c1, sk_c7))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[181, 113])).
% 0.21/0.43 tff(183,plain,
% 0.21/0.43 ((multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7) <=> (multiply(sk_c1, sk_c7) = sk_c8)),
% 0.21/0.43 inference(transitivity,[status(thm)],[182, 101])).
% 0.21/0.43 tff(184,plain,
% 0.21/0.43 ((multiply(sk_c1, sk_c7) = sk_c8) <=> (multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)),
% 0.21/0.43 inference(symmetry,[status(thm)],[183])).
% 0.21/0.43 tff(185,plain,
% 0.21/0.43 (multiply(multiply(sk_c6, identity), sk_c1) = multiply(identity, sk_c1)),
% 0.21/0.43 inference(symmetry,[status(thm)],[152])).
% 0.21/0.43 tff(186,plain,
% 0.21/0.43 (multiply(sk_c6, multiply(identity, sk_c1)) = multiply(multiply(sk_c6, identity), sk_c1)),
% 0.21/0.43 inference(symmetry,[status(thm)],[135])).
% 0.21/0.43 tff(187,plain,
% 0.21/0.43 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c6, multiply(identity, sk_c1))),
% 0.21/0.43 inference(symmetry,[status(thm)],[133])).
% 0.21/0.43 tff(188,plain,
% 0.21/0.43 (identity = multiply(inverse(sk_c1), sk_c1)),
% 0.21/0.43 inference(symmetry,[status(thm)],[87])).
% 0.21/0.43 tff(189,plain,
% 0.21/0.43 (multiply(sk_c6, sk_c2) = sk_c1),
% 0.21/0.43 inference(transitivity,[status(thm)],[136, 109, 66, 188, 187, 186, 185, 129])).
% 0.21/0.43 tff(190,plain,
% 0.21/0.43 (multiply(multiply(sk_c6, sk_c2), sk_c8) = multiply(sk_c1, sk_c8)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[189])).
% 0.21/0.43 tff(191,plain,
% 0.21/0.43 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c2), sk_c8) = multiply(sk_c6, multiply(sk_c2, sk_c8)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(192,plain,
% 0.21/0.43 (multiply(multiply(sk_c6, sk_c2), sk_c8) = multiply(sk_c6, multiply(sk_c2, sk_c8))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[191, 52])).
% 0.21/0.43 tff(193,plain,
% 0.21/0.43 (multiply(sk_c6, multiply(sk_c2, sk_c8)) = multiply(multiply(sk_c6, sk_c2), sk_c8)),
% 0.21/0.43 inference(symmetry,[status(thm)],[192])).
% 0.21/0.43 tff(194,plain,
% 0.21/0.43 (multiply(sk_c8, sk_c6) = sk_c8),
% 0.21/0.43 inference(transitivity,[status(thm)],[166, 169, 96, 172, 105])).
% 0.21/0.43 tff(195,plain,
% 0.21/0.43 (multiply(sk_c2, multiply(sk_c8, sk_c6)) = multiply(sk_c2, sk_c8)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[194])).
% 0.21/0.43 tff(196,plain,
% 0.21/0.43 (multiply(sk_c6, sk_c6) = sk_c6),
% 0.21/0.43 inference(transitivity,[status(thm)],[147, 146, 145, 54, 106, 104])).
% 0.21/0.43 tff(197,plain,
% 0.21/0.43 (multiply(multiply(sk_c6, sk_c6), multiply(sk_c2, multiply(sk_c8, sk_c6))) = multiply(sk_c6, multiply(sk_c2, sk_c8))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[196, 195])).
% 0.21/0.43 tff(198,plain,
% 0.21/0.43 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c6), multiply(sk_c2, multiply(sk_c8, sk_c6))) = multiply(sk_c6, multiply(sk_c6, multiply(sk_c2, multiply(sk_c8, sk_c6)))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(199,plain,
% 0.21/0.43 (multiply(multiply(sk_c6, sk_c6), multiply(sk_c2, multiply(sk_c8, sk_c6))) = multiply(sk_c6, multiply(sk_c6, multiply(sk_c2, multiply(sk_c8, sk_c6))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[198, 52])).
% 0.21/0.43 tff(200,plain,
% 0.21/0.43 (multiply(sk_c6, multiply(sk_c6, multiply(sk_c2, multiply(sk_c8, sk_c6)))) = multiply(multiply(sk_c6, sk_c6), multiply(sk_c2, multiply(sk_c8, sk_c6)))),
% 0.21/0.43 inference(symmetry,[status(thm)],[199])).
% 0.21/0.43 tff(201,plain,
% 0.21/0.43 (multiply(sk_c6, multiply(sk_c2, multiply(sk_c8, sk_c6))) = multiply(sk_c6, multiply(sk_c2, sk_c8))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[195])).
% 0.21/0.43 tff(202,plain,
% 0.21/0.43 (multiply(sk_c6, multiply(sk_c2, sk_c8)) = multiply(sk_c6, multiply(sk_c2, multiply(sk_c8, sk_c6)))),
% 0.21/0.43 inference(symmetry,[status(thm)],[201])).
% 0.21/0.43 tff(203,plain,
% 0.21/0.43 (multiply(sk_c6, multiply(sk_c6, multiply(sk_c2, sk_c8))) = multiply(sk_c6, multiply(sk_c6, multiply(sk_c2, multiply(sk_c8, sk_c6))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[202])).
% 0.21/0.43 tff(204,plain,
% 0.21/0.43 (multiply(sk_c1, sk_c8) = multiply(multiply(sk_c6, sk_c2), sk_c8)),
% 0.21/0.43 inference(symmetry,[status(thm)],[190])).
% 0.21/0.43 tff(205,plain,
% 0.21/0.43 (sk_c8 = multiply(identity, sk_c8)),
% 0.21/0.43 inference(symmetry,[status(thm)],[9])).
% 0.21/0.43 tff(206,plain,
% 0.21/0.43 (sk_c8 = multiply(sk_c6, multiply(sk_c2, sk_c8))),
% 0.21/0.43 inference(transitivity,[status(thm)],[205, 158, 204, 192])).
% 0.21/0.43 tff(207,plain,
% 0.21/0.43 (multiply(sk_c7, sk_c8) = multiply(sk_c6, multiply(sk_c6, multiply(sk_c2, sk_c8)))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[168, 206])).
% 0.21/0.43 tff(208,plain,
% 0.21/0.43 (multiply(sk_c1, sk_c7) = sk_c8),
% 0.21/0.43 inference(transitivity,[status(thm)],[102, 116, 207, 203, 200, 197, 193, 190, 155, 9])).
% 0.21/0.43 tff(209,plain,
% 0.21/0.43 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[208, 184])).
% 0.21/0.43 tff(210,assumption,(~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)), introduced(assumption)).
% 0.21/0.43 tff(211,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[210, 209])).
% 0.21/0.43 tff(212,plain,((multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c2, sk_c7) = sk_c8)) | (~(inverse(sk_c2) = sk_c7)) | (~(inverse(sk_c1) = sk_c7))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(213,plain,
% 0.21/0.43 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[212, 29, 38, 44, 20, 15])).
% 0.21/0.43 tff(214,plain,
% 0.21/0.43 (sk_c7 = multiply(sk_c8, multiply(sk_c2, sk_c8))),
% 0.21/0.43 inference(symmetry,[status(thm)],[213])).
% 0.21/0.43 tff(215,plain,
% 0.21/0.43 (multiply(sk_c8, sk_c7) = multiply(sk_c8, multiply(sk_c8, multiply(sk_c2, sk_c8)))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[214])).
% 0.21/0.43 tff(216,plain,
% 0.21/0.43 (multiply(sk_c8, multiply(sk_c8, multiply(sk_c2, sk_c8))) = multiply(sk_c8, sk_c7)),
% 0.21/0.43 inference(symmetry,[status(thm)],[215])).
% 0.21/0.43 tff(217,plain,
% 0.21/0.43 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c8), multiply(sk_c2, sk_c8)) = multiply(sk_c8, multiply(sk_c8, multiply(sk_c2, sk_c8))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(218,plain,
% 0.21/0.43 (multiply(multiply(sk_c8, sk_c8), multiply(sk_c2, sk_c8)) = multiply(sk_c8, multiply(sk_c8, multiply(sk_c2, sk_c8)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[217, 52])).
% 0.21/0.43 tff(219,plain,
% 0.21/0.43 (multiply(sk_c6, sk_c8) = multiply(sk_c7, sk_c8)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[81])).
% 0.21/0.43 tff(220,plain,
% 0.21/0.43 (multiply(sk_c6, sk_c8) = sk_c7),
% 0.21/0.43 inference(transitivity,[status(thm)],[219, 79, 78, 77, 71])).
% 0.21/0.43 tff(221,plain,
% 0.21/0.43 (multiply(sk_c2, multiply(sk_c6, sk_c8)) = multiply(sk_c2, sk_c7)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[220])).
% 0.21/0.43 tff(222,plain,
% 0.21/0.43 (multiply(sk_c2, sk_c7) = multiply(sk_c2, sk_c6)),
% 0.21/0.43 inference(symmetry,[status(thm)],[97])).
% 0.21/0.43 tff(223,plain,
% 0.21/0.43 (sk_c8 = multiply(sk_c2, sk_c7)),
% 0.21/0.43 inference(symmetry,[status(thm)],[44])).
% 0.21/0.43 tff(224,plain,
% 0.21/0.43 (sk_c8 = multiply(sk_c2, sk_c6)),
% 0.21/0.43 inference(transitivity,[status(thm)],[223, 222])).
% 0.21/0.43 tff(225,plain,
% 0.21/0.43 (multiply(sk_c8, sk_c8) = multiply(multiply(sk_c2, sk_c6), sk_c8)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[224])).
% 0.21/0.43 tff(226,plain,
% 0.21/0.43 (multiply(sk_c8, sk_c8) = sk_c8),
% 0.21/0.43 inference(transitivity,[status(thm)],[225, 122, 221, 44])).
% 0.21/0.43 tff(227,plain,
% 0.21/0.43 (multiply(multiply(sk_c8, sk_c8), multiply(sk_c2, sk_c8)) = multiply(sk_c8, multiply(sk_c2, sk_c8))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[226])).
% 0.21/0.43 tff(228,plain,
% 0.21/0.43 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = multiply(multiply(sk_c8, sk_c8), multiply(sk_c2, sk_c8))),
% 0.21/0.43 inference(symmetry,[status(thm)],[227])).
% 0.21/0.43 tff(229,plain,
% 0.21/0.43 (multiply(sk_c1, sk_c7) = sk_c8),
% 0.21/0.43 inference(transitivity,[status(thm)],[29, 80, 79, 78, 77, 71, 214, 228, 218, 216, 100, 96, 94, 44])).
% 0.21/0.43 tff(230,plain,
% 0.21/0.43 (inverse(sk_c2) = sk_c8),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[229, 76])).
% 0.21/0.43 tff(231,plain,
% 0.21/0.43 (multiply(sk_c8, multiply(sk_c8, multiply(sk_c2, sk_c8))) = multiply(multiply(sk_c8, sk_c8), multiply(sk_c2, sk_c8))),
% 0.21/0.43 inference(symmetry,[status(thm)],[218])).
% 0.21/0.43 tff(232,plain,
% 0.21/0.43 (sk_c8 = sk_c7),
% 0.21/0.43 inference(transitivity,[status(thm)],[223, 93, 171, 99, 215, 231, 227, 213])).
% 0.21/0.43 tff(233,plain,
% 0.21/0.43 (multiply(sk_c2, sk_c8) = multiply(sk_c2, sk_c7)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[232])).
% 0.21/0.43 tff(234,plain,
% 0.21/0.43 (multiply(sk_c2, sk_c8) = sk_c7),
% 0.21/0.43 inference(transitivity,[status(thm)],[233, 93, 171, 99, 215, 231, 227, 213])).
% 0.21/0.43 tff(235,plain,
% 0.21/0.43 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(sk_c6, sk_c6)),
% 0.21/0.43 inference(symmetry,[status(thm)],[147])).
% 0.21/0.43 tff(236,plain,
% 0.21/0.43 (multiply(multiply(sk_c7, sk_c2), sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.21/0.43 inference(symmetry,[status(thm)],[145])).
% 0.21/0.43 tff(237,plain,
% 0.21/0.43 (sk_c7 = multiply(sk_c6, sk_c6)),
% 0.21/0.43 inference(transitivity,[status(thm)],[72, 112, 236, 85, 235])).
% 0.21/0.43 tff(238,plain,
% 0.21/0.43 (multiply(sk_c2, sk_c7) = multiply(sk_c2, multiply(sk_c6, sk_c6))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[237])).
% 0.21/0.43 tff(239,plain,
% 0.21/0.43 (multiply(sk_c2, multiply(sk_c6, sk_c6)) = multiply(sk_c2, sk_c7)),
% 0.21/0.43 inference(symmetry,[status(thm)],[238])).
% 0.21/0.43 tff(240,plain,
% 0.21/0.43 (multiply(sk_c2, sk_c6) = sk_c8),
% 0.21/0.43 inference(transitivity,[status(thm)],[123, 105])).
% 0.21/0.43 tff(241,plain,
% 0.21/0.43 (multiply(multiply(sk_c2, sk_c6), sk_c6) = multiply(sk_c8, sk_c7)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[240, 117])).
% 0.21/0.43 tff(242,plain,
% 0.21/0.43 (multiply(sk_c8, sk_c7) = multiply(multiply(sk_c2, sk_c6), sk_c6)),
% 0.21/0.43 inference(symmetry,[status(thm)],[241])).
% 0.21/0.43 tff(243,plain,
% 0.21/0.43 (multiply(sk_c8, sk_c7) = sk_c8),
% 0.21/0.43 inference(transitivity,[status(thm)],[242, 96, 239, 105])).
% 0.21/0.43 tff(244,plain,
% 0.21/0.43 ((multiply(sk_c8, sk_c7) = sk_c6) <=> (sk_c8 = multiply(sk_c1, sk_c7))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[243, 103])).
% 0.21/0.43 tff(245,plain,
% 0.21/0.43 ((multiply(sk_c8, sk_c7) = sk_c6) <=> (multiply(sk_c1, sk_c7) = sk_c8)),
% 0.21/0.43 inference(transitivity,[status(thm)],[244, 101])).
% 0.21/0.43 tff(246,plain,
% 0.21/0.43 ((~(multiply(sk_c8, sk_c7) = sk_c6)) <=> (~(multiply(sk_c1, sk_c7) = sk_c8))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[245])).
% 0.21/0.43 tff(247,assumption,(~(multiply(sk_c8, sk_c7) = sk_c6)), introduced(assumption)).
% 0.21/0.43 tff(248,plain,
% 0.21/0.43 (~(multiply(sk_c1, sk_c7) = sk_c8)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.21/0.43 tff(249,plain,
% 0.21/0.43 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[212, 102, 104, 105, 107, 130])).
% 0.21/0.43 tff(250,plain,
% 0.21/0.43 (sk_c7 = multiply(sk_c8, multiply(sk_c2, sk_c8))),
% 0.21/0.43 inference(symmetry,[status(thm)],[249])).
% 0.21/0.43 tff(251,plain,
% 0.21/0.43 (multiply(sk_c8, sk_c7) = multiply(sk_c8, multiply(sk_c8, multiply(sk_c2, sk_c8)))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[250])).
% 0.21/0.43 tff(252,plain,
% 0.21/0.43 (multiply(sk_c8, multiply(sk_c8, multiply(sk_c2, sk_c8))) = multiply(sk_c8, sk_c7)),
% 0.21/0.43 inference(symmetry,[status(thm)],[251])).
% 0.21/0.43 tff(253,plain,
% 0.21/0.43 (multiply(sk_c8, sk_c8) = sk_c8),
% 0.21/0.43 inference(transitivity,[status(thm)],[127, 122, 120, 105])).
% 0.21/0.43 tff(254,plain,
% 0.21/0.43 (multiply(multiply(sk_c8, sk_c8), multiply(sk_c2, sk_c8)) = multiply(sk_c8, multiply(sk_c2, sk_c8))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[253])).
% 0.21/0.43 tff(255,plain,
% 0.21/0.43 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = multiply(multiply(sk_c8, sk_c8), multiply(sk_c2, sk_c8))),
% 0.21/0.43 inference(symmetry,[status(thm)],[254])).
% 0.21/0.43 tff(256,plain,
% 0.21/0.43 (multiply(sk_c1, sk_c7) = sk_c8),
% 0.21/0.43 inference(transitivity,[status(thm)],[102, 116, 115, 78, 114, 71, 250, 255, 218, 252, 242, 96, 239, 105])).
% 0.21/0.43 tff(257,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[256, 248])).
% 0.21/0.43 tff(258,plain,((multiply(sk_c8, sk_c7) = sk_c6) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c2, sk_c7) = sk_c8)) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(inverse(sk_c2) = sk_c7)) | (~(inverse(sk_c1) = sk_c7))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(259,plain,
% 0.21/0.44 (multiply(sk_c8, sk_c7) = sk_c6),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[258, 29, 44, 38, 20, 15])).
% 0.21/0.44 tff(260,plain,
% 0.21/0.44 (^[X4: $i, X3: $i, X5: $i, X1: $i] : refl(((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(261,plain,
% 0.21/0.44 (![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7))) <=> ![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[260])).
% 0.21/0.44 tff(262,plain,
% 0.21/0.44 (![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7))) <=> ![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(263,plain,
% 0.21/0.44 (^[X4: $i, X3: $i, X5: $i, X1: $i] : rewrite(((~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(264,plain,
% 0.21/0.44 (![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7))) <=> ![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[263])).
% 0.21/0.44 tff(265,plain,
% 0.21/0.44 (![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7))) <=> ![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))),
% 0.21/0.44 inference(elim_unused_vars,[status(thm)],[])).
% 0.21/0.44 tff(266,plain,
% 0.21/0.44 (![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) <=> ![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))),
% 0.21/0.44 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.21/0.44 tff(267,plain,
% 0.21/0.44 (![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) <=> ![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[266, 265])).
% 0.21/0.44 tff(268,plain,
% 0.21/0.44 (![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) <=> ![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[267, 264])).
% 0.21/0.44 tff(269,plain,
% 0.21/0.44 (^[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(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))), (((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c7) = sk_c8))) <=> (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(multiply(X4, sk_c7) = sk_c8))))), rewrite((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(multiply(X4, sk_c7) = sk_c8))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))), (((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c7) = sk_c8))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))))), ((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) <=> (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X4) = sk_c7))))), rewrite((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X4) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))), ((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))))), (((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, sk_c7) = sk_c6))) <=> (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(multiply(sk_c8, sk_c7) = sk_c6))))), rewrite((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(multiply(sk_c8, sk_c7) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))), (((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, sk_c7) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))))), ((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, sk_c7) = sk_c6))) | (~(multiply(X1, sk_c8) = sk_c7))) <=> (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(multiply(X1, sk_c8) = sk_c7))))), rewrite((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(multiply(X1, sk_c8) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))), ((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, sk_c7) = sk_c6))) | (~(multiply(X1, sk_c8) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))))), (((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, sk_c7) = sk_c6))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) <=> (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c8))))), rewrite((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X1) = sk_c8))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))), (((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, sk_c7) = sk_c6))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))))), ((((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, sk_c7) = sk_c6))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) <=> (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(multiply(sk_c8, X2) = sk_c7))))), rewrite((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(multiply(sk_c8, X2) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))), ((((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, sk_c7) = sk_c6))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))))), (((((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, sk_c7) = sk_c6))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X5, sk_c8) = X2))) <=> (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(multiply(X5, sk_c8) = X2))))), rewrite((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(multiply(X5, sk_c8) = X2))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(multiply(X5, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))), (((((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, sk_c7) = sk_c6))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X5, sk_c8) = X2))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(multiply(X5, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))))), ((((((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, sk_c7) = sk_c6))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X5, sk_c8) = X2))) | (~(inverse(X5) = sk_c8))) <=> (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(multiply(X5, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X5) = sk_c8))))), rewrite((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(multiply(X5, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X5) = sk_c8))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))), ((((((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, sk_c7) = sk_c6))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X5, sk_c8) = X2))) | (~(inverse(X5) = sk_c8))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(270,plain,
% 0.21/0.46 (![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : (((((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, sk_c7) = sk_c6))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X5, sk_c8) = X2))) | (~(inverse(X5) = sk_c8))) <=> ![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[269])).
% 0.21/0.46 tff(271,plain,
% 0.21/0.46 (![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : (((((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, sk_c7) = sk_c6))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X5, sk_c8) = X2))) | (~(inverse(X5) = sk_c8))) <=> ![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[270, 268])).
% 0.21/0.46 tff(272,axiom,(![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : (((((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c6))) | (~(inverse(X3) = sk_c7))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(inverse(X4) = sk_c7))) | (~(multiply(sk_c8, sk_c7) = sk_c6))) | (~(multiply(X1, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X5, sk_c8) = X2))) | (~(inverse(X5) = sk_c8)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_31')).
% 0.21/0.46 tff(273,plain,
% 0.21/0.46 (![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.21/0.46 tff(274,plain,
% 0.21/0.46 (![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[273, 262])).
% 0.21/0.46 tff(275,plain,(
% 0.21/0.46 ![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[274])).
% 0.21/0.46 tff(276,plain,
% 0.21/0.46 (![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[275, 261])).
% 0.21/0.46 tff(277,plain,
% 0.21/0.46 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c2, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c2, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(278,plain,
% 0.21/0.46 (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c2, sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c2, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(279,plain,
% 0.21/0.46 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c2, sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c2, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[278])).
% 0.21/0.46 tff(280,plain,
% 0.21/0.46 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c2, sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c2, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[279, 277])).
% 0.21/0.46 tff(281,plain,
% 0.21/0.46 ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c2) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c2, sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(282,plain,
% 0.21/0.46 ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c2, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.21/0.46 tff(283,plain,
% 0.21/0.46 ((~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c2, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[282, 38, 29, 15, 276])).
% 0.21/0.46 tff(284,plain,
% 0.21/0.46 (~(inverse(sk_c2) = sk_c8)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[283, 259, 229, 234, 213])).
% 0.21/0.46 tff(285,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[284, 230])).
% 0.21/0.46 tff(286,plain,(inverse(sk_c3) = sk_c8), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(287,plain,
% 0.21/0.46 (sk_c8 = inverse(sk_c3)),
% 0.21/0.46 inference(symmetry,[status(thm)],[286])).
% 0.21/0.46 tff(288,assumption,(~(inverse(sk_c2) = sk_c7)), introduced(assumption)).
% 0.21/0.46 tff(289,plain,
% 0.21/0.46 (((inverse(sk_c2) = sk_c7) | (multiply(sk_c8, sk_c7) = sk_c6)) <=> ((inverse(sk_c2) = sk_c7) | (multiply(sk_c8, sk_c7) = sk_c6))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(290,axiom,((inverse(sk_c2) = sk_c7) | (multiply(sk_c8, sk_c7) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_25')).
% 0.21/0.46 tff(291,plain,
% 0.21/0.46 ((inverse(sk_c2) = sk_c7) | (multiply(sk_c8, sk_c7) = sk_c6)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.21/0.46 tff(292,plain,
% 0.21/0.46 (multiply(sk_c8, sk_c7) = sk_c6),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[291, 288])).
% 0.21/0.46 tff(293,plain,
% 0.21/0.47 (((inverse(sk_c2) = sk_c7) | (multiply(sk_c3, sk_c8) = sk_c7)) <=> ((inverse(sk_c2) = sk_c7) | (multiply(sk_c3, sk_c8) = sk_c7))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(294,axiom,((inverse(sk_c2) = sk_c7) | (multiply(sk_c3, sk_c8) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_26')).
% 0.21/0.47 tff(295,plain,
% 0.21/0.47 ((inverse(sk_c2) = sk_c7) | (multiply(sk_c3, sk_c8) = sk_c7)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[294, 293])).
% 0.21/0.47 tff(296,plain,
% 0.21/0.47 (multiply(sk_c3, sk_c8) = sk_c7),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[295, 288])).
% 0.21/0.47 tff(297,plain,
% 0.21/0.47 (multiply(sk_c8, multiply(sk_c3, sk_c8)) = multiply(sk_c8, sk_c7)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[296])).
% 0.21/0.47 tff(298,plain,
% 0.21/0.47 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c3), sk_c8) = multiply(sk_c8, multiply(sk_c3, sk_c8)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(299,plain,
% 0.21/0.47 (multiply(multiply(sk_c8, sk_c3), sk_c8) = multiply(sk_c8, multiply(sk_c3, sk_c8))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[298, 52])).
% 0.21/0.47 tff(300,plain,
% 0.21/0.47 (multiply(sk_c8, sk_c3) = multiply(inverse(sk_c3), sk_c3)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[287])).
% 0.21/0.47 tff(301,plain,
% 0.21/0.47 (multiply(inverse(sk_c3), sk_c3) = multiply(sk_c8, sk_c3)),
% 0.21/0.47 inference(symmetry,[status(thm)],[300])).
% 0.21/0.47 tff(302,plain,
% 0.21/0.47 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c3), sk_c3) = identity)),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(303,plain,
% 0.21/0.47 (multiply(inverse(sk_c3), sk_c3) = identity),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[302, 64])).
% 0.21/0.47 tff(304,plain,
% 0.21/0.47 (identity = multiply(inverse(sk_c3), sk_c3)),
% 0.21/0.47 inference(symmetry,[status(thm)],[303])).
% 0.21/0.47 tff(305,plain,
% 0.21/0.47 (identity = multiply(sk_c8, sk_c3)),
% 0.21/0.47 inference(transitivity,[status(thm)],[304, 301])).
% 0.21/0.47 tff(306,plain,
% 0.21/0.47 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c3), sk_c8)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[305])).
% 0.21/0.47 tff(307,plain,
% 0.21/0.47 (sk_c8 = sk_c6),
% 0.21/0.47 inference(transitivity,[status(thm)],[205, 306, 299, 297, 292])).
% 0.21/0.47 tff(308,plain,
% 0.21/0.47 ((multiply(sk_c3, sk_c7) = sk_c8) <=> (multiply(sk_c3, sk_c7) = sk_c6)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[307])).
% 0.21/0.47 tff(309,plain,
% 0.21/0.47 ((multiply(sk_c3, sk_c7) = sk_c6) <=> (multiply(sk_c3, sk_c7) = sk_c8)),
% 0.21/0.47 inference(symmetry,[status(thm)],[308])).
% 0.21/0.47 tff(310,plain,
% 0.21/0.47 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c4), sk_c4) = identity)),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(311,plain,
% 0.21/0.47 (multiply(inverse(sk_c4), sk_c4) = identity),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[310, 64])).
% 0.21/0.47 tff(312,plain,
% 0.21/0.47 (((inverse(sk_c2) = sk_c7) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c2) = sk_c7) | (inverse(sk_c4) = sk_c8))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(313,axiom,((inverse(sk_c2) = sk_c7) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_30')).
% 0.21/0.47 tff(314,plain,
% 0.21/0.47 ((inverse(sk_c2) = sk_c7) | (inverse(sk_c4) = sk_c8)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.21/0.47 tff(315,plain,
% 0.21/0.47 (inverse(sk_c4) = sk_c8),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[314, 288])).
% 0.21/0.47 tff(316,plain,
% 0.21/0.47 (sk_c8 = inverse(sk_c4)),
% 0.21/0.47 inference(symmetry,[status(thm)],[315])).
% 0.21/0.47 tff(317,plain,
% 0.21/0.47 (multiply(sk_c8, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[316])).
% 0.21/0.47 tff(318,plain,
% 0.21/0.47 (multiply(sk_c8, sk_c4) = multiply(sk_c8, sk_c3)),
% 0.21/0.47 inference(transitivity,[status(thm)],[317, 311, 304, 301])).
% 0.21/0.47 tff(319,plain,
% 0.21/0.47 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(multiply(sk_c8, sk_c3), sk_c8)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[318])).
% 0.21/0.47 tff(320,plain,
% 0.21/0.47 ((~![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)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(321,plain,
% 0.21/0.47 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[320, 52])).
% 0.21/0.47 tff(322,plain,
% 0.21/0.47 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.21/0.47 inference(symmetry,[status(thm)],[321])).
% 0.21/0.47 tff(323,plain,
% 0.21/0.47 (((inverse(sk_c2) = sk_c7) | (multiply(sk_c4, sk_c8) = sk_c5)) <=> ((inverse(sk_c2) = sk_c7) | (multiply(sk_c4, sk_c8) = sk_c5))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(324,axiom,((inverse(sk_c2) = sk_c7) | (multiply(sk_c4, sk_c8) = sk_c5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_29')).
% 0.21/0.47 tff(325,plain,
% 0.21/0.47 ((inverse(sk_c2) = sk_c7) | (multiply(sk_c4, sk_c8) = sk_c5)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[324, 323])).
% 0.21/0.47 tff(326,plain,
% 0.21/0.47 (multiply(sk_c4, sk_c8) = sk_c5),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[325, 288])).
% 0.21/0.47 tff(327,plain,
% 0.21/0.47 (sk_c5 = multiply(sk_c4, sk_c8)),
% 0.21/0.47 inference(symmetry,[status(thm)],[326])).
% 0.21/0.47 tff(328,plain,
% 0.21/0.47 (multiply(sk_c8, sk_c5) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[327])).
% 0.21/0.47 tff(329,plain,
% 0.21/0.47 (((inverse(sk_c2) = sk_c7) | (multiply(sk_c8, sk_c5) = sk_c7)) <=> ((inverse(sk_c2) = sk_c7) | (multiply(sk_c8, sk_c5) = sk_c7))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(330,axiom,((inverse(sk_c2) = sk_c7) | (multiply(sk_c8, sk_c5) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_28')).
% 0.21/0.47 tff(331,plain,
% 0.21/0.47 ((inverse(sk_c2) = sk_c7) | (multiply(sk_c8, sk_c5) = sk_c7)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[330, 329])).
% 0.21/0.47 tff(332,plain,
% 0.21/0.47 (multiply(sk_c8, sk_c5) = sk_c7),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[331, 288])).
% 0.21/0.47 tff(333,plain,
% 0.21/0.47 (sk_c7 = multiply(sk_c8, sk_c5)),
% 0.21/0.47 inference(symmetry,[status(thm)],[332])).
% 0.21/0.47 tff(334,plain,
% 0.21/0.47 (multiply(multiply(sk_c8, sk_c3), sk_c8) = multiply(identity, sk_c8)),
% 0.21/0.47 inference(symmetry,[status(thm)],[306])).
% 0.21/0.47 tff(335,plain,
% 0.21/0.47 (sk_c7 = sk_c8),
% 0.21/0.47 inference(transitivity,[status(thm)],[333, 328, 322, 319, 334, 9])).
% 0.21/0.47 tff(336,plain,
% 0.21/0.47 (multiply(sk_c3, sk_c7) = multiply(sk_c3, sk_c8)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[335])).
% 0.21/0.47 tff(337,plain,
% 0.21/0.47 (multiply(sk_c3, sk_c7) = sk_c6),
% 0.21/0.47 inference(transitivity,[status(thm)],[336, 296, 333, 328, 322, 319, 299, 297, 292])).
% 0.21/0.47 tff(338,plain,
% 0.21/0.47 (multiply(sk_c3, sk_c7) = sk_c8),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[337, 309])).
% 0.21/0.47 tff(339,plain,
% 0.21/0.47 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = multiply(sk_c8, sk_c5)),
% 0.21/0.47 inference(symmetry,[status(thm)],[328])).
% 0.21/0.47 tff(340,plain,
% 0.21/0.47 (multiply(multiply(sk_c8, sk_c3), sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.21/0.47 inference(symmetry,[status(thm)],[319])).
% 0.21/0.47 tff(341,plain,
% 0.21/0.47 (multiply(sk_c8, multiply(sk_c3, sk_c8)) = multiply(multiply(sk_c8, sk_c3), sk_c8)),
% 0.21/0.47 inference(symmetry,[status(thm)],[299])).
% 0.21/0.47 tff(342,plain,
% 0.21/0.47 (multiply(sk_c8, multiply(sk_c3, sk_c8)) = sk_c7),
% 0.21/0.47 inference(transitivity,[status(thm)],[341, 340, 321, 339, 332])).
% 0.21/0.47 tff(343,plain,
% 0.21/0.47 (inverse(sk_c3) = sk_c7),
% 0.21/0.47 inference(transitivity,[status(thm)],[286, 205, 306, 340, 321, 339, 332])).
% 0.21/0.47 tff(344,plain,
% 0.21/0.47 (sk_c8 = sk_c7),
% 0.21/0.47 inference(transitivity,[status(thm)],[205, 306, 340, 321, 339, 332])).
% 0.21/0.47 tff(345,plain,
% 0.21/0.47 (multiply(sk_c7, sk_c8) = multiply(sk_c8, sk_c7)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[335, 344])).
% 0.21/0.47 tff(346,plain,
% 0.21/0.47 (multiply(sk_c7, sk_c8) = sk_c6),
% 0.21/0.47 inference(transitivity,[status(thm)],[345, 292])).
% 0.21/0.47 tff(347,plain,
% 0.21/0.47 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c3, sk_c8)) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c8)) | (~(inverse(sk_c3) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c3, sk_c8)) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c8)) | (~(inverse(sk_c3) = sk_c8)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(348,plain,
% 0.21/0.47 (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c3) = sk_c8)) | (~(inverse(sk_c3) = sk_c8)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c3, sk_c8)) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(multiply(sk_c3, sk_c7) = sk_c8)) | (~(inverse(sk_c3) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c3, sk_c8)) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c8)) | (~(inverse(sk_c3) = sk_c8)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(349,plain,
% 0.21/0.47 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c3) = sk_c8)) | (~(inverse(sk_c3) = sk_c8)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c3, sk_c8)) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(multiply(sk_c3, sk_c7) = sk_c8)) | (~(inverse(sk_c3) = sk_c7)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c3, sk_c8)) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c8)) | (~(inverse(sk_c3) = sk_c8))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[348])).
% 0.21/0.47 tff(350,plain,
% 0.21/0.47 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c3) = sk_c8)) | (~(inverse(sk_c3) = sk_c8)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c3, sk_c8)) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(multiply(sk_c3, sk_c7) = sk_c8)) | (~(inverse(sk_c3) = sk_c7)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c3, sk_c8)) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c8)) | (~(inverse(sk_c3) = sk_c8)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[349, 347])).
% 0.21/0.47 tff(351,plain,
% 0.21/0.47 ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c3) = sk_c8)) | (~(inverse(sk_c3) = sk_c8)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c3, sk_c8)) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(multiply(sk_c3, sk_c7) = sk_c8)) | (~(inverse(sk_c3) = sk_c7)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(352,plain,
% 0.21/0.47 ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c3, sk_c8)) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c8)) | (~(inverse(sk_c3) = sk_c8))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[351, 350])).
% 0.21/0.47 tff(353,plain,
% 0.21/0.47 ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c3, sk_c8)) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c8))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[352, 286, 276])).
% 0.21/0.47 tff(354,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[353, 346, 343, 296, 292, 337, 342, 338])).
% 0.21/0.47 tff(355,plain,(inverse(sk_c2) = sk_c7), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(356,plain,
% 0.21/0.47 (sk_c7 = inverse(sk_c2)),
% 0.21/0.47 inference(symmetry,[status(thm)],[355])).
% 0.21/0.47 tff(357,plain,
% 0.21/0.47 (multiply(sk_c7, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[356])).
% 0.21/0.47 tff(358,plain,
% 0.21/0.47 (multiply(inverse(sk_c2), sk_c2) = multiply(sk_c7, sk_c2)),
% 0.21/0.47 inference(symmetry,[status(thm)],[357])).
% 0.21/0.47 tff(359,plain,
% 0.21/0.47 (identity = multiply(sk_c7, sk_c2)),
% 0.21/0.47 inference(transitivity,[status(thm)],[67, 358])).
% 0.21/0.47 tff(360,plain,
% 0.21/0.47 (multiply(identity, sk_c7) = multiply(multiply(sk_c7, sk_c2), sk_c7)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[359])).
% 0.21/0.47 tff(361,plain,
% 0.21/0.47 (multiply(multiply(sk_c7, sk_c2), sk_c7) = multiply(identity, sk_c7)),
% 0.21/0.47 inference(symmetry,[status(thm)],[360])).
% 0.21/0.47 tff(362,assumption,(~(multiply(sk_c7, sk_c8) = sk_c6)), introduced(assumption)).
% 0.21/0.47 tff(363,plain,
% 0.21/0.47 (((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c8, sk_c7) = sk_c6)) <=> ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c8, sk_c7) = sk_c6))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(364,axiom,((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c8, sk_c7) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_1')).
% 0.21/0.47 tff(365,plain,
% 0.21/0.47 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c8, sk_c7) = sk_c6)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[364, 363])).
% 0.21/0.47 tff(366,plain,
% 0.21/0.47 (multiply(sk_c8, sk_c7) = sk_c6),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[365, 362])).
% 0.21/0.47 tff(367,plain,
% 0.21/0.47 (((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c8, sk_c5) = sk_c7)) <=> ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c8, sk_c5) = sk_c7))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(368,axiom,((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c8, sk_c5) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_4')).
% 0.21/0.47 tff(369,plain,
% 0.21/0.47 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c8, sk_c5) = sk_c7)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[368, 367])).
% 0.21/0.47 tff(370,plain,
% 0.21/0.47 (multiply(sk_c8, sk_c5) = sk_c7),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[369, 362])).
% 0.21/0.47 tff(371,plain,
% 0.21/0.47 (((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c5)) <=> ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c5))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(372,axiom,((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_5')).
% 0.21/0.47 tff(373,plain,
% 0.21/0.47 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c5)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[372, 371])).
% 0.21/0.47 tff(374,plain,
% 0.21/0.47 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c5)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[373, 371])).
% 0.21/0.47 tff(375,plain,
% 0.21/0.47 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c5)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[374, 371])).
% 0.21/0.47 tff(376,plain,
% 0.21/0.47 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c5)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[375, 371])).
% 0.21/0.47 tff(377,plain,
% 0.21/0.47 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c5)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[376, 371])).
% 0.21/0.47 tff(378,plain,
% 0.21/0.47 (multiply(sk_c4, sk_c8) = sk_c5),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[377, 362])).
% 0.21/0.47 tff(379,plain,
% 0.21/0.47 (sk_c5 = multiply(sk_c4, sk_c8)),
% 0.21/0.47 inference(symmetry,[status(thm)],[378])).
% 0.21/0.47 tff(380,plain,
% 0.21/0.47 (multiply(sk_c8, sk_c5) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[379])).
% 0.21/0.47 tff(381,plain,
% 0.21/0.47 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = multiply(sk_c8, sk_c5)),
% 0.21/0.47 inference(symmetry,[status(thm)],[380])).
% 0.21/0.47 tff(382,plain,
% 0.21/0.47 (((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8)) <=> ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(383,axiom,((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_6')).
% 0.21/0.47 tff(384,plain,
% 0.21/0.47 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[383, 382])).
% 0.21/0.47 tff(385,plain,
% 0.21/0.47 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[384, 382])).
% 0.21/0.47 tff(386,plain,
% 0.21/0.47 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[385, 382])).
% 0.21/0.47 tff(387,plain,
% 0.21/0.47 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[386, 382])).
% 0.21/0.47 tff(388,plain,
% 0.21/0.47 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[387, 382])).
% 0.21/0.47 tff(389,plain,
% 0.21/0.47 (inverse(sk_c4) = sk_c8),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[388, 362])).
% 0.21/0.47 tff(390,plain,
% 0.21/0.47 (sk_c8 = inverse(sk_c4)),
% 0.21/0.47 inference(symmetry,[status(thm)],[389])).
% 0.21/0.47 tff(391,plain,
% 0.21/0.47 (multiply(sk_c8, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[390])).
% 0.21/0.47 tff(392,plain,
% 0.21/0.47 (multiply(sk_c8, sk_c4) = multiply(sk_c8, sk_c3)),
% 0.21/0.47 inference(transitivity,[status(thm)],[391, 311, 304, 301])).
% 0.21/0.47 tff(393,plain,
% 0.21/0.47 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(multiply(sk_c8, sk_c3), sk_c8)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[392])).
% 0.21/0.47 tff(394,plain,
% 0.21/0.47 (multiply(multiply(sk_c8, sk_c3), sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.21/0.47 inference(symmetry,[status(thm)],[393])).
% 0.21/0.47 tff(395,plain,
% 0.21/0.47 (sk_c8 = sk_c7),
% 0.21/0.47 inference(transitivity,[status(thm)],[205, 306, 394, 321, 381, 370])).
% 0.21/0.47 tff(396,plain,
% 0.21/0.47 (sk_c7 = multiply(sk_c8, sk_c5)),
% 0.21/0.47 inference(symmetry,[status(thm)],[370])).
% 0.21/0.47 tff(397,plain,
% 0.21/0.47 (sk_c7 = sk_c8),
% 0.21/0.48 inference(transitivity,[status(thm)],[396, 380, 322, 393, 334, 9])).
% 0.21/0.48 tff(398,plain,
% 0.21/0.48 (multiply(sk_c7, sk_c8) = multiply(sk_c8, sk_c7)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[397, 395])).
% 0.21/0.48 tff(399,plain,
% 0.21/0.48 (multiply(sk_c7, sk_c8) = sk_c6),
% 0.21/0.48 inference(transitivity,[status(thm)],[398, 366])).
% 0.21/0.48 tff(400,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[362, 399])).
% 0.21/0.48 tff(401,plain,(multiply(sk_c7, sk_c8) = sk_c6), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(402,plain,
% 0.21/0.48 (sk_c6 = multiply(sk_c7, sk_c8)),
% 0.21/0.48 inference(symmetry,[status(thm)],[401])).
% 0.21/0.48 tff(403,plain,
% 0.21/0.48 (((inverse(sk_c1) = sk_c7) | (multiply(sk_c8, sk_c7) = sk_c6)) <=> ((inverse(sk_c1) = sk_c7) | (multiply(sk_c8, sk_c7) = sk_c6))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(404,axiom,((inverse(sk_c1) = sk_c7) | (multiply(sk_c8, sk_c7) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_13')).
% 0.21/0.48 tff(405,plain,
% 0.21/0.48 ((inverse(sk_c1) = sk_c7) | (multiply(sk_c8, sk_c7) = sk_c6)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[404, 403])).
% 0.21/0.48 tff(406,plain,
% 0.21/0.48 (inverse(sk_c1) = sk_c7),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[405, 247])).
% 0.21/0.48 tff(407,plain,
% 0.21/0.48 (((multiply(sk_c2, sk_c7) = sk_c8) | (multiply(sk_c8, sk_c7) = sk_c6)) <=> ((multiply(sk_c2, sk_c7) = sk_c8) | (multiply(sk_c8, sk_c7) = sk_c6))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(408,axiom,((multiply(sk_c2, sk_c7) = sk_c8) | (multiply(sk_c8, sk_c7) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_19')).
% 0.21/0.48 tff(409,plain,
% 0.21/0.48 ((multiply(sk_c2, sk_c7) = sk_c8) | (multiply(sk_c8, sk_c7) = sk_c6)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[408, 407])).
% 0.21/0.48 tff(410,plain,
% 0.21/0.48 (multiply(sk_c2, sk_c7) = sk_c8),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[409, 247])).
% 0.21/0.48 tff(411,plain,
% 0.21/0.48 (((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c8, sk_c7) = sk_c6)) <=> ((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c8, sk_c7) = sk_c6))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(412,axiom,((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c8, sk_c7) = sk_c6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_7')).
% 0.21/0.48 tff(413,plain,
% 0.21/0.48 ((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c8, sk_c7) = sk_c6)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[412, 411])).
% 0.21/0.48 tff(414,plain,
% 0.21/0.48 (multiply(sk_c1, sk_c7) = sk_c6),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[413, 247])).
% 0.21/0.48 tff(415,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[258, 414, 247, 410, 401, 355, 406])).
% 0.21/0.48 tff(416,plain,(multiply(sk_c8, sk_c7) = sk_c6), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(417,assumption,(~(multiply(sk_c1, sk_c7) = sk_c6)), introduced(assumption)).
% 0.21/0.48 tff(418,plain,
% 0.21/0.48 (((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c3, sk_c8) = sk_c7)) <=> ((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c3, sk_c8) = sk_c7))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(419,axiom,((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c3, sk_c8) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_8')).
% 0.21/0.48 tff(420,plain,
% 0.21/0.48 ((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c3, sk_c8) = sk_c7)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[419, 418])).
% 0.21/0.48 tff(421,plain,
% 0.21/0.48 (multiply(sk_c3, sk_c8) = sk_c7),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[420, 417])).
% 0.21/0.48 tff(422,plain,
% 0.21/0.48 (multiply(sk_c8, multiply(sk_c3, sk_c8)) = multiply(sk_c8, sk_c7)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[421])).
% 0.21/0.48 tff(423,plain,
% 0.21/0.48 (((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c6)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c6))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(424,plain,
% 0.21/0.48 (((multiply(sk_c1, sk_c7) = sk_c6) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c6))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(425,axiom,((multiply(sk_c1, sk_c7) = sk_c6) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_12')).
% 0.21/0.48 tff(426,plain,
% 0.21/0.48 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c6)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[425, 424])).
% 0.21/0.48 tff(427,plain,
% 0.21/0.48 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c6)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[426, 423])).
% 0.21/0.48 tff(428,plain,
% 0.21/0.48 (inverse(sk_c4) = sk_c8),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[427, 417])).
% 0.21/0.48 tff(429,plain,
% 0.21/0.48 (sk_c8 = inverse(sk_c4)),
% 0.21/0.48 inference(symmetry,[status(thm)],[428])).
% 0.21/0.48 tff(430,plain,
% 0.21/0.48 (multiply(sk_c8, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[429])).
% 0.21/0.48 tff(431,plain,
% 0.21/0.48 (multiply(sk_c8, sk_c4) = multiply(sk_c8, sk_c3)),
% 0.21/0.48 inference(transitivity,[status(thm)],[430, 311, 304, 301])).
% 0.21/0.48 tff(432,plain,
% 0.21/0.48 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(multiply(sk_c8, sk_c3), sk_c8)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[431])).
% 0.21/0.48 tff(433,plain,
% 0.21/0.48 (multiply(inverse(sk_c4), sk_c4) = multiply(sk_c8, sk_c4)),
% 0.21/0.48 inference(symmetry,[status(thm)],[430])).
% 0.21/0.48 tff(434,plain,
% 0.21/0.48 (identity = multiply(inverse(sk_c4), sk_c4)),
% 0.21/0.48 inference(symmetry,[status(thm)],[311])).
% 0.21/0.48 tff(435,plain,
% 0.21/0.48 (identity = multiply(sk_c8, sk_c4)),
% 0.21/0.48 inference(transitivity,[status(thm)],[434, 433])).
% 0.21/0.48 tff(436,plain,
% 0.21/0.48 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[435])).
% 0.21/0.48 tff(437,plain,
% 0.21/0.48 (sk_c8 = sk_c6),
% 0.21/0.48 inference(transitivity,[status(thm)],[205, 436, 432, 299, 422, 416])).
% 0.21/0.48 tff(438,plain,
% 0.21/0.48 ((multiply(sk_c3, sk_c7) = sk_c8) <=> (multiply(sk_c3, sk_c7) = sk_c6)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[437])).
% 0.21/0.48 tff(439,plain,
% 0.21/0.48 ((multiply(sk_c3, sk_c7) = sk_c6) <=> (multiply(sk_c3, sk_c7) = sk_c8)),
% 0.21/0.48 inference(symmetry,[status(thm)],[438])).
% 0.21/0.48 tff(440,plain,
% 0.21/0.48 (((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c5)) <=> ((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c5))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(441,axiom,((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_11')).
% 0.21/0.48 tff(442,plain,
% 0.21/0.48 ((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c5)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[441, 440])).
% 0.21/0.48 tff(443,plain,
% 0.21/0.48 (multiply(sk_c4, sk_c8) = sk_c5),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[442, 417])).
% 0.21/0.48 tff(444,plain,
% 0.21/0.48 (sk_c5 = multiply(sk_c4, sk_c8)),
% 0.21/0.48 inference(symmetry,[status(thm)],[443])).
% 0.21/0.48 tff(445,plain,
% 0.21/0.48 (multiply(sk_c8, sk_c5) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[444])).
% 0.21/0.48 tff(446,plain,
% 0.21/0.48 (((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c8, sk_c5) = sk_c7)) <=> ((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c8, sk_c5) = sk_c7))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(447,axiom,((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c8, sk_c5) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_10')).
% 0.21/0.48 tff(448,plain,
% 0.21/0.48 ((multiply(sk_c1, sk_c7) = sk_c6) | (multiply(sk_c8, sk_c5) = sk_c7)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[447, 446])).
% 0.21/0.48 tff(449,plain,
% 0.21/0.48 (multiply(sk_c8, sk_c5) = sk_c7),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[448, 417])).
% 0.21/0.48 tff(450,plain,
% 0.21/0.48 (sk_c7 = multiply(sk_c8, sk_c5)),
% 0.21/0.48 inference(symmetry,[status(thm)],[449])).
% 0.21/0.48 tff(451,plain,
% 0.21/0.48 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(identity, sk_c8)),
% 0.21/0.48 inference(symmetry,[status(thm)],[436])).
% 0.21/0.48 tff(452,plain,
% 0.21/0.48 (sk_c7 = sk_c8),
% 0.21/0.48 inference(transitivity,[status(thm)],[450, 445, 322, 451, 9])).
% 0.21/0.48 tff(453,plain,
% 0.21/0.48 (multiply(sk_c3, sk_c7) = multiply(sk_c3, sk_c8)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[452])).
% 0.21/0.48 tff(454,plain,
% 0.21/0.48 (multiply(sk_c3, sk_c7) = sk_c6),
% 0.21/0.48 inference(transitivity,[status(thm)],[453, 421, 450, 445, 322, 432, 299, 422, 416])).
% 0.21/0.48 tff(455,plain,
% 0.21/0.48 (multiply(sk_c3, sk_c7) = sk_c8),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[454, 439])).
% 0.21/0.48 tff(456,plain,
% 0.21/0.48 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = multiply(sk_c8, sk_c5)),
% 0.21/0.48 inference(symmetry,[status(thm)],[445])).
% 0.21/0.48 tff(457,plain,
% 0.21/0.48 (multiply(multiply(sk_c8, sk_c3), sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.21/0.48 inference(symmetry,[status(thm)],[432])).
% 0.21/0.48 tff(458,plain,
% 0.21/0.48 (multiply(sk_c8, multiply(sk_c3, sk_c8)) = sk_c7),
% 0.21/0.48 inference(transitivity,[status(thm)],[341, 457, 321, 456, 449])).
% 0.21/0.48 tff(459,plain,
% 0.21/0.48 (inverse(sk_c3) = sk_c7),
% 0.21/0.48 inference(transitivity,[status(thm)],[286, 205, 436, 321, 456, 449])).
% 0.21/0.48 tff(460,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[353, 454, 459, 401, 416, 421, 458, 455])).
% 0.21/0.48 tff(461,plain,(multiply(sk_c1, sk_c7) = sk_c6), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(462,plain,
% 0.21/0.48 (multiply(sk_c1, sk_c7) = sk_c7),
% 0.21/0.48 inference(transitivity,[status(thm)],[461, 402, 115, 78, 361, 71])).
% 0.21/0.48 tff(463,plain,
% 0.21/0.48 ((multiply(sk_c1, sk_c7) = sk_c8) <=> (sk_c7 = inverse(sk_c3))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[462, 287])).
% 0.21/0.48 tff(464,plain,
% 0.21/0.48 ((multiply(sk_c1, sk_c7) = sk_c8) <=> (inverse(sk_c3) = sk_c7)),
% 0.21/0.48 inference(transitivity,[status(thm)],[463, 10])).
% 0.21/0.48 tff(465,plain,
% 0.21/0.48 ((inverse(sk_c3) = sk_c7) <=> (multiply(sk_c1, sk_c7) = sk_c8)),
% 0.21/0.48 inference(symmetry,[status(thm)],[464])).
% 0.21/0.48 tff(466,assumption,(~(inverse(sk_c1) = sk_c7)), introduced(assumption)).
% 0.21/0.48 tff(467,plain,
% 0.21/0.48 (((inverse(sk_c1) = sk_c7) | (multiply(sk_c3, sk_c8) = sk_c7)) <=> ((inverse(sk_c1) = sk_c7) | (multiply(sk_c3, sk_c8) = sk_c7))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(468,axiom,((inverse(sk_c1) = sk_c7) | (multiply(sk_c3, sk_c8) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_14')).
% 0.21/0.48 tff(469,plain,
% 0.21/0.48 ((inverse(sk_c1) = sk_c7) | (multiply(sk_c3, sk_c8) = sk_c7)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[468, 467])).
% 0.21/0.48 tff(470,plain,
% 0.21/0.48 (multiply(sk_c3, sk_c8) = sk_c7),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[469, 466])).
% 0.21/0.48 tff(471,plain,
% 0.21/0.48 (multiply(sk_c8, multiply(sk_c3, sk_c8)) = multiply(sk_c8, sk_c7)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[470])).
% 0.21/0.48 tff(472,plain,
% 0.21/0.48 (((inverse(sk_c1) = sk_c7) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c1) = sk_c7) | (inverse(sk_c4) = sk_c8))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(473,axiom,((inverse(sk_c1) = sk_c7) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_18')).
% 0.21/0.48 tff(474,plain,
% 0.21/0.48 ((inverse(sk_c1) = sk_c7) | (inverse(sk_c4) = sk_c8)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[473, 472])).
% 0.21/0.48 tff(475,plain,
% 0.21/0.48 (inverse(sk_c4) = sk_c8),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[474, 466])).
% 0.21/0.48 tff(476,plain,
% 0.21/0.48 (sk_c8 = inverse(sk_c4)),
% 0.21/0.48 inference(symmetry,[status(thm)],[475])).
% 0.21/0.48 tff(477,plain,
% 0.21/0.48 (multiply(sk_c8, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[476])).
% 0.21/0.48 tff(478,plain,
% 0.21/0.48 (multiply(sk_c8, sk_c4) = multiply(sk_c8, sk_c3)),
% 0.21/0.48 inference(transitivity,[status(thm)],[477, 311, 304, 301])).
% 0.21/0.48 tff(479,plain,
% 0.21/0.48 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(multiply(sk_c8, sk_c3), sk_c8)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[478])).
% 0.21/0.48 tff(480,plain,
% 0.21/0.48 (multiply(inverse(sk_c4), sk_c4) = multiply(sk_c8, sk_c4)),
% 0.21/0.48 inference(symmetry,[status(thm)],[477])).
% 0.21/0.48 tff(481,plain,
% 0.21/0.48 (identity = multiply(sk_c8, sk_c4)),
% 0.21/0.48 inference(transitivity,[status(thm)],[434, 480])).
% 0.21/0.48 tff(482,plain,
% 0.21/0.48 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[481])).
% 0.21/0.48 tff(483,plain,
% 0.21/0.48 (sk_c8 = sk_c6),
% 0.21/0.48 inference(transitivity,[status(thm)],[205, 482, 479, 299, 471, 416])).
% 0.21/0.48 tff(484,plain,
% 0.21/0.48 ((multiply(sk_c3, sk_c7) = sk_c8) <=> (multiply(sk_c3, sk_c7) = sk_c6)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[483])).
% 0.21/0.48 tff(485,plain,
% 0.21/0.48 ((multiply(sk_c3, sk_c7) = sk_c6) <=> (multiply(sk_c3, sk_c7) = sk_c8)),
% 0.21/0.48 inference(symmetry,[status(thm)],[484])).
% 0.21/0.48 tff(486,plain,
% 0.21/0.48 (((inverse(sk_c1) = sk_c7) | (multiply(sk_c4, sk_c8) = sk_c5)) <=> ((inverse(sk_c1) = sk_c7) | (multiply(sk_c4, sk_c8) = sk_c5))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(487,axiom,((inverse(sk_c1) = sk_c7) | (multiply(sk_c4, sk_c8) = sk_c5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_17')).
% 0.21/0.48 tff(488,plain,
% 0.21/0.48 ((inverse(sk_c1) = sk_c7) | (multiply(sk_c4, sk_c8) = sk_c5)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[487, 486])).
% 0.21/0.48 tff(489,plain,
% 0.21/0.48 (multiply(sk_c4, sk_c8) = sk_c5),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[488, 466])).
% 0.21/0.48 tff(490,plain,
% 0.21/0.48 (sk_c5 = multiply(sk_c4, sk_c8)),
% 0.21/0.48 inference(symmetry,[status(thm)],[489])).
% 0.21/0.48 tff(491,plain,
% 0.21/0.48 (multiply(sk_c8, sk_c5) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[490])).
% 0.21/0.48 tff(492,plain,
% 0.21/0.48 (((inverse(sk_c1) = sk_c7) | (multiply(sk_c8, sk_c5) = sk_c7)) <=> ((inverse(sk_c1) = sk_c7) | (multiply(sk_c8, sk_c5) = sk_c7))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(493,axiom,((inverse(sk_c1) = sk_c7) | (multiply(sk_c8, sk_c5) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_16')).
% 0.21/0.48 tff(494,plain,
% 0.21/0.48 ((inverse(sk_c1) = sk_c7) | (multiply(sk_c8, sk_c5) = sk_c7)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[493, 492])).
% 0.21/0.48 tff(495,plain,
% 0.21/0.48 (multiply(sk_c8, sk_c5) = sk_c7),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[494, 466])).
% 0.21/0.48 tff(496,plain,
% 0.21/0.48 (sk_c7 = multiply(sk_c8, sk_c5)),
% 0.21/0.48 inference(symmetry,[status(thm)],[495])).
% 0.21/0.48 tff(497,plain,
% 0.21/0.48 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(identity, sk_c8)),
% 0.21/0.48 inference(symmetry,[status(thm)],[482])).
% 0.21/0.48 tff(498,plain,
% 0.21/0.48 (sk_c7 = sk_c8),
% 0.21/0.48 inference(transitivity,[status(thm)],[496, 491, 322, 497, 9])).
% 0.21/0.48 tff(499,plain,
% 0.21/0.48 (multiply(sk_c3, sk_c7) = multiply(sk_c3, sk_c8)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[498])).
% 0.21/0.48 tff(500,plain,
% 0.21/0.48 (multiply(sk_c3, sk_c7) = sk_c6),
% 0.21/0.48 inference(transitivity,[status(thm)],[499, 470, 496, 491, 322, 479, 299, 471, 416])).
% 0.21/0.48 tff(501,plain,
% 0.21/0.48 (multiply(sk_c3, sk_c7) = sk_c8),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[500, 485])).
% 0.21/0.48 tff(502,plain,
% 0.21/0.48 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = multiply(sk_c8, sk_c5)),
% 0.21/0.48 inference(symmetry,[status(thm)],[491])).
% 0.21/0.48 tff(503,plain,
% 0.21/0.48 (multiply(multiply(sk_c8, sk_c3), sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.21/0.48 inference(symmetry,[status(thm)],[479])).
% 0.21/0.48 tff(504,plain,
% 0.21/0.48 (multiply(sk_c8, multiply(sk_c3, sk_c8)) = sk_c7),
% 0.21/0.48 inference(transitivity,[status(thm)],[341, 503, 321, 502, 495])).
% 0.21/0.48 tff(505,plain,
% 0.21/0.48 (inverse(sk_c3) = sk_c7),
% 0.21/0.48 inference(transitivity,[status(thm)],[286, 205, 482, 321, 502, 495])).
% 0.21/0.48 tff(506,plain,
% 0.21/0.48 ((~(inverse(sk_c3) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c6)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c3, sk_c8)) = sk_c7)) | (~(multiply(sk_c3, sk_c7) = sk_c8))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[353, 401, 416])).
% 0.21/0.48 tff(507,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[506, 500, 505, 470, 504, 501])).
% 0.21/0.48 tff(508,plain,(inverse(sk_c1) = sk_c7), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(509,plain,
% 0.21/0.48 ((inverse(sk_c1) = sk_c8) <=> (sk_c7 = inverse(sk_c3))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[508, 287])).
% 0.21/0.48 tff(510,plain,
% 0.21/0.48 ((inverse(sk_c1) = sk_c8) <=> (inverse(sk_c3) = sk_c7)),
% 0.21/0.48 inference(transitivity,[status(thm)],[509, 10])).
% 0.21/0.48 tff(511,plain,
% 0.21/0.48 ((inverse(sk_c1) = sk_c8) <=> (multiply(sk_c1, sk_c7) = sk_c8)),
% 0.21/0.48 inference(transitivity,[status(thm)],[510, 465])).
% 0.21/0.48 tff(512,plain,
% 0.21/0.48 ((~(inverse(sk_c1) = sk_c8)) <=> (~(multiply(sk_c1, sk_c7) = sk_c8))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[511])).
% 0.21/0.48 tff(513,plain,
% 0.21/0.48 (sk_c7 = inverse(sk_c1)),
% 0.21/0.48 inference(symmetry,[status(thm)],[508])).
% 0.21/0.48 tff(514,plain,
% 0.21/0.48 (multiply(sk_c7, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[513])).
% 0.21/0.48 tff(515,plain,
% 0.21/0.48 (multiply(sk_c7, sk_c1) = multiply(sk_c7, sk_c2)),
% 0.21/0.48 inference(transitivity,[status(thm)],[514, 87, 67, 358])).
% 0.21/0.48 tff(516,plain,
% 0.21/0.48 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(multiply(sk_c7, sk_c2), sk_c7)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[515])).
% 0.21/0.48 tff(517,plain,
% 0.21/0.48 (sk_c6 = multiply(sk_c1, sk_c7)),
% 0.21/0.48 inference(symmetry,[status(thm)],[461])).
% 0.21/0.48 tff(518,plain,
% 0.21/0.48 (sk_c7 = multiply(sk_c1, sk_c7)),
% 0.21/0.48 inference(transitivity,[status(thm)],[72, 360, 54, 106, 401, 517])).
% 0.21/0.48 tff(519,plain,
% 0.21/0.48 (multiply(sk_c7, sk_c7) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[518])).
% 0.21/0.48 tff(520,plain,
% 0.21/0.48 (multiply(multiply(sk_c2, sk_c7), sk_c7) = multiply(sk_c8, sk_c7)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[105])).
% 0.21/0.48 tff(521,plain,
% 0.21/0.48 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, sk_c7), sk_c7) = multiply(sk_c2, multiply(sk_c7, sk_c7)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(522,plain,
% 0.21/0.48 (multiply(multiply(sk_c2, sk_c7), sk_c7) = multiply(sk_c2, multiply(sk_c7, sk_c7))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[521, 52])).
% 0.21/0.48 tff(523,plain,
% 0.21/0.48 (multiply(sk_c2, multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c2, sk_c7), sk_c7)),
% 0.21/0.48 inference(symmetry,[status(thm)],[522])).
% 0.21/0.48 tff(524,plain,
% 0.21/0.48 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(sk_c7, sk_c7)),
% 0.21/0.48 inference(symmetry,[status(thm)],[519])).
% 0.21/0.48 tff(525,plain,
% 0.21/0.48 (multiply(multiply(sk_c7, sk_c2), sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.21/0.48 inference(symmetry,[status(thm)],[516])).
% 0.21/0.48 tff(526,plain,
% 0.21/0.48 (sk_c7 = multiply(sk_c7, sk_c7)),
% 0.21/0.48 inference(transitivity,[status(thm)],[72, 360, 525, 85, 524])).
% 0.21/0.48 tff(527,plain,
% 0.21/0.48 (multiply(sk_c2, sk_c7) = multiply(sk_c2, multiply(sk_c7, sk_c7))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[526])).
% 0.21/0.48 tff(528,plain,
% 0.21/0.48 (sk_c8 = sk_c7),
% 0.21/0.48 inference(transitivity,[status(thm)],[125, 527, 523, 520, 416, 402, 115, 78, 361, 71])).
% 0.21/0.48 tff(529,plain,
% 0.21/0.48 (multiply(sk_c1, sk_c8) = multiply(sk_c1, sk_c7)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[528])).
% 0.21/0.48 tff(530,plain,
% 0.21/0.48 (multiply(sk_c1, sk_c8) = sk_c7),
% 0.21/0.48 inference(transitivity,[status(thm)],[529, 461, 402, 115, 78, 361, 71])).
% 0.21/0.48 tff(531,plain,
% 0.21/0.48 (multiply(sk_c8, multiply(sk_c1, sk_c8)) = multiply(sk_c7, sk_c7)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[528, 530])).
% 0.21/0.48 tff(532,plain,
% 0.21/0.48 (multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7),
% 0.21/0.48 inference(transitivity,[status(thm)],[531, 519, 146, 516, 361, 71])).
% 0.21/0.48 tff(533,plain,
% 0.21/0.48 (multiply(sk_c2, multiply(sk_c7, sk_c7)) = multiply(sk_c2, sk_c7)),
% 0.21/0.48 inference(symmetry,[status(thm)],[527])).
% 0.21/0.48 tff(534,plain,
% 0.21/0.48 (multiply(sk_c8, sk_c7) = multiply(multiply(sk_c2, sk_c7), sk_c7)),
% 0.21/0.48 inference(symmetry,[status(thm)],[520])).
% 0.21/0.48 tff(535,plain,
% 0.21/0.48 (sk_c6 = multiply(sk_c8, sk_c7)),
% 0.21/0.48 inference(symmetry,[status(thm)],[416])).
% 0.21/0.48 tff(536,plain,
% 0.21/0.48 (multiply(sk_c1, sk_c7) = sk_c8),
% 0.21/0.48 inference(transitivity,[status(thm)],[461, 535, 534, 522, 533, 105])).
% 0.21/0.48 tff(537,plain,
% 0.21/0.48 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(538,plain,
% 0.21/0.48 (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(539,plain,
% 0.21/0.48 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[538])).
% 0.21/0.48 tff(540,plain,
% 0.21/0.48 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[539, 537])).
% 0.21/0.48 tff(541,plain,
% 0.21/0.48 ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(542,plain,
% 0.21/0.49 ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[541, 540])).
% 0.21/0.49 tff(543,plain,
% 0.21/0.49 ((~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c8) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[542, 401, 416, 461, 508, 276])).
% 0.21/0.49 tff(544,plain,
% 0.21/0.49 (~(inverse(sk_c1) = sk_c8)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[543, 536, 530, 532])).
% 0.21/0.49 tff(545,plain,
% 0.21/0.49 (~(multiply(sk_c1, sk_c7) = sk_c8)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[544, 512])).
% 0.21/0.49 tff(546,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[536, 545])).
% 0.21/0.49 tff(547,plain,(~(multiply(sk_c2, sk_c7) = sk_c8)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(548,plain,
% 0.21/0.49 (((inverse(sk_c4) = sk_c8) | (multiply(sk_c2, sk_c7) = sk_c8)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c2, sk_c7) = sk_c8))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(549,plain,
% 0.21/0.49 (((multiply(sk_c2, sk_c7) = sk_c8) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c2, sk_c7) = sk_c8))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(550,axiom,((multiply(sk_c2, sk_c7) = sk_c8) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_24')).
% 0.21/0.49 tff(551,plain,
% 0.21/0.49 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c2, sk_c7) = sk_c8)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[550, 549])).
% 0.21/0.49 tff(552,plain,
% 0.21/0.49 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c2, sk_c7) = sk_c8)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[551, 548])).
% 0.21/0.49 tff(553,plain,
% 0.21/0.49 (inverse(sk_c4) = sk_c8),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[552, 547])).
% 0.21/0.49 tff(554,plain,
% 0.21/0.49 (sk_c8 = inverse(sk_c4)),
% 0.21/0.49 inference(symmetry,[status(thm)],[553])).
% 0.21/0.49 tff(555,plain,
% 0.21/0.49 (multiply(sk_c8, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[554])).
% 0.21/0.49 tff(556,plain,
% 0.21/0.49 (multiply(inverse(sk_c4), sk_c4) = multiply(sk_c8, sk_c4)),
% 0.21/0.49 inference(symmetry,[status(thm)],[555])).
% 0.21/0.49 tff(557,plain,
% 0.21/0.49 (identity = multiply(sk_c8, sk_c4)),
% 0.21/0.49 inference(transitivity,[status(thm)],[434, 556])).
% 0.21/0.49 tff(558,plain,
% 0.21/0.49 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[557])).
% 0.21/0.49 tff(559,plain,
% 0.21/0.49 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(identity, sk_c8)),
% 0.21/0.49 inference(symmetry,[status(thm)],[558])).
% 0.21/0.49 tff(560,plain,
% 0.21/0.49 (multiply(sk_c8, sk_c4) = multiply(sk_c8, sk_c3)),
% 0.21/0.49 inference(transitivity,[status(thm)],[555, 311, 304, 301])).
% 0.21/0.49 tff(561,plain,
% 0.21/0.49 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(multiply(sk_c8, sk_c3), sk_c8)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[560])).
% 0.21/0.49 tff(562,plain,
% 0.21/0.49 (multiply(multiply(sk_c8, sk_c3), sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.21/0.49 inference(symmetry,[status(thm)],[561])).
% 0.21/0.49 tff(563,plain,
% 0.21/0.49 (((multiply(sk_c2, sk_c7) = sk_c8) | (multiply(sk_c3, sk_c8) = sk_c7)) <=> ((multiply(sk_c2, sk_c7) = sk_c8) | (multiply(sk_c3, sk_c8) = sk_c7))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(564,axiom,((multiply(sk_c2, sk_c7) = sk_c8) | (multiply(sk_c3, sk_c8) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_20')).
% 0.21/0.49 tff(565,plain,
% 0.21/0.49 ((multiply(sk_c2, sk_c7) = sk_c8) | (multiply(sk_c3, sk_c8) = sk_c7)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[564, 563])).
% 0.21/0.49 tff(566,plain,
% 0.21/0.49 (multiply(sk_c3, sk_c8) = sk_c7),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[565, 547])).
% 0.21/0.49 tff(567,plain,
% 0.21/0.49 (multiply(sk_c8, multiply(sk_c3, sk_c8)) = multiply(sk_c8, sk_c7)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[566])).
% 0.21/0.49 tff(568,plain,
% 0.21/0.49 (multiply(sk_c8, sk_c7) = multiply(sk_c8, multiply(sk_c3, sk_c8))),
% 0.21/0.49 inference(symmetry,[status(thm)],[567])).
% 0.21/0.49 tff(569,plain,
% 0.21/0.49 (multiply(sk_c1, sk_c7) = sk_c8),
% 0.21/0.49 inference(transitivity,[status(thm)],[461, 535, 568, 341, 562, 559, 9])).
% 0.21/0.49 tff(570,plain,
% 0.21/0.49 (((multiply(sk_c2, sk_c7) = sk_c8) | (multiply(sk_c8, sk_c5) = sk_c7)) <=> ((multiply(sk_c2, sk_c7) = sk_c8) | (multiply(sk_c8, sk_c5) = sk_c7))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(571,axiom,((multiply(sk_c2, sk_c7) = sk_c8) | (multiply(sk_c8, sk_c5) = sk_c7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_22')).
% 0.21/0.49 tff(572,plain,
% 0.21/0.49 ((multiply(sk_c2, sk_c7) = sk_c8) | (multiply(sk_c8, sk_c5) = sk_c7)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[571, 570])).
% 0.21/0.49 tff(573,plain,
% 0.21/0.49 (multiply(sk_c8, sk_c5) = sk_c7),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[572, 547])).
% 0.21/0.49 tff(574,plain,
% 0.21/0.49 (((multiply(sk_c2, sk_c7) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c5)) <=> ((multiply(sk_c2, sk_c7) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c5))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(575,axiom,((multiply(sk_c2, sk_c7) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this_23')).
% 0.21/0.49 tff(576,plain,
% 0.21/0.49 ((multiply(sk_c2, sk_c7) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c5)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[575, 574])).
% 0.21/0.49 tff(577,plain,
% 0.21/0.49 (multiply(sk_c4, sk_c8) = sk_c5),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[576, 547])).
% 0.21/0.49 tff(578,plain,
% 0.21/0.49 (sk_c5 = multiply(sk_c4, sk_c8)),
% 0.21/0.49 inference(symmetry,[status(thm)],[577])).
% 0.21/0.49 tff(579,plain,
% 0.21/0.49 (multiply(sk_c8, sk_c5) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[578])).
% 0.21/0.49 tff(580,plain,
% 0.21/0.49 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = multiply(sk_c8, sk_c5)),
% 0.21/0.49 inference(symmetry,[status(thm)],[579])).
% 0.21/0.49 tff(581,plain,
% 0.21/0.49 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7),
% 0.21/0.49 inference(transitivity,[status(thm)],[580, 573])).
% 0.21/0.49 tff(582,plain,
% 0.21/0.49 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(sk_c3) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(sk_c3) = sk_c8)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(583,plain,
% 0.21/0.49 (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(inverse(sk_c3) = sk_c8)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(sk_c3) = sk_c8)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(584,plain,
% 0.21/0.49 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(inverse(sk_c3) = sk_c8)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(sk_c3) = sk_c8))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[583])).
% 0.21/0.49 tff(585,plain,
% 0.21/0.49 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(inverse(sk_c3) = sk_c8)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(sk_c3) = sk_c8)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[584, 582])).
% 0.21/0.49 tff(586,plain,
% 0.21/0.49 ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(inverse(sk_c3) = sk_c8)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(587,plain,
% 0.21/0.49 ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X1, sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c7)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c6)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X3) = sk_c7)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, sk_c7) = sk_c6)) | (~(inverse(sk_c1) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c6)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(multiply(sk_c3, sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(sk_c3) = sk_c8))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[586, 585])).
% 0.21/0.49 tff(588,plain,
% 0.21/0.49 ((~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[587, 401, 416, 566, 286, 553, 461, 508, 276])).
% 0.21/0.49 tff(589,plain,
% 0.21/0.49 (~(multiply(sk_c1, sk_c7) = sk_c8)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[588, 581])).
% 0.21/0.49 tff(590,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[589, 569])).
% 0.21/0.49 % SZS output end Proof
% 0.21/0.50 % E exiting
%------------------------------------------------------------------------------