%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP328-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:07:37 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.51s
% Output : Proof 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP328-1 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 15:58:41 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.51 % SZS status Unsatisfiable
% 0.20/0.51 % SZS output start Proof
% 0.20/0.51 tff(sk_c7_type, type, (
% 0.20/0.51 sk_c7: $i)).
% 0.20/0.51 tff(inverse_type, type, (
% 0.20/0.51 inverse: $i > $i)).
% 0.20/0.51 tff(multiply_type, type, (
% 0.20/0.51 multiply: ( $i * $i ) > $i)).
% 0.20/0.51 tff(sk_c1_type, type, (
% 0.20/0.51 sk_c1: $i)).
% 0.20/0.51 tff(identity_type, type, (
% 0.20/0.51 identity: $i)).
% 0.20/0.51 tff(sk_c8_type, type, (
% 0.20/0.51 sk_c8: $i)).
% 0.20/0.51 tff(sk_c4_type, type, (
% 0.20/0.51 sk_c4: $i)).
% 0.20/0.51 tff(sk_c5_type, type, (
% 0.20/0.51 sk_c5: $i)).
% 0.20/0.51 tff(sk_c6_type, type, (
% 0.20/0.51 sk_c6: $i)).
% 0.20/0.51 tff(sk_c2_type, type, (
% 0.20/0.51 sk_c2: $i)).
% 0.20/0.51 tff(sk_c3_type, type, (
% 0.20/0.51 sk_c3: $i)).
% 0.20/0.51 tff(1,plain,
% 0.20/0.51 ((sk_c8 = multiply(sk_c4, sk_c7)) <=> (multiply(sk_c4, sk_c7) = sk_c8)),
% 0.20/0.51 inference(commutativity,[status(thm)],[])).
% 0.20/0.51 tff(2,plain,
% 0.20/0.51 (^[X: $i] : refl((multiply(identity, X) = X) <=> (multiply(identity, X) = X))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(3,plain,
% 0.20/0.51 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.20/0.51 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.51 tff(4,plain,
% 0.20/0.51 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(5,axiom,(![X: $i] : (multiply(identity, X) = X)), file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax','left_identity')).
% 0.20/0.51 tff(6,plain,
% 0.20/0.51 (![X: $i] : (multiply(identity, X) = X)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.51 tff(7,plain,(
% 0.20/0.51 ![X: $i] : (multiply(identity, X) = X)),
% 0.20/0.51 inference(skolemize,[status(sab)],[6])).
% 0.20/0.51 tff(8,plain,
% 0.20/0.51 (![X: $i] : (multiply(identity, X) = X)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.51 tff(9,plain,
% 0.20/0.51 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c8) = sk_c8)),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(10,plain,
% 0.20/0.51 (multiply(identity, sk_c8) = sk_c8),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.20/0.51 tff(11,assumption,(~(multiply(sk_c7, sk_c6) = sk_c8)), introduced(assumption)).
% 0.20/0.51 tff(12,plain,
% 0.20/0.51 (((inverse(sk_c2) = sk_c8) | (multiply(sk_c7, sk_c6) = sk_c8)) <=> ((inverse(sk_c2) = sk_c8) | (multiply(sk_c7, sk_c6) = sk_c8))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(13,axiom,((inverse(sk_c2) = sk_c8) | (multiply(sk_c7, sk_c6) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_26')).
% 0.20/0.51 tff(14,plain,
% 0.20/0.51 ((inverse(sk_c2) = sk_c8) | (multiply(sk_c7, sk_c6) = sk_c8)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.51 tff(15,plain,
% 0.20/0.51 (inverse(sk_c2) = sk_c8),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[14, 11])).
% 0.20/0.51 tff(16,plain,
% 0.20/0.51 (sk_c8 = inverse(sk_c2)),
% 0.20/0.51 inference(symmetry,[status(thm)],[15])).
% 0.20/0.51 tff(17,plain,
% 0.20/0.51 (multiply(sk_c8, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[16])).
% 0.20/0.51 tff(18,plain,
% 0.20/0.51 (multiply(inverse(sk_c2), sk_c2) = multiply(sk_c8, sk_c2)),
% 0.20/0.51 inference(symmetry,[status(thm)],[17])).
% 0.20/0.51 tff(19,plain,
% 0.20/0.51 (^[X: $i] : refl((multiply(inverse(X), X) = identity) <=> (multiply(inverse(X), X) = identity))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(20,plain,
% 0.20/0.51 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.20/0.51 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.51 tff(21,plain,
% 0.20/0.51 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(22,axiom,(![X: $i] : (multiply(inverse(X), X) = identity)), file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax','left_inverse')).
% 0.20/0.51 tff(23,plain,
% 0.20/0.51 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.51 tff(24,plain,(
% 0.20/0.51 ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.20/0.51 inference(skolemize,[status(sab)],[23])).
% 0.20/0.51 tff(25,plain,
% 0.20/0.51 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.20/0.51 tff(26,plain,
% 0.20/0.51 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c2), sk_c2) = identity)),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(27,plain,
% 0.20/0.51 (multiply(inverse(sk_c2), sk_c2) = identity),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.20/0.51 tff(28,plain,
% 0.20/0.51 (identity = multiply(inverse(sk_c2), sk_c2)),
% 0.20/0.51 inference(symmetry,[status(thm)],[27])).
% 0.20/0.51 tff(29,plain,
% 0.20/0.51 (identity = multiply(sk_c8, sk_c2)),
% 0.20/0.51 inference(transitivity,[status(thm)],[28, 18])).
% 0.20/0.51 tff(30,plain,
% 0.20/0.51 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c2), sk_c8)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[29])).
% 0.20/0.51 tff(31,plain,
% 0.20/0.51 (multiply(multiply(sk_c8, sk_c2), sk_c8) = multiply(identity, sk_c8)),
% 0.20/0.51 inference(symmetry,[status(thm)],[30])).
% 0.20/0.51 tff(32,plain,
% 0.20/0.51 (^[Z: $i, Y: $i, X: $i] : refl((multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))) <=> (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(33,plain,
% 0.20/0.51 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.51 tff(34,plain,
% 0.20/0.51 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(35,axiom,(![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax','associativity')).
% 0.20/0.51 tff(36,plain,
% 0.20/0.51 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.51 tff(37,plain,(
% 0.20/0.51 ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[36])).
% 0.20/0.51 tff(38,plain,
% 0.20/0.51 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.20/0.51 tff(39,plain,
% 0.20/0.51 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c2), sk_c8) = multiply(sk_c8, multiply(sk_c2, sk_c8)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(40,plain,
% 0.20/0.51 (multiply(multiply(sk_c8, sk_c2), sk_c8) = multiply(sk_c8, multiply(sk_c2, sk_c8))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.20/0.51 tff(41,plain,
% 0.20/0.51 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = multiply(multiply(sk_c8, sk_c2), sk_c8)),
% 0.20/0.51 inference(symmetry,[status(thm)],[40])).
% 0.20/0.51 tff(42,plain,
% 0.20/0.51 (((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c7, sk_c6) = sk_c8)) <=> ((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c7, sk_c6) = sk_c8))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(43,axiom,((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c7, sk_c6) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_21')).
% 0.20/0.51 tff(44,plain,
% 0.20/0.51 ((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c7, sk_c6) = sk_c8)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.51 tff(45,plain,
% 0.20/0.51 (multiply(sk_c2, sk_c8) = sk_c3),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[44, 11])).
% 0.20/0.51 tff(46,plain,
% 0.20/0.51 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = multiply(sk_c8, sk_c3)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[45])).
% 0.20/0.51 tff(47,plain,
% 0.20/0.51 (multiply(sk_c8, sk_c3) = multiply(sk_c8, multiply(sk_c2, sk_c8))),
% 0.20/0.51 inference(symmetry,[status(thm)],[46])).
% 0.20/0.51 tff(48,plain,
% 0.20/0.51 (((multiply(sk_c7, sk_c6) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7)) <=> ((multiply(sk_c7, sk_c6) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(49,plain,
% 0.20/0.51 (((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c7, sk_c6) = sk_c8)) <=> ((multiply(sk_c7, sk_c6) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(50,axiom,((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c7, sk_c6) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_16')).
% 0.20/0.51 tff(51,plain,
% 0.20/0.51 ((multiply(sk_c7, sk_c6) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.51 tff(52,plain,
% 0.20/0.51 ((multiply(sk_c7, sk_c6) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[51, 48])).
% 0.20/0.51 tff(53,plain,
% 0.20/0.51 (multiply(sk_c8, sk_c3) = sk_c7),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[52, 11])).
% 0.20/0.51 tff(54,plain,
% 0.20/0.51 (sk_c7 = multiply(sk_c8, sk_c3)),
% 0.20/0.51 inference(symmetry,[status(thm)],[53])).
% 0.20/0.51 tff(55,plain,
% 0.20/0.51 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c7) = sk_c7)),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(56,plain,
% 0.20/0.51 (multiply(identity, sk_c7) = sk_c7),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[55, 8])).
% 0.20/0.51 tff(57,plain,
% 0.20/0.51 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c1), sk_c1) = identity)),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(58,plain,
% 0.20/0.51 (multiply(inverse(sk_c1), sk_c1) = identity),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[57, 25])).
% 0.20/0.51 tff(59,plain,
% 0.20/0.51 (((inverse(sk_c1) = sk_c7) | (multiply(sk_c7, sk_c6) = sk_c8)) <=> ((inverse(sk_c1) = sk_c7) | (multiply(sk_c7, sk_c6) = sk_c8))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(60,axiom,((inverse(sk_c1) = sk_c7) | (multiply(sk_c7, sk_c6) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_11')).
% 0.20/0.51 tff(61,plain,
% 0.20/0.51 ((inverse(sk_c1) = sk_c7) | (multiply(sk_c7, sk_c6) = sk_c8)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.51 tff(62,plain,
% 0.20/0.51 (inverse(sk_c1) = sk_c7),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[61, 11])).
% 0.20/0.51 tff(63,plain,
% 0.20/0.51 (sk_c7 = inverse(sk_c1)),
% 0.20/0.51 inference(symmetry,[status(thm)],[62])).
% 0.20/0.51 tff(64,plain,
% 0.20/0.51 (multiply(sk_c7, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[63])).
% 0.20/0.51 tff(65,plain,
% 0.20/0.51 (multiply(sk_c7, sk_c1) = identity),
% 0.20/0.51 inference(transitivity,[status(thm)],[64, 58])).
% 0.20/0.51 tff(66,plain,
% 0.20/0.51 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(identity, sk_c7)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[65])).
% 0.20/0.51 tff(67,plain,
% 0.20/0.51 ((~![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)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(68,plain,
% 0.20/0.51 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[67, 38])).
% 0.20/0.51 tff(69,plain,
% 0.20/0.51 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.20/0.51 inference(symmetry,[status(thm)],[68])).
% 0.20/0.51 tff(70,plain,
% 0.20/0.51 (((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c7, sk_c6) = sk_c8)) <=> ((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c7, sk_c6) = sk_c8))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(71,axiom,((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c7, sk_c6) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_6')).
% 0.20/0.51 tff(72,plain,
% 0.20/0.51 ((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c7, sk_c6) = sk_c8)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.51 tff(73,plain,
% 0.20/0.51 (multiply(sk_c1, sk_c7) = sk_c8),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[72, 11])).
% 0.20/0.51 tff(74,plain,
% 0.20/0.51 (sk_c8 = multiply(sk_c1, sk_c7)),
% 0.20/0.51 inference(symmetry,[status(thm)],[73])).
% 0.20/0.51 tff(75,plain,
% 0.20/0.51 (multiply(sk_c7, sk_c8) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[74])).
% 0.20/0.51 tff(76,plain,
% 0.20/0.51 (sk_c7 = sk_c8),
% 0.20/0.51 inference(transitivity,[status(thm)],[54, 47, 41, 31, 10])).
% 0.20/0.51 tff(77,plain,
% 0.20/0.51 (multiply(sk_c7, sk_c7) = multiply(sk_c7, sk_c8)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[76])).
% 0.20/0.51 tff(78,plain,
% 0.20/0.51 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c4), sk_c4) = identity)),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(79,plain,
% 0.20/0.51 (multiply(inverse(sk_c4), sk_c4) = identity),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[78, 25])).
% 0.20/0.51 tff(80,assumption,(~(multiply(sk_c7, sk_c8) = sk_c6)), introduced(assumption)).
% 0.20/0.51 tff(81,plain,
% 0.20/0.51 (((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8)) <=> ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(82,axiom,((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_5')).
% 0.20/0.51 tff(83,plain,
% 0.20/0.51 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.51 tff(84,plain,
% 0.20/0.51 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[83, 81])).
% 0.20/0.51 tff(85,plain,
% 0.20/0.51 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[84, 81])).
% 0.20/0.51 tff(86,plain,
% 0.20/0.51 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.20/0.51 tff(87,plain,
% 0.20/0.51 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c4) = sk_c8)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[86, 81])).
% 0.20/0.51 tff(88,plain,
% 0.20/0.51 (inverse(sk_c4) = sk_c8),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[87, 80])).
% 0.20/0.51 tff(89,plain,
% 0.20/0.51 (sk_c8 = inverse(sk_c4)),
% 0.20/0.51 inference(symmetry,[status(thm)],[88])).
% 0.20/0.51 tff(90,plain,
% 0.20/0.51 (multiply(sk_c8, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[89])).
% 0.20/0.51 tff(91,plain,
% 0.20/0.51 (multiply(sk_c8, sk_c4) = identity),
% 0.20/0.51 inference(transitivity,[status(thm)],[90, 79])).
% 0.20/0.51 tff(92,plain,
% 0.20/0.51 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(identity, sk_c8)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[91])).
% 0.20/0.51 tff(93,plain,
% 0.20/0.51 (multiply(inverse(sk_c4), sk_c4) = multiply(sk_c8, sk_c4)),
% 0.20/0.51 inference(symmetry,[status(thm)],[90])).
% 0.20/0.51 tff(94,plain,
% 0.20/0.51 (identity = multiply(inverse(sk_c4), sk_c4)),
% 0.20/0.51 inference(symmetry,[status(thm)],[79])).
% 0.20/0.51 tff(95,plain,
% 0.20/0.51 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c8), sk_c8) = identity)),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(96,plain,
% 0.20/0.51 (multiply(inverse(sk_c8), sk_c8) = identity),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[95, 25])).
% 0.20/0.51 tff(97,plain,
% 0.20/0.51 (((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c7, sk_c6) = sk_c8)) <=> ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c7, sk_c6) = sk_c8))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(98,axiom,((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c7, sk_c6) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_1')).
% 0.20/0.51 tff(99,plain,
% 0.20/0.51 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c7, sk_c6) = sk_c8)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.20/0.51 tff(100,plain,
% 0.20/0.51 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c7, sk_c6) = sk_c8)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[99, 97])).
% 0.20/0.51 tff(101,plain,
% 0.20/0.51 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c7, sk_c6) = sk_c8)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[100, 97])).
% 0.20/0.51 tff(102,plain,
% 0.20/0.51 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c7, sk_c6) = sk_c8)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.20/0.51 tff(103,plain,
% 0.20/0.51 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c7, sk_c6) = sk_c8)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[102, 97])).
% 0.20/0.51 tff(104,plain,
% 0.20/0.51 (multiply(sk_c7, sk_c6) = sk_c8),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[103, 80])).
% 0.20/0.51 tff(105,assumption,(~(inverse(sk_c8) = sk_c6)), introduced(assumption)).
% 0.20/0.51 tff(106,plain,
% 0.20/0.51 (((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c8) = sk_c6)) <=> ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c8) = sk_c6))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(107,axiom,((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c8) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_2')).
% 0.20/0.51 tff(108,plain,
% 0.20/0.51 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c8) = sk_c6)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.20/0.51 tff(109,plain,
% 0.20/0.51 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c8) = sk_c6)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[108, 106])).
% 0.20/0.51 tff(110,plain,
% 0.20/0.51 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c8) = sk_c6)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[109, 106])).
% 0.20/0.51 tff(111,plain,
% 0.20/0.51 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c8) = sk_c6)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.20/0.51 tff(112,plain,
% 0.20/0.51 ((multiply(sk_c7, sk_c8) = sk_c6) | (inverse(sk_c8) = sk_c6)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[111, 106])).
% 0.20/0.51 tff(113,plain,
% 0.20/0.51 (multiply(sk_c7, sk_c8) = sk_c6),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[112, 105])).
% 0.20/0.52 tff(114,plain,
% 0.20/0.52 (((inverse(sk_c8) = sk_c6) | (multiply(sk_c1, sk_c7) = sk_c8)) <=> ((inverse(sk_c8) = sk_c6) | (multiply(sk_c1, sk_c7) = sk_c8))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(115,plain,
% 0.20/0.52 (((multiply(sk_c1, sk_c7) = sk_c8) | (inverse(sk_c8) = sk_c6)) <=> ((inverse(sk_c8) = sk_c6) | (multiply(sk_c1, sk_c7) = sk_c8))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(116,axiom,((multiply(sk_c1, sk_c7) = sk_c8) | (inverse(sk_c8) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_7')).
% 0.20/0.52 tff(117,plain,
% 0.20/0.52 ((inverse(sk_c8) = sk_c6) | (multiply(sk_c1, sk_c7) = sk_c8)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.20/0.52 tff(118,plain,
% 0.20/0.52 ((inverse(sk_c8) = sk_c6) | (multiply(sk_c1, sk_c7) = sk_c8)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[117, 114])).
% 0.20/0.52 tff(119,plain,
% 0.20/0.52 (multiply(sk_c1, sk_c7) = sk_c8),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[118, 105])).
% 0.20/0.52 tff(120,plain,
% 0.20/0.52 (sk_c8 = multiply(sk_c1, sk_c7)),
% 0.20/0.52 inference(symmetry,[status(thm)],[119])).
% 0.20/0.52 tff(121,plain,
% 0.20/0.52 (multiply(sk_c7, sk_c8) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[120])).
% 0.20/0.52 tff(122,plain,
% 0.20/0.52 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(sk_c7, sk_c8)),
% 0.20/0.52 inference(symmetry,[status(thm)],[121])).
% 0.20/0.52 tff(123,plain,
% 0.20/0.52 (((inverse(sk_c1) = sk_c7) | (inverse(sk_c8) = sk_c6)) <=> ((inverse(sk_c1) = sk_c7) | (inverse(sk_c8) = sk_c6))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(124,axiom,((inverse(sk_c1) = sk_c7) | (inverse(sk_c8) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_12')).
% 0.20/0.52 tff(125,plain,
% 0.20/0.52 ((inverse(sk_c1) = sk_c7) | (inverse(sk_c8) = sk_c6)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.20/0.52 tff(126,plain,
% 0.20/0.52 (inverse(sk_c1) = sk_c7),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[125, 105])).
% 0.20/0.52 tff(127,plain,
% 0.20/0.52 (sk_c7 = inverse(sk_c1)),
% 0.20/0.52 inference(symmetry,[status(thm)],[126])).
% 0.20/0.52 tff(128,plain,
% 0.20/0.52 (multiply(sk_c7, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[127])).
% 0.20/0.52 tff(129,plain,
% 0.20/0.52 (multiply(sk_c7, sk_c1) = identity),
% 0.20/0.52 inference(transitivity,[status(thm)],[128, 58])).
% 0.20/0.52 tff(130,plain,
% 0.20/0.52 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(identity, sk_c7)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[129])).
% 0.20/0.52 tff(131,plain,
% 0.20/0.52 (multiply(identity, sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.20/0.52 inference(symmetry,[status(thm)],[130])).
% 0.20/0.52 tff(132,plain,
% 0.20/0.52 (sk_c7 = multiply(identity, sk_c7)),
% 0.20/0.52 inference(symmetry,[status(thm)],[56])).
% 0.20/0.52 tff(133,plain,
% 0.20/0.52 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c1) = sk_c1)),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(134,plain,
% 0.20/0.52 (multiply(identity, sk_c1) = sk_c1),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[133, 8])).
% 0.20/0.52 tff(135,plain,
% 0.20/0.52 (((inverse(sk_c2) = sk_c8) | (inverse(sk_c8) = sk_c6)) <=> ((inverse(sk_c2) = sk_c8) | (inverse(sk_c8) = sk_c6))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(136,axiom,((inverse(sk_c2) = sk_c8) | (inverse(sk_c8) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_27')).
% 0.20/0.52 tff(137,plain,
% 0.20/0.52 ((inverse(sk_c2) = sk_c8) | (inverse(sk_c8) = sk_c6)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.20/0.52 tff(138,plain,
% 0.20/0.52 (inverse(sk_c2) = sk_c8),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[137, 105])).
% 0.20/0.52 tff(139,plain,
% 0.20/0.52 (sk_c8 = inverse(sk_c2)),
% 0.20/0.52 inference(symmetry,[status(thm)],[138])).
% 0.20/0.52 tff(140,plain,
% 0.20/0.52 (multiply(sk_c8, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[139])).
% 0.20/0.52 tff(141,plain,
% 0.20/0.52 (multiply(inverse(sk_c2), sk_c2) = multiply(sk_c8, sk_c2)),
% 0.20/0.52 inference(symmetry,[status(thm)],[140])).
% 0.20/0.52 tff(142,plain,
% 0.20/0.52 (identity = multiply(sk_c8, sk_c2)),
% 0.20/0.52 inference(transitivity,[status(thm)],[28, 141])).
% 0.20/0.52 tff(143,plain,
% 0.20/0.52 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c2), sk_c8)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[142])).
% 0.20/0.52 tff(144,plain,
% 0.20/0.52 (multiply(multiply(sk_c8, sk_c2), sk_c8) = multiply(identity, sk_c8)),
% 0.20/0.52 inference(symmetry,[status(thm)],[143])).
% 0.20/0.52 tff(145,plain,
% 0.20/0.52 (((inverse(sk_c8) = sk_c6) | (multiply(sk_c2, sk_c8) = sk_c3)) <=> ((inverse(sk_c8) = sk_c6) | (multiply(sk_c2, sk_c8) = sk_c3))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(146,plain,
% 0.20/0.52 (((multiply(sk_c2, sk_c8) = sk_c3) | (inverse(sk_c8) = sk_c6)) <=> ((inverse(sk_c8) = sk_c6) | (multiply(sk_c2, sk_c8) = sk_c3))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(147,axiom,((multiply(sk_c2, sk_c8) = sk_c3) | (inverse(sk_c8) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_22')).
% 0.20/0.52 tff(148,plain,
% 0.20/0.52 ((inverse(sk_c8) = sk_c6) | (multiply(sk_c2, sk_c8) = sk_c3)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.20/0.52 tff(149,plain,
% 0.20/0.52 ((inverse(sk_c8) = sk_c6) | (multiply(sk_c2, sk_c8) = sk_c3)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[148, 145])).
% 0.20/0.52 tff(150,plain,
% 0.20/0.52 (multiply(sk_c2, sk_c8) = sk_c3),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[149, 105])).
% 0.20/0.52 tff(151,plain,
% 0.20/0.52 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = multiply(sk_c8, sk_c3)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[150])).
% 0.20/0.52 tff(152,plain,
% 0.20/0.52 (multiply(sk_c8, sk_c3) = multiply(sk_c8, multiply(sk_c2, sk_c8))),
% 0.20/0.52 inference(symmetry,[status(thm)],[151])).
% 0.20/0.52 tff(153,plain,
% 0.20/0.52 (((inverse(sk_c8) = sk_c6) | (multiply(sk_c8, sk_c3) = sk_c7)) <=> ((inverse(sk_c8) = sk_c6) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(154,plain,
% 0.20/0.52 (((multiply(sk_c8, sk_c3) = sk_c7) | (inverse(sk_c8) = sk_c6)) <=> ((inverse(sk_c8) = sk_c6) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(155,axiom,((multiply(sk_c8, sk_c3) = sk_c7) | (inverse(sk_c8) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_17')).
% 0.20/0.52 tff(156,plain,
% 0.20/0.52 ((inverse(sk_c8) = sk_c6) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.20/0.52 tff(157,plain,
% 0.20/0.52 ((inverse(sk_c8) = sk_c6) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[156, 153])).
% 0.20/0.52 tff(158,plain,
% 0.20/0.52 (multiply(sk_c8, sk_c3) = sk_c7),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[157, 105])).
% 0.20/0.52 tff(159,plain,
% 0.20/0.52 (sk_c7 = multiply(sk_c8, sk_c3)),
% 0.20/0.52 inference(symmetry,[status(thm)],[158])).
% 0.20/0.52 tff(160,plain,
% 0.20/0.52 (sk_c7 = sk_c8),
% 0.20/0.52 inference(transitivity,[status(thm)],[159, 152, 41, 144, 10])).
% 0.20/0.52 tff(161,plain,
% 0.20/0.52 (multiply(inverse(sk_c8), sk_c7) = multiply(inverse(sk_c8), sk_c8)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[160])).
% 0.20/0.52 tff(162,plain,
% 0.20/0.52 (multiply(inverse(sk_c8), sk_c8) = multiply(inverse(sk_c8), sk_c7)),
% 0.20/0.52 inference(symmetry,[status(thm)],[161])).
% 0.20/0.52 tff(163,plain,
% 0.20/0.52 (identity = multiply(inverse(sk_c8), sk_c8)),
% 0.20/0.52 inference(symmetry,[status(thm)],[96])).
% 0.20/0.52 tff(164,plain,
% 0.20/0.52 (identity = multiply(inverse(sk_c8), sk_c7)),
% 0.20/0.52 inference(transitivity,[status(thm)],[163, 162])).
% 0.20/0.52 tff(165,plain,
% 0.20/0.52 (multiply(identity, sk_c1) = multiply(multiply(inverse(sk_c8), sk_c7), sk_c1)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[164])).
% 0.20/0.52 tff(166,plain,
% 0.20/0.52 (multiply(multiply(inverse(sk_c8), sk_c7), sk_c1) = multiply(identity, sk_c1)),
% 0.20/0.52 inference(symmetry,[status(thm)],[165])).
% 0.20/0.52 tff(167,plain,
% 0.20/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(inverse(sk_c8), sk_c7), sk_c1) = multiply(inverse(sk_c8), multiply(sk_c7, sk_c1)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(168,plain,
% 0.20/0.52 (multiply(multiply(inverse(sk_c8), sk_c7), sk_c1) = multiply(inverse(sk_c8), multiply(sk_c7, sk_c1))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[167, 38])).
% 0.20/0.52 tff(169,plain,
% 0.20/0.52 (multiply(inverse(sk_c8), multiply(sk_c7, sk_c1)) = multiply(multiply(inverse(sk_c8), sk_c7), sk_c1)),
% 0.20/0.52 inference(symmetry,[status(thm)],[168])).
% 0.20/0.52 tff(170,plain,
% 0.20/0.52 (multiply(sk_c7, sk_c2) = multiply(sk_c8, sk_c2)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[160])).
% 0.20/0.52 tff(171,plain,
% 0.20/0.52 (multiply(sk_c8, sk_c2) = multiply(sk_c7, sk_c2)),
% 0.20/0.52 inference(symmetry,[status(thm)],[170])).
% 0.20/0.52 tff(172,plain,
% 0.20/0.52 (identity = multiply(sk_c7, sk_c2)),
% 0.20/0.52 inference(transitivity,[status(thm)],[28, 141, 171])).
% 0.20/0.52 tff(173,plain,
% 0.20/0.52 (multiply(sk_c1, identity) = multiply(sk_c1, multiply(sk_c7, sk_c2))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[172])).
% 0.20/0.52 tff(174,plain,
% 0.20/0.52 (multiply(sk_c1, multiply(sk_c7, sk_c2)) = multiply(sk_c1, identity)),
% 0.20/0.52 inference(symmetry,[status(thm)],[173])).
% 0.20/0.52 tff(175,plain,
% 0.20/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c7), sk_c2) = multiply(sk_c1, multiply(sk_c7, sk_c2)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(176,plain,
% 0.20/0.52 (multiply(multiply(sk_c1, sk_c7), sk_c2) = multiply(sk_c1, multiply(sk_c7, sk_c2))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[175, 38])).
% 0.20/0.52 tff(177,plain,
% 0.20/0.52 (multiply(multiply(sk_c1, sk_c7), sk_c2) = multiply(sk_c8, sk_c2)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[119])).
% 0.20/0.52 tff(178,plain,
% 0.20/0.52 (multiply(sk_c8, sk_c2) = multiply(multiply(sk_c1, sk_c7), sk_c2)),
% 0.20/0.52 inference(symmetry,[status(thm)],[177])).
% 0.20/0.52 tff(179,plain,
% 0.20/0.52 (identity = multiply(sk_c1, identity)),
% 0.20/0.52 inference(transitivity,[status(thm)],[28, 141, 178, 176, 174])).
% 0.20/0.52 tff(180,plain,
% 0.20/0.52 (multiply(sk_c7, identity) = multiply(sk_c7, multiply(sk_c1, identity))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[179])).
% 0.20/0.52 tff(181,plain,
% 0.20/0.52 (multiply(sk_c7, multiply(sk_c1, identity)) = multiply(sk_c7, identity)),
% 0.20/0.52 inference(symmetry,[status(thm)],[180])).
% 0.20/0.52 tff(182,plain,
% 0.20/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c1), identity) = multiply(sk_c7, multiply(sk_c1, identity)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(183,plain,
% 0.20/0.52 (multiply(multiply(sk_c7, sk_c1), identity) = multiply(sk_c7, multiply(sk_c1, identity))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[182, 38])).
% 0.20/0.52 tff(184,plain,
% 0.20/0.52 (multiply(multiply(sk_c7, sk_c1), identity) = multiply(identity, identity)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[129])).
% 0.20/0.52 tff(185,plain,
% 0.20/0.52 (multiply(identity, identity) = multiply(multiply(sk_c7, sk_c1), identity)),
% 0.20/0.52 inference(symmetry,[status(thm)],[184])).
% 0.20/0.52 tff(186,plain,
% 0.20/0.52 (sk_c8 = multiply(identity, sk_c8)),
% 0.20/0.52 inference(symmetry,[status(thm)],[10])).
% 0.20/0.52 tff(187,plain,
% 0.20/0.52 (sk_c8 = sk_c7),
% 0.20/0.52 inference(transitivity,[status(thm)],[186, 143, 40, 151, 158])).
% 0.20/0.52 tff(188,plain,
% 0.20/0.52 (multiply(sk_c8, sk_c1) = multiply(sk_c7, sk_c1)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[187])).
% 0.20/0.52 tff(189,plain,
% 0.20/0.52 (multiply(sk_c7, sk_c1) = multiply(sk_c8, sk_c1)),
% 0.20/0.52 inference(symmetry,[status(thm)],[188])).
% 0.20/0.52 tff(190,plain,
% 0.20/0.52 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c7, sk_c1)),
% 0.20/0.52 inference(symmetry,[status(thm)],[128])).
% 0.20/0.52 tff(191,plain,
% 0.20/0.52 (identity = multiply(inverse(sk_c1), sk_c1)),
% 0.20/0.52 inference(symmetry,[status(thm)],[58])).
% 0.20/0.52 tff(192,plain,
% 0.20/0.52 (identity = multiply(sk_c8, sk_c1)),
% 0.20/0.52 inference(transitivity,[status(thm)],[191, 190, 189])).
% 0.20/0.52 tff(193,plain,
% 0.20/0.52 (multiply(identity, identity) = multiply(identity, multiply(sk_c8, sk_c1))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[192])).
% 0.20/0.52 tff(194,plain,
% 0.20/0.52 (multiply(identity, multiply(sk_c8, sk_c1)) = multiply(identity, identity)),
% 0.20/0.52 inference(symmetry,[status(thm)],[193])).
% 0.20/0.52 tff(195,plain,
% 0.20/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, sk_c8), sk_c1) = multiply(identity, multiply(sk_c8, sk_c1)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(196,plain,
% 0.20/0.52 (multiply(multiply(identity, sk_c8), sk_c1) = multiply(identity, multiply(sk_c8, sk_c1))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[195, 38])).
% 0.20/0.52 tff(197,plain,
% 0.20/0.52 (multiply(multiply(identity, sk_c8), sk_c1) = multiply(sk_c8, sk_c1)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[10])).
% 0.20/0.52 tff(198,plain,
% 0.20/0.52 (multiply(sk_c8, sk_c1) = multiply(multiply(identity, sk_c8), sk_c1)),
% 0.20/0.52 inference(symmetry,[status(thm)],[197])).
% 0.20/0.52 tff(199,plain,
% 0.20/0.52 (multiply(sk_c7, sk_c1) = multiply(sk_c7, identity)),
% 0.20/0.52 inference(transitivity,[status(thm)],[189, 198, 196, 194, 185, 183, 181])).
% 0.20/0.52 tff(200,plain,
% 0.20/0.52 (multiply(inverse(sk_c8), multiply(sk_c7, sk_c1)) = multiply(inverse(sk_c8), multiply(sk_c7, identity))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[199])).
% 0.20/0.52 tff(201,plain,
% 0.20/0.52 (multiply(inverse(sk_c8), multiply(sk_c7, identity)) = multiply(inverse(sk_c8), multiply(sk_c7, sk_c1))),
% 0.20/0.52 inference(symmetry,[status(thm)],[200])).
% 0.20/0.52 tff(202,plain,
% 0.20/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(inverse(sk_c8), sk_c7), identity) = multiply(inverse(sk_c8), multiply(sk_c7, identity)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(203,plain,
% 0.20/0.52 (multiply(multiply(inverse(sk_c8), sk_c7), identity) = multiply(inverse(sk_c8), multiply(sk_c7, identity))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[202, 38])).
% 0.20/0.52 tff(204,plain,
% 0.20/0.52 (multiply(inverse(sk_c8), sk_c7) = identity),
% 0.20/0.52 inference(transitivity,[status(thm)],[161, 96])).
% 0.20/0.52 tff(205,plain,
% 0.20/0.52 (multiply(multiply(inverse(sk_c8), sk_c7), identity) = multiply(identity, identity)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[204])).
% 0.20/0.52 tff(206,plain,
% 0.20/0.52 (multiply(identity, identity) = multiply(multiply(inverse(sk_c8), sk_c7), identity)),
% 0.20/0.52 inference(symmetry,[status(thm)],[205])).
% 0.20/0.52 tff(207,plain,
% 0.20/0.52 (multiply(sk_c7, sk_c7) = multiply(sk_c7, sk_c8)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[160])).
% 0.20/0.52 tff(208,plain,
% 0.20/0.52 (multiply(sk_c7, sk_c8) = multiply(sk_c7, sk_c7)),
% 0.20/0.52 inference(symmetry,[status(thm)],[207])).
% 0.20/0.52 tff(209,plain,
% 0.20/0.52 (sk_c8 = multiply(sk_c7, sk_c7)),
% 0.20/0.52 inference(transitivity,[status(thm)],[186, 143, 40, 151, 158, 132, 131, 68, 122, 208])).
% 0.20/0.52 tff(210,plain,
% 0.20/0.52 (multiply(inverse(sk_c8), sk_c8) = multiply(inverse(sk_c8), multiply(sk_c7, sk_c7))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[209])).
% 0.20/0.52 tff(211,plain,
% 0.20/0.52 (multiply(inverse(sk_c8), multiply(sk_c7, sk_c7)) = multiply(inverse(sk_c8), sk_c8)),
% 0.20/0.52 inference(symmetry,[status(thm)],[210])).
% 0.20/0.52 tff(212,plain,
% 0.20/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(inverse(sk_c8), sk_c7), sk_c7) = multiply(inverse(sk_c8), multiply(sk_c7, sk_c7)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(213,plain,
% 0.20/0.52 (multiply(multiply(inverse(sk_c8), sk_c7), sk_c7) = multiply(inverse(sk_c8), multiply(sk_c7, sk_c7))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[212, 38])).
% 0.20/0.52 tff(214,plain,
% 0.20/0.52 (multiply(inverse(sk_c8), sk_c7) = multiply(sk_c7, sk_c1)),
% 0.20/0.52 inference(transitivity,[status(thm)],[161, 96, 191, 190])).
% 0.20/0.52 tff(215,plain,
% 0.20/0.52 (multiply(multiply(inverse(sk_c8), sk_c7), sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[214])).
% 0.20/0.52 tff(216,plain,
% 0.20/0.52 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(multiply(inverse(sk_c8), sk_c7), sk_c7)),
% 0.20/0.52 inference(symmetry,[status(thm)],[215])).
% 0.20/0.52 tff(217,plain,
% 0.20/0.52 (sk_c8 = sk_c1),
% 0.20/0.52 inference(transitivity,[status(thm)],[186, 143, 40, 151, 158, 132, 131, 216, 213, 211, 96, 191, 190, 189, 198, 196, 194, 206, 203, 201, 169, 166, 134])).
% 0.20/0.52 tff(218,plain,
% 0.20/0.52 (inverse(sk_c8) = inverse(sk_c1)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[217])).
% 0.20/0.52 tff(219,plain,
% 0.20/0.52 (inverse(sk_c8) = sk_c6),
% 0.20/0.52 inference(transitivity,[status(thm)],[218, 126, 132, 131, 68, 122, 113])).
% 0.20/0.52 tff(220,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[105, 219])).
% 0.20/0.52 tff(221,plain,(inverse(sk_c8) = sk_c6), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(222,plain,
% 0.20/0.52 (sk_c6 = inverse(sk_c8)),
% 0.20/0.52 inference(symmetry,[status(thm)],[221])).
% 0.20/0.52 tff(223,plain,
% 0.20/0.52 (multiply(sk_c6, multiply(sk_c7, sk_c6)) = multiply(inverse(sk_c8), sk_c8)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[222, 104])).
% 0.20/0.52 tff(224,plain,
% 0.20/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c7), sk_c6) = multiply(sk_c6, multiply(sk_c7, sk_c6)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(225,plain,
% 0.20/0.52 (multiply(multiply(sk_c6, sk_c7), sk_c6) = multiply(sk_c6, multiply(sk_c7, sk_c6))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[224, 38])).
% 0.20/0.52 tff(226,plain,
% 0.20/0.52 (multiply(multiply(sk_c6, sk_c7), sk_c6) = multiply(sk_c8, sk_c4)),
% 0.20/0.52 inference(transitivity,[status(thm)],[225, 223, 96, 94, 93])).
% 0.20/0.52 tff(227,plain,
% 0.20/0.52 (multiply(multiply(multiply(sk_c6, sk_c7), sk_c6), sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[226])).
% 0.20/0.52 tff(228,plain,
% 0.20/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c6, sk_c7), sk_c6), sk_c8) = multiply(multiply(sk_c6, sk_c7), multiply(sk_c6, sk_c8)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(229,plain,
% 0.20/0.52 (multiply(multiply(multiply(sk_c6, sk_c7), sk_c6), sk_c8) = multiply(multiply(sk_c6, sk_c7), multiply(sk_c6, sk_c8))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[228, 38])).
% 0.20/0.52 tff(230,plain,
% 0.20/0.52 (multiply(multiply(sk_c6, sk_c7), multiply(sk_c6, sk_c8)) = multiply(multiply(multiply(sk_c6, sk_c7), sk_c6), sk_c8)),
% 0.20/0.52 inference(symmetry,[status(thm)],[229])).
% 0.20/0.52 tff(231,plain,
% 0.20/0.52 (multiply(sk_c6, sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[222])).
% 0.20/0.52 tff(232,plain,
% 0.20/0.52 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c6, sk_c8)),
% 0.20/0.52 inference(symmetry,[status(thm)],[231])).
% 0.20/0.52 tff(233,plain,
% 0.20/0.52 (identity = multiply(sk_c6, sk_c8)),
% 0.20/0.52 inference(transitivity,[status(thm)],[163, 232])).
% 0.20/0.52 tff(234,plain,
% 0.20/0.52 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(sk_c8, multiply(sk_c4, sk_c8)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(235,plain,
% 0.20/0.52 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[234, 38])).
% 0.20/0.52 tff(236,plain,
% 0.20/0.52 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.20/0.52 inference(symmetry,[status(thm)],[235])).
% 0.20/0.52 tff(237,plain,
% 0.20/0.52 (((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))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(238,axiom,((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_4')).
% 0.20/0.52 tff(239,plain,
% 0.20/0.52 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c5)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.20/0.52 tff(240,plain,
% 0.20/0.52 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c5)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[239, 237])).
% 0.20/0.52 tff(241,plain,
% 0.20/0.52 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c5)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[240, 237])).
% 0.20/0.52 tff(242,plain,
% 0.20/0.52 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c5)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[241, 237])).
% 0.20/0.52 tff(243,plain,
% 0.20/0.52 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c4, sk_c8) = sk_c5)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[242, 237])).
% 0.20/0.52 tff(244,plain,
% 0.20/0.52 (multiply(sk_c4, sk_c8) = sk_c5),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[243, 80])).
% 0.20/0.52 tff(245,plain,
% 0.20/0.52 (sk_c5 = multiply(sk_c4, sk_c8)),
% 0.20/0.52 inference(symmetry,[status(thm)],[244])).
% 0.20/0.52 tff(246,plain,
% 0.20/0.52 (multiply(sk_c8, sk_c5) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[245])).
% 0.20/0.52 tff(247,assumption,(~(multiply(sk_c8, sk_c5) = sk_c7)), introduced(assumption)).
% 0.20/0.52 tff(248,plain,
% 0.20/0.52 (((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))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(249,axiom,((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c8, sk_c5) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_3')).
% 0.20/0.52 tff(250,plain,
% 0.20/0.52 ((multiply(sk_c7, sk_c8) = sk_c6) | (multiply(sk_c8, sk_c5) = sk_c7)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.20/0.52 tff(251,plain,
% 0.20/0.52 (multiply(sk_c7, sk_c8) = sk_c6),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[250, 247])).
% 0.20/0.52 tff(252,plain,
% 0.20/0.52 (((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c8, sk_c5) = sk_c7)) <=> ((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c8, sk_c5) = sk_c7))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(253,axiom,((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c8, sk_c5) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_8')).
% 0.20/0.52 tff(254,plain,
% 0.20/0.52 ((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c8, sk_c5) = sk_c7)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[253, 252])).
% 0.20/0.52 tff(255,plain,
% 0.20/0.52 (multiply(sk_c1, sk_c7) = sk_c8),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[254, 247])).
% 0.20/0.52 tff(256,plain,
% 0.20/0.52 (sk_c8 = multiply(sk_c1, sk_c7)),
% 0.20/0.52 inference(symmetry,[status(thm)],[255])).
% 0.20/0.52 tff(257,plain,
% 0.20/0.52 (multiply(sk_c7, sk_c8) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[256])).
% 0.20/0.52 tff(258,plain,
% 0.20/0.52 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(sk_c7, sk_c8)),
% 0.20/0.52 inference(symmetry,[status(thm)],[257])).
% 0.20/0.52 tff(259,plain,
% 0.20/0.52 (((inverse(sk_c1) = sk_c7) | (multiply(sk_c8, sk_c5) = sk_c7)) <=> ((inverse(sk_c1) = sk_c7) | (multiply(sk_c8, sk_c5) = sk_c7))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(260,axiom,((inverse(sk_c1) = sk_c7) | (multiply(sk_c8, sk_c5) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_13')).
% 0.20/0.52 tff(261,plain,
% 0.20/0.52 ((inverse(sk_c1) = sk_c7) | (multiply(sk_c8, sk_c5) = sk_c7)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.20/0.52 tff(262,plain,
% 0.20/0.52 (inverse(sk_c1) = sk_c7),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[261, 247])).
% 0.20/0.52 tff(263,plain,
% 0.20/0.52 (sk_c7 = inverse(sk_c1)),
% 0.20/0.52 inference(symmetry,[status(thm)],[262])).
% 0.20/0.52 tff(264,plain,
% 0.20/0.52 (multiply(sk_c7, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[263])).
% 0.20/0.52 tff(265,plain,
% 0.20/0.52 (multiply(sk_c7, sk_c1) = identity),
% 0.20/0.52 inference(transitivity,[status(thm)],[264, 58])).
% 0.20/0.52 tff(266,plain,
% 0.20/0.52 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(identity, sk_c7)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[265])).
% 0.20/0.52 tff(267,plain,
% 0.20/0.52 (multiply(identity, sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.20/0.52 inference(symmetry,[status(thm)],[266])).
% 0.20/0.52 tff(268,plain,
% 0.20/0.52 (((inverse(sk_c2) = sk_c8) | (multiply(sk_c8, sk_c5) = sk_c7)) <=> ((inverse(sk_c2) = sk_c8) | (multiply(sk_c8, sk_c5) = sk_c7))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(269,axiom,((inverse(sk_c2) = sk_c8) | (multiply(sk_c8, sk_c5) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_28')).
% 0.20/0.52 tff(270,plain,
% 0.20/0.52 ((inverse(sk_c2) = sk_c8) | (multiply(sk_c8, sk_c5) = sk_c7)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.20/0.52 tff(271,plain,
% 0.20/0.52 (inverse(sk_c2) = sk_c8),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[270, 247])).
% 0.20/0.52 tff(272,plain,
% 0.20/0.52 (sk_c8 = inverse(sk_c2)),
% 0.20/0.52 inference(symmetry,[status(thm)],[271])).
% 0.20/0.52 tff(273,plain,
% 0.20/0.52 (multiply(sk_c8, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[272])).
% 0.20/0.52 tff(274,plain,
% 0.20/0.52 (multiply(inverse(sk_c2), sk_c2) = multiply(sk_c8, sk_c2)),
% 0.20/0.52 inference(symmetry,[status(thm)],[273])).
% 0.20/0.52 tff(275,plain,
% 0.20/0.52 (identity = multiply(sk_c8, sk_c2)),
% 0.20/0.52 inference(transitivity,[status(thm)],[28, 274])).
% 0.20/0.52 tff(276,plain,
% 0.20/0.52 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c2), sk_c8)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[275])).
% 0.20/0.52 tff(277,plain,
% 0.20/0.52 (multiply(multiply(sk_c8, sk_c2), sk_c8) = multiply(identity, sk_c8)),
% 0.20/0.52 inference(symmetry,[status(thm)],[276])).
% 0.20/0.52 tff(278,plain,
% 0.20/0.52 (((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c8, sk_c5) = sk_c7)) <=> ((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c8, sk_c5) = sk_c7))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(279,axiom,((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c8, sk_c5) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_23')).
% 0.20/0.52 tff(280,plain,
% 0.20/0.52 ((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c8, sk_c5) = sk_c7)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.20/0.52 tff(281,plain,
% 0.20/0.52 (multiply(sk_c2, sk_c8) = sk_c3),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[280, 247])).
% 0.20/0.52 tff(282,plain,
% 0.20/0.52 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = multiply(sk_c8, sk_c3)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[281])).
% 0.20/0.53 tff(283,plain,
% 0.20/0.53 (multiply(sk_c8, sk_c3) = multiply(sk_c8, multiply(sk_c2, sk_c8))),
% 0.20/0.53 inference(symmetry,[status(thm)],[282])).
% 0.20/0.53 tff(284,plain,
% 0.20/0.53 (((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c8, sk_c5) = sk_c7)) <=> ((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c8, sk_c5) = sk_c7))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(285,axiom,((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c8, sk_c5) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_18')).
% 0.20/0.53 tff(286,plain,
% 0.20/0.53 ((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c8, sk_c5) = sk_c7)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.20/0.53 tff(287,plain,
% 0.20/0.53 (multiply(sk_c8, sk_c3) = sk_c7),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[286, 247])).
% 0.20/0.53 tff(288,plain,
% 0.20/0.53 (sk_c7 = multiply(sk_c8, sk_c3)),
% 0.20/0.53 inference(symmetry,[status(thm)],[287])).
% 0.20/0.53 tff(289,plain,
% 0.20/0.53 (sk_c7 = sk_c8),
% 0.20/0.53 inference(transitivity,[status(thm)],[288, 283, 41, 277, 10])).
% 0.20/0.53 tff(290,plain,
% 0.20/0.53 (multiply(sk_c7, sk_c2) = multiply(sk_c8, sk_c2)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[289])).
% 0.20/0.53 tff(291,plain,
% 0.20/0.53 (multiply(sk_c8, sk_c2) = multiply(sk_c7, sk_c2)),
% 0.20/0.53 inference(symmetry,[status(thm)],[290])).
% 0.20/0.53 tff(292,plain,
% 0.20/0.53 (identity = multiply(sk_c7, sk_c2)),
% 0.20/0.53 inference(transitivity,[status(thm)],[28, 274, 291])).
% 0.20/0.53 tff(293,plain,
% 0.20/0.53 (multiply(identity, sk_c1) = multiply(multiply(sk_c7, sk_c2), sk_c1)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[292])).
% 0.20/0.53 tff(294,plain,
% 0.20/0.53 (multiply(multiply(sk_c7, sk_c2), sk_c1) = multiply(identity, sk_c1)),
% 0.20/0.53 inference(symmetry,[status(thm)],[293])).
% 0.20/0.53 tff(295,plain,
% 0.20/0.53 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c2), sk_c1) = multiply(sk_c7, multiply(sk_c2, sk_c1)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(296,plain,
% 0.20/0.53 (multiply(multiply(sk_c7, sk_c2), sk_c1) = multiply(sk_c7, multiply(sk_c2, sk_c1))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[295, 38])).
% 0.20/0.53 tff(297,plain,
% 0.20/0.53 (multiply(sk_c7, multiply(sk_c2, sk_c1)) = multiply(multiply(sk_c7, sk_c2), sk_c1)),
% 0.20/0.53 inference(symmetry,[status(thm)],[296])).
% 0.20/0.53 tff(298,plain,
% 0.20/0.53 (multiply(sk_c7, sk_c7) = multiply(sk_c7, sk_c8)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[289])).
% 0.20/0.53 tff(299,plain,
% 0.20/0.53 (multiply(sk_c7, sk_c8) = multiply(sk_c7, sk_c7)),
% 0.20/0.53 inference(symmetry,[status(thm)],[298])).
% 0.20/0.53 tff(300,plain,
% 0.20/0.53 (sk_c7 = multiply(sk_c7, sk_c7)),
% 0.20/0.53 inference(transitivity,[status(thm)],[132, 267, 68, 258, 299])).
% 0.20/0.53 tff(301,plain,
% 0.20/0.53 (multiply(sk_c7, multiply(sk_c2, sk_c1)) = multiply(multiply(sk_c7, sk_c7), multiply(sk_c2, sk_c1))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[300])).
% 0.20/0.53 tff(302,plain,
% 0.20/0.53 (multiply(multiply(sk_c7, sk_c7), multiply(sk_c2, sk_c1)) = multiply(sk_c7, multiply(sk_c2, sk_c1))),
% 0.20/0.53 inference(symmetry,[status(thm)],[301])).
% 0.20/0.53 tff(303,plain,
% 0.20/0.53 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c7), multiply(sk_c2, sk_c1)) = multiply(sk_c7, multiply(sk_c7, multiply(sk_c2, sk_c1))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(304,plain,
% 0.20/0.53 (multiply(multiply(sk_c7, sk_c7), multiply(sk_c2, sk_c1)) = multiply(sk_c7, multiply(sk_c7, multiply(sk_c2, sk_c1)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[303, 38])).
% 0.20/0.53 tff(305,plain,
% 0.20/0.53 (multiply(sk_c7, multiply(sk_c7, multiply(sk_c2, sk_c1))) = multiply(multiply(sk_c7, sk_c7), multiply(sk_c2, sk_c1))),
% 0.20/0.53 inference(symmetry,[status(thm)],[304])).
% 0.20/0.53 tff(306,plain,
% 0.20/0.53 (multiply(sk_c7, multiply(sk_c2, sk_c1)) = sk_c1),
% 0.20/0.53 inference(transitivity,[status(thm)],[297, 294, 134])).
% 0.20/0.53 tff(307,plain,
% 0.20/0.53 (multiply(sk_c7, multiply(sk_c7, multiply(sk_c2, sk_c1))) = multiply(sk_c7, sk_c1)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[306])).
% 0.20/0.53 tff(308,plain,
% 0.20/0.53 (multiply(sk_c7, sk_c1) = multiply(sk_c7, multiply(sk_c7, multiply(sk_c2, sk_c1)))),
% 0.20/0.53 inference(symmetry,[status(thm)],[307])).
% 0.20/0.53 tff(309,plain,
% 0.20/0.53 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c7, sk_c1)),
% 0.20/0.53 inference(symmetry,[status(thm)],[264])).
% 0.20/0.53 tff(310,plain,
% 0.20/0.53 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c7), sk_c7) = identity)),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(311,plain,
% 0.20/0.53 (multiply(inverse(sk_c7), sk_c7) = identity),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[310, 25])).
% 0.20/0.53 tff(312,plain,
% 0.20/0.53 (inverse(sk_c7) = inverse(sk_c8)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[289])).
% 0.20/0.53 tff(313,plain,
% 0.20/0.53 (multiply(inverse(sk_c7), sk_c7) = multiply(inverse(sk_c8), multiply(sk_c7, sk_c7))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[312, 300])).
% 0.20/0.53 tff(314,plain,
% 0.20/0.53 (multiply(inverse(sk_c8), multiply(sk_c7, sk_c7)) = multiply(inverse(sk_c7), sk_c7)),
% 0.20/0.53 inference(symmetry,[status(thm)],[313])).
% 0.20/0.53 tff(315,plain,
% 0.20/0.53 (inverse(sk_c8) = inverse(sk_c7)),
% 0.20/0.53 inference(symmetry,[status(thm)],[312])).
% 0.20/0.53 tff(316,plain,
% 0.20/0.53 (multiply(inverse(sk_c8), sk_c7) = multiply(inverse(sk_c7), sk_c7)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[315])).
% 0.20/0.53 tff(317,plain,
% 0.20/0.53 (multiply(inverse(sk_c8), sk_c7) = multiply(sk_c7, sk_c1)),
% 0.20/0.53 inference(transitivity,[status(thm)],[316, 311, 191, 309])).
% 0.20/0.53 tff(318,plain,
% 0.20/0.53 (multiply(multiply(inverse(sk_c8), sk_c7), sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[317])).
% 0.20/0.53 tff(319,plain,
% 0.20/0.53 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(multiply(inverse(sk_c8), sk_c7), sk_c7)),
% 0.20/0.53 inference(symmetry,[status(thm)],[318])).
% 0.20/0.53 tff(320,plain,
% 0.20/0.53 (sk_c8 = sk_c1),
% 0.20/0.53 inference(transitivity,[status(thm)],[186, 276, 40, 282, 287, 132, 267, 319, 213, 314, 311, 191, 309, 308, 305, 302, 297, 294, 134])).
% 0.20/0.53 tff(321,plain,
% 0.20/0.53 (inverse(sk_c8) = inverse(sk_c1)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[320])).
% 0.20/0.53 tff(322,plain,
% 0.20/0.53 (inverse(sk_c8) = sk_c6),
% 0.20/0.53 inference(transitivity,[status(thm)],[321, 262, 132, 267, 68, 258, 251])).
% 0.20/0.53 tff(323,plain,
% 0.20/0.53 (multiply(sk_c7, sk_c1) = multiply(sk_c8, sk_c2)),
% 0.20/0.53 inference(transitivity,[status(thm)],[264, 58, 28, 274])).
% 0.20/0.53 tff(324,plain,
% 0.20/0.53 (multiply(multiply(sk_c7, sk_c1), sk_c8) = multiply(multiply(sk_c8, sk_c2), sk_c8)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[323])).
% 0.20/0.53 tff(325,plain,
% 0.20/0.53 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c1), sk_c8) = multiply(sk_c7, multiply(sk_c1, sk_c8)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(326,plain,
% 0.20/0.53 (multiply(multiply(sk_c7, sk_c1), sk_c8) = multiply(sk_c7, multiply(sk_c1, sk_c8))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[325, 38])).
% 0.20/0.53 tff(327,plain,
% 0.20/0.53 (multiply(sk_c7, multiply(sk_c1, sk_c8)) = multiply(multiply(sk_c7, sk_c1), sk_c8)),
% 0.20/0.53 inference(symmetry,[status(thm)],[326])).
% 0.20/0.53 tff(328,plain,
% 0.20/0.53 (sk_c8 = sk_c7),
% 0.20/0.53 inference(transitivity,[status(thm)],[186, 276, 40, 282, 287])).
% 0.20/0.53 tff(329,plain,
% 0.20/0.53 (multiply(sk_c8, multiply(sk_c1, sk_c8)) = multiply(sk_c7, multiply(sk_c1, sk_c8))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[328])).
% 0.20/0.53 tff(330,plain,
% 0.20/0.53 (multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7),
% 0.20/0.53 inference(transitivity,[status(thm)],[329, 327, 324, 40, 282, 287])).
% 0.20/0.53 tff(331,plain,
% 0.20/0.53 (inverse(sk_c1) = sk_c8),
% 0.20/0.53 inference(transitivity,[status(thm)],[262, 288, 283, 41, 277, 10])).
% 0.20/0.53 tff(332,plain,
% 0.20/0.53 (sk_c6 = multiply(sk_c7, sk_c8)),
% 0.20/0.53 inference(symmetry,[status(thm)],[251])).
% 0.20/0.53 tff(333,plain,
% 0.20/0.53 (sk_c6 = sk_c8),
% 0.20/0.53 inference(transitivity,[status(thm)],[332, 257, 69, 266, 56, 288, 283, 41, 277, 10])).
% 0.20/0.53 tff(334,plain,
% 0.20/0.53 (multiply(sk_c7, sk_c6) = multiply(sk_c7, sk_c8)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[333])).
% 0.20/0.53 tff(335,plain,
% 0.20/0.53 (multiply(sk_c7, sk_c6) = sk_c8),
% 0.20/0.53 inference(transitivity,[status(thm)],[334, 257, 69, 266, 56, 288, 283, 41, 277, 10])).
% 0.20/0.53 tff(336,plain,
% 0.20/0.53 (^[X3: $i, X2: $i, X5: $i] : refl(((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(337,plain,
% 0.20/0.53 (![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7))) <=> ![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[336])).
% 0.20/0.53 tff(338,plain,
% 0.20/0.53 (![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7))) <=> ![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(339,plain,
% 0.20/0.53 (^[X3: $i, X2: $i, X5: $i] : rewrite(((~(multiply(X3, sk_c7) = sk_c8)) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(340,plain,
% 0.20/0.53 (![X3: $i, X2: $i, X5: $i] : ((~(multiply(X3, sk_c7) = sk_c8)) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7))) <=> ![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[339])).
% 0.20/0.53 tff(341,plain,
% 0.20/0.53 (![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(X3, sk_c7) = sk_c8)) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7))) <=> ![X3: $i, X2: $i, X5: $i] : ((~(multiply(X3, sk_c7) = sk_c8)) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))),
% 0.20/0.53 inference(elim_unused_vars,[status(thm)],[])).
% 0.20/0.53 tff(342,plain,
% 0.20/0.53 (![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = X1)) | (~(multiply(sk_c8, X1) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) <=> ![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(X3, sk_c7) = sk_c8)) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))),
% 0.20/0.53 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.20/0.53 tff(343,plain,
% 0.20/0.53 (![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = X1)) | (~(multiply(sk_c8, X1) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) <=> ![X3: $i, X2: $i, X5: $i] : ((~(multiply(X3, sk_c7) = sk_c8)) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))),
% 0.20/0.53 inference(transitivity,[status(thm)],[342, 341])).
% 0.20/0.53 tff(344,plain,
% 0.20/0.53 (![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = X1)) | (~(multiply(sk_c8, X1) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) <=> ![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))),
% 0.20/0.53 inference(transitivity,[status(thm)],[343, 340])).
% 0.20/0.53 tff(345,plain,
% 0.20/0.53 (^[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_c8))) | (~(inverse(X3) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))), (((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) <=> (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X4) = sk_c7))))), rewrite((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X4) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))), (((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))))), ((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) <=> (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(multiply(X5, sk_c8) = X4))))), rewrite((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(multiply(X5, sk_c8) = X4))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))), ((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))))), (((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) | (~(inverse(X5) = sk_c8))) <=> (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X5) = sk_c8))))), rewrite((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X5) = sk_c8))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))), (((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) | (~(inverse(X5) = sk_c8))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))))), ((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) | (~(inverse(X5) = sk_c8))) | (~(multiply(sk_c7, sk_c6) = sk_c8))) <=> (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(multiply(sk_c7, sk_c6) = sk_c8))))), rewrite((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(multiply(sk_c7, sk_c6) = sk_c8))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))), ((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) | (~(inverse(X5) = sk_c8))) | (~(multiply(sk_c7, sk_c6) = sk_c8))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))))), (((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) | (~(inverse(X5) = sk_c8))) | (~(multiply(sk_c7, sk_c6) = sk_c8))) | (~(inverse(sk_c8) = sk_c6))) <=> (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(sk_c8) = sk_c6))))), rewrite((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(sk_c8) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))), (((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) | (~(inverse(X5) = sk_c8))) | (~(multiply(sk_c7, sk_c6) = sk_c8))) | (~(inverse(sk_c8) = sk_c6))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))))), ((((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) | (~(inverse(X5) = sk_c8))) | (~(multiply(sk_c7, sk_c6) = sk_c8))) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c8, X1) = sk_c7))) <=> (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X1) = sk_c7))))), rewrite((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X1) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c8, X1) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))), ((((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) | (~(inverse(X5) = sk_c8))) | (~(multiply(sk_c7, sk_c6) = sk_c8))) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c8, X1) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c8, X1) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))))), (((((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) | (~(inverse(X5) = sk_c8))) | (~(multiply(sk_c7, sk_c6) = sk_c8))) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c8, X1) = sk_c7))) | (~(multiply(X2, sk_c8) = X1))) <=> (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c8, X1) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(multiply(X2, sk_c8) = X1))))), rewrite((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c8, X1) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(multiply(X2, sk_c8) = X1))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(X2, sk_c8) = X1)) | (~(multiply(sk_c8, X1) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))), (((((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) | (~(inverse(X5) = sk_c8))) | (~(multiply(sk_c7, sk_c6) = sk_c8))) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c8, X1) = sk_c7))) | (~(multiply(X2, sk_c8) = X1))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(X2, sk_c8) = X1)) | (~(multiply(sk_c8, X1) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))))), ((((((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) | (~(inverse(X5) = sk_c8))) | (~(multiply(sk_c7, sk_c6) = sk_c8))) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c8, X1) = sk_c7))) | (~(multiply(X2, sk_c8) = X1))) | (~(inverse(X2) = sk_c8))) <=> (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(X2, sk_c8) = X1)) | (~(multiply(sk_c8, X1) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X2) = sk_c8))))), rewrite((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(X2, sk_c8) = X1)) | (~(multiply(sk_c8, X1) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X2) = sk_c8))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = X1)) | (~(multiply(sk_c8, X1) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))), ((((((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) | (~(inverse(X5) = sk_c8))) | (~(multiply(sk_c7, sk_c6) = sk_c8))) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c8, X1) = sk_c7))) | (~(multiply(X2, sk_c8) = X1))) | (~(inverse(X2) = sk_c8))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = X1)) | (~(multiply(sk_c8, X1) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(346,plain,
% 0.20/0.54 (![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : (((((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) | (~(inverse(X5) = sk_c8))) | (~(multiply(sk_c7, sk_c6) = sk_c8))) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c8, X1) = sk_c7))) | (~(multiply(X2, sk_c8) = X1))) | (~(inverse(X2) = sk_c8))) <=> ![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(X2, sk_c8) = X1)) | (~(multiply(sk_c8, X1) = sk_c7)) | (~(inverse(X5) = sk_c8)) | (~(multiply(X5, sk_c8) = X4)) | (~(multiply(sk_c8, X4) = sk_c7)) | (~(inverse(X3) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[345])).
% 0.20/0.54 tff(347,plain,
% 0.20/0.54 (![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : (((((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) | (~(inverse(X5) = sk_c8))) | (~(multiply(sk_c7, sk_c6) = sk_c8))) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c8, X1) = sk_c7))) | (~(multiply(X2, sk_c8) = X1))) | (~(inverse(X2) = sk_c8))) <=> ![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))),
% 0.20/0.54 inference(transitivity,[status(thm)],[346, 344])).
% 0.20/0.54 tff(348,axiom,(![X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : (((((((((((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(X3, sk_c7) = sk_c8))) | (~(inverse(X3) = sk_c7))) | (~(multiply(sk_c8, X4) = sk_c7))) | (~(multiply(X5, sk_c8) = X4))) | (~(inverse(X5) = sk_c8))) | (~(multiply(sk_c7, sk_c6) = sk_c8))) | (~(inverse(sk_c8) = sk_c6))) | (~(multiply(sk_c8, X1) = sk_c7))) | (~(multiply(X2, sk_c8) = X1))) | (~(inverse(X2) = sk_c8)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_31')).
% 0.20/0.54 tff(349,plain,
% 0.20/0.54 (![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[348, 347])).
% 0.20/0.54 tff(350,plain,
% 0.20/0.54 (![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[349, 338])).
% 0.20/0.54 tff(351,plain,(
% 0.20/0.54 ![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))),
% 0.20/0.54 inference(skolemize,[status(sab)],[350])).
% 0.20/0.54 tff(352,plain,
% 0.20/0.54 (![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[351, 337])).
% 0.20/0.54 tff(353,plain,
% 0.20/0.54 (((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)))) <=> ((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(354,plain,
% 0.20/0.54 (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(355,plain,
% 0.20/0.54 (((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)))) <=> ((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[354])).
% 0.20/0.54 tff(356,plain,
% 0.20/0.54 (((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)))) <=> ((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7)))),
% 0.20/0.54 inference(transitivity,[status(thm)],[355, 353])).
% 0.20/0.54 tff(357,plain,
% 0.20/0.54 ((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c7)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(358,plain,
% 0.20/0.55 ((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c7))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[357, 356])).
% 0.20/0.55 tff(359,plain,
% 0.20/0.55 ((~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[358, 251, 255, 262, 352])).
% 0.20/0.55 tff(360,plain,
% 0.20/0.55 (~(inverse(sk_c8) = sk_c6)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[359, 335, 331, 330])).
% 0.20/0.55 tff(361,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[360, 322])).
% 0.20/0.55 tff(362,plain,(multiply(sk_c8, sk_c5) = sk_c7), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(363,plain,
% 0.20/0.55 (sk_c7 = multiply(sk_c8, sk_c5)),
% 0.20/0.55 inference(symmetry,[status(thm)],[362])).
% 0.20/0.55 tff(364,plain,
% 0.20/0.55 (sk_c7 = sk_c8),
% 0.20/0.55 inference(transitivity,[status(thm)],[363, 246, 236, 92, 10])).
% 0.20/0.55 tff(365,plain,
% 0.20/0.55 (multiply(sk_c6, sk_c7) = multiply(inverse(sk_c8), sk_c8)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[222, 364])).
% 0.20/0.55 tff(366,plain,
% 0.20/0.55 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c6, sk_c7)),
% 0.20/0.55 inference(symmetry,[status(thm)],[365])).
% 0.20/0.55 tff(367,plain,
% 0.20/0.55 (identity = multiply(sk_c6, sk_c7)),
% 0.20/0.55 inference(transitivity,[status(thm)],[163, 366])).
% 0.20/0.55 tff(368,plain,
% 0.20/0.55 (multiply(identity, identity) = multiply(multiply(sk_c6, sk_c7), multiply(sk_c6, sk_c8))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[367, 233])).
% 0.20/0.55 tff(369,plain,
% 0.20/0.55 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, identity) = identity)),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(370,plain,
% 0.20/0.55 (multiply(identity, identity) = identity),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[369, 8])).
% 0.20/0.55 tff(371,plain,
% 0.20/0.55 (identity = multiply(identity, identity)),
% 0.20/0.55 inference(symmetry,[status(thm)],[370])).
% 0.20/0.55 tff(372,plain,
% 0.20/0.55 (multiply(identity, sk_c6) = multiply(multiply(sk_c6, sk_c7), sk_c6)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[367])).
% 0.20/0.55 tff(373,plain,
% 0.20/0.55 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c6) = sk_c6)),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(374,plain,
% 0.20/0.55 (multiply(identity, sk_c6) = sk_c6),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[373, 8])).
% 0.20/0.55 tff(375,plain,
% 0.20/0.55 (sk_c6 = multiply(identity, sk_c6)),
% 0.20/0.55 inference(symmetry,[status(thm)],[374])).
% 0.20/0.55 tff(376,plain,
% 0.20/0.55 (sk_c6 = sk_c8),
% 0.20/0.55 inference(transitivity,[status(thm)],[375, 372, 225, 223, 96, 371, 368, 230, 227, 92, 10])).
% 0.20/0.55 tff(377,plain,
% 0.20/0.55 (multiply(sk_c8, sk_c7) = multiply(sk_c8, sk_c8)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[364])).
% 0.20/0.55 tff(378,plain,
% 0.20/0.55 (multiply(sk_c8, sk_c8) = multiply(sk_c8, sk_c7)),
% 0.20/0.55 inference(symmetry,[status(thm)],[377])).
% 0.20/0.55 tff(379,plain,
% 0.20/0.55 (multiply(sk_c7, sk_c8) = multiply(sk_c8, sk_c8)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[364])).
% 0.20/0.55 tff(380,plain,
% 0.20/0.55 (multiply(sk_c7, sk_c8) = multiply(sk_c8, sk_c7)),
% 0.20/0.55 inference(transitivity,[status(thm)],[379, 378])).
% 0.20/0.55 tff(381,plain,
% 0.20/0.55 ((multiply(sk_c7, sk_c8) = sk_c6) <=> (multiply(sk_c8, sk_c7) = sk_c8)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[380, 376])).
% 0.20/0.55 tff(382,plain,
% 0.20/0.55 ((multiply(sk_c8, sk_c7) = sk_c8) <=> (multiply(sk_c7, sk_c8) = sk_c6)),
% 0.20/0.55 inference(symmetry,[status(thm)],[381])).
% 0.20/0.55 tff(383,plain,
% 0.20/0.55 (multiply(multiply(sk_c6, sk_c7), multiply(sk_c6, sk_c8)) = multiply(identity, identity)),
% 0.20/0.55 inference(symmetry,[status(thm)],[368])).
% 0.20/0.55 tff(384,plain,
% 0.20/0.55 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(multiply(multiply(sk_c6, sk_c7), sk_c6), sk_c8)),
% 0.20/0.55 inference(symmetry,[status(thm)],[227])).
% 0.20/0.55 tff(385,plain,
% 0.20/0.55 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.20/0.55 inference(symmetry,[status(thm)],[92])).
% 0.20/0.55 tff(386,plain,
% 0.20/0.55 (sk_c8 = multiply(sk_c8, sk_c4)),
% 0.20/0.55 inference(transitivity,[status(thm)],[186, 385, 384, 229, 383, 370, 94, 93])).
% 0.20/0.55 tff(387,plain,
% 0.20/0.55 (multiply(sk_c8, sk_c8) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[386])).
% 0.20/0.55 tff(388,plain,
% 0.20/0.55 (multiply(sk_c8, sk_c7) = sk_c8),
% 0.20/0.55 inference(transitivity,[status(thm)],[377, 387, 92, 10])).
% 0.20/0.55 tff(389,plain,
% 0.20/0.55 (multiply(sk_c7, sk_c8) = sk_c6),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[388, 382])).
% 0.20/0.55 tff(390,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[80, 389])).
% 0.20/0.55 tff(391,plain,(multiply(sk_c7, sk_c8) = sk_c6), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(392,plain,
% 0.20/0.55 (sk_c6 = multiply(sk_c7, sk_c8)),
% 0.20/0.55 inference(symmetry,[status(thm)],[391])).
% 0.20/0.55 tff(393,plain,
% 0.20/0.55 (sk_c6 = sk_c7),
% 0.20/0.55 inference(transitivity,[status(thm)],[392, 75, 69, 66, 56])).
% 0.20/0.55 tff(394,plain,
% 0.20/0.55 (multiply(sk_c7, sk_c6) = multiply(sk_c7, sk_c7)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[393])).
% 0.20/0.55 tff(395,plain,
% 0.20/0.55 (multiply(sk_c7, sk_c6) = sk_c8),
% 0.20/0.55 inference(transitivity,[status(thm)],[394, 77, 75, 69, 66, 56, 54, 47, 41, 31, 10])).
% 0.20/0.55 tff(396,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[11, 395])).
% 0.20/0.55 tff(397,plain,(multiply(sk_c7, sk_c6) = sk_c8), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(398,plain,
% 0.20/0.55 (multiply(sk_c5, multiply(sk_c7, sk_c6)) = multiply(sk_c5, sk_c8)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[397])).
% 0.20/0.55 tff(399,plain,
% 0.20/0.55 (multiply(sk_c8, multiply(sk_c5, multiply(sk_c7, sk_c6))) = multiply(sk_c8, multiply(sk_c5, sk_c8))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[398])).
% 0.20/0.55 tff(400,plain,
% 0.20/0.55 (multiply(sk_c8, multiply(sk_c5, sk_c8)) = multiply(sk_c8, multiply(sk_c5, multiply(sk_c7, sk_c6)))),
% 0.20/0.55 inference(symmetry,[status(thm)],[399])).
% 0.20/0.55 tff(401,plain,
% 0.20/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c5), sk_c8) = multiply(sk_c8, multiply(sk_c5, sk_c8)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(402,plain,
% 0.20/0.55 (multiply(multiply(sk_c8, sk_c5), sk_c8) = multiply(sk_c8, multiply(sk_c5, sk_c8))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[401, 38])).
% 0.20/0.55 tff(403,plain,
% 0.20/0.55 (multiply(multiply(sk_c8, sk_c5), sk_c8) = multiply(sk_c7, sk_c8)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[362])).
% 0.20/0.55 tff(404,plain,
% 0.20/0.55 (multiply(sk_c7, sk_c8) = multiply(multiply(sk_c8, sk_c5), sk_c8)),
% 0.20/0.55 inference(symmetry,[status(thm)],[403])).
% 0.20/0.55 tff(405,plain,
% 0.20/0.55 (sk_c6 = multiply(sk_c8, multiply(sk_c5, multiply(sk_c7, sk_c6)))),
% 0.20/0.55 inference(transitivity,[status(thm)],[392, 404, 402, 400])).
% 0.20/0.55 tff(406,plain,
% 0.20/0.55 (multiply(sk_c6, sk_c7) = multiply(multiply(sk_c8, multiply(sk_c5, multiply(sk_c7, sk_c6))), sk_c7)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[405])).
% 0.20/0.55 tff(407,plain,
% 0.20/0.55 (multiply(multiply(sk_c8, multiply(sk_c5, multiply(sk_c7, sk_c6))), sk_c7) = multiply(sk_c6, sk_c7)),
% 0.20/0.55 inference(symmetry,[status(thm)],[406])).
% 0.20/0.55 tff(408,plain,
% 0.20/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, multiply(sk_c5, multiply(sk_c7, sk_c6))), sk_c7) = multiply(sk_c8, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c7)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(409,plain,
% 0.20/0.55 (multiply(multiply(sk_c8, multiply(sk_c5, multiply(sk_c7, sk_c6))), sk_c7) = multiply(sk_c8, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c7))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[408, 38])).
% 0.20/0.55 tff(410,plain,
% 0.20/0.55 (multiply(sk_c8, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c7)) = multiply(multiply(sk_c8, multiply(sk_c5, multiply(sk_c7, sk_c6))), sk_c7)),
% 0.20/0.55 inference(symmetry,[status(thm)],[409])).
% 0.20/0.55 tff(411,plain,
% 0.20/0.55 (multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c7) = multiply(multiply(sk_c5, sk_c8), sk_c7)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[398])).
% 0.20/0.55 tff(412,plain,
% 0.20/0.55 (multiply(sk_c8, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c7)) = multiply(sk_c8, multiply(multiply(sk_c5, sk_c8), sk_c7))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[411])).
% 0.20/0.55 tff(413,plain,
% 0.20/0.55 (multiply(sk_c8, multiply(multiply(sk_c5, sk_c8), sk_c7)) = multiply(sk_c8, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c7))),
% 0.20/0.55 inference(symmetry,[status(thm)],[412])).
% 0.20/0.55 tff(414,plain,
% 0.20/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, sk_c8), sk_c7) = multiply(sk_c5, multiply(sk_c8, sk_c7)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(415,plain,
% 0.20/0.55 (multiply(multiply(sk_c5, sk_c8), sk_c7) = multiply(sk_c5, multiply(sk_c8, sk_c7))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[414, 38])).
% 0.20/0.55 tff(416,plain,
% 0.20/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, multiply(sk_c5, multiply(sk_c7, sk_c6))), multiply(sk_c5, multiply(sk_c8, sk_c8))) = multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(417,plain,
% 0.20/0.55 (multiply(multiply(sk_c6, multiply(sk_c5, multiply(sk_c7, sk_c6))), multiply(sk_c5, multiply(sk_c8, sk_c8))) = multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[416, 38])).
% 0.20/0.55 tff(418,plain,
% 0.20/0.55 (multiply(sk_c8, multiply(sk_c5, sk_c8)) = multiply(multiply(sk_c8, sk_c5), sk_c8)),
% 0.20/0.55 inference(symmetry,[status(thm)],[402])).
% 0.20/0.55 tff(419,plain,
% 0.20/0.55 (multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c6),
% 0.20/0.55 inference(transitivity,[status(thm)],[418, 403, 391])).
% 0.20/0.55 tff(420,plain,
% 0.20/0.55 (multiply(sk_c7, multiply(sk_c8, multiply(sk_c5, sk_c8))) = multiply(sk_c7, sk_c6)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[419])).
% 0.20/0.55 tff(421,plain,
% 0.20/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c8), multiply(sk_c5, sk_c8)) = multiply(sk_c7, multiply(sk_c8, multiply(sk_c5, sk_c8))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(422,plain,
% 0.20/0.55 (multiply(multiply(sk_c7, sk_c8), multiply(sk_c5, sk_c8)) = multiply(sk_c7, multiply(sk_c8, multiply(sk_c5, sk_c8)))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[421, 38])).
% 0.20/0.55 tff(423,plain,
% 0.20/0.55 (multiply(sk_c6, multiply(sk_c5, multiply(sk_c7, sk_c6))) = multiply(multiply(sk_c7, sk_c8), multiply(sk_c5, sk_c8))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[392, 398])).
% 0.20/0.55 tff(424,plain,
% 0.20/0.55 (multiply(sk_c6, multiply(sk_c5, multiply(sk_c7, sk_c6))) = sk_c8),
% 0.20/0.55 inference(transitivity,[status(thm)],[423, 422, 420, 397])).
% 0.20/0.55 tff(425,plain,
% 0.20/0.55 (multiply(multiply(sk_c6, multiply(sk_c5, multiply(sk_c7, sk_c6))), multiply(sk_c5, multiply(sk_c8, sk_c8))) = multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c8)))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[424])).
% 0.20/0.55 tff(426,plain,
% 0.20/0.55 (multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c8))) = multiply(multiply(sk_c6, multiply(sk_c5, multiply(sk_c7, sk_c6))), multiply(sk_c5, multiply(sk_c8, sk_c8)))),
% 0.20/0.55 inference(symmetry,[status(thm)],[425])).
% 0.20/0.55 tff(427,plain,
% 0.20/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c5), multiply(sk_c8, sk_c8)) = multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c8))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(428,plain,
% 0.20/0.55 (multiply(multiply(sk_c8, sk_c5), multiply(sk_c8, sk_c8)) = multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c8)))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[427, 38])).
% 0.20/0.55 tff(429,plain,
% 0.20/0.55 (multiply(multiply(sk_c8, sk_c5), multiply(sk_c8, sk_c8)) = multiply(sk_c7, multiply(sk_c8, sk_c8))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[362])).
% 0.20/0.55 tff(430,plain,
% 0.20/0.55 (multiply(sk_c7, multiply(sk_c8, sk_c8)) = multiply(multiply(sk_c8, sk_c5), multiply(sk_c8, sk_c8))),
% 0.20/0.55 inference(symmetry,[status(thm)],[429])).
% 0.20/0.55 tff(431,plain,
% 0.20/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c8), sk_c8) = multiply(sk_c7, multiply(sk_c8, sk_c8)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(432,plain,
% 0.20/0.55 (multiply(multiply(sk_c7, sk_c8), sk_c8) = multiply(sk_c7, multiply(sk_c8, sk_c8))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[431, 38])).
% 0.20/0.55 tff(433,plain,
% 0.20/0.55 (multiply(sk_c7, sk_c8) = inverse(sk_c8)),
% 0.20/0.55 inference(transitivity,[status(thm)],[391, 222])).
% 0.20/0.55 tff(434,plain,
% 0.20/0.55 (multiply(multiply(sk_c7, sk_c8), sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[433])).
% 0.20/0.55 tff(435,plain,
% 0.20/0.55 (multiply(inverse(sk_c8), sk_c8) = multiply(multiply(sk_c7, sk_c8), sk_c8)),
% 0.20/0.55 inference(symmetry,[status(thm)],[434])).
% 0.20/0.55 tff(436,plain,
% 0.20/0.55 (identity = multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))),
% 0.20/0.55 inference(transitivity,[status(thm)],[163, 435, 432, 430, 428, 426, 417])).
% 0.20/0.55 tff(437,plain,
% 0.20/0.55 (multiply(sk_c5, identity) = multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[436])).
% 0.20/0.55 tff(438,plain,
% 0.20/0.55 (multiply(sk_c6, sk_c8) = identity),
% 0.20/0.55 inference(transitivity,[status(thm)],[231, 96])).
% 0.20/0.55 tff(439,plain,
% 0.20/0.55 (multiply(sk_c5, multiply(sk_c6, sk_c8)) = multiply(sk_c5, identity)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[438])).
% 0.20/0.55 tff(440,plain,
% 0.20/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, sk_c6), sk_c8) = multiply(sk_c5, multiply(sk_c6, sk_c8)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(441,plain,
% 0.20/0.55 (multiply(multiply(sk_c5, sk_c6), sk_c8) = multiply(sk_c5, multiply(sk_c6, sk_c8))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[440, 38])).
% 0.20/0.55 tff(442,plain,
% 0.20/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c7), sk_c6) = multiply(sk_c7, multiply(sk_c7, sk_c6)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(443,plain,
% 0.20/0.55 (multiply(multiply(sk_c7, sk_c7), sk_c6) = multiply(sk_c7, multiply(sk_c7, sk_c6))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[442, 38])).
% 0.20/0.55 tff(444,plain,
% 0.20/0.55 (multiply(sk_c7, multiply(sk_c7, sk_c6)) = multiply(multiply(sk_c7, sk_c7), sk_c6)),
% 0.20/0.55 inference(symmetry,[status(thm)],[443])).
% 0.20/0.55 tff(445,plain,
% 0.20/0.55 (multiply(sk_c7, multiply(sk_c7, sk_c6)) = multiply(sk_c7, sk_c8)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[397])).
% 0.20/0.55 tff(446,plain,
% 0.20/0.55 (multiply(sk_c7, sk_c8) = multiply(sk_c7, multiply(sk_c7, sk_c6))),
% 0.20/0.55 inference(symmetry,[status(thm)],[445])).
% 0.20/0.55 tff(447,plain,
% 0.20/0.55 (sk_c6 = multiply(multiply(sk_c7, sk_c7), sk_c6)),
% 0.20/0.55 inference(transitivity,[status(thm)],[392, 446, 444])).
% 0.20/0.55 tff(448,plain,
% 0.20/0.55 (multiply(sk_c5, sk_c6) = multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[447])).
% 0.20/0.55 tff(449,plain,
% 0.20/0.55 (multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)) = multiply(sk_c5, sk_c6)),
% 0.20/0.55 inference(symmetry,[status(thm)],[448])).
% 0.20/0.55 tff(450,plain,
% 0.20/0.55 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))) = multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(451,plain,
% 0.20/0.55 (multiply(identity, multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))) = multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[450, 8])).
% 0.20/0.55 tff(452,plain,
% 0.20/0.55 (multiply(identity, multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))) = multiply(multiply(sk_c6, sk_c8), multiply(sk_c5, sk_c6))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[233, 449])).
% 0.20/0.55 tff(453,plain,
% 0.20/0.55 (multiply(multiply(sk_c6, sk_c8), multiply(sk_c5, sk_c6)) = multiply(identity, multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)))),
% 0.20/0.55 inference(symmetry,[status(thm)],[452])).
% 0.20/0.55 tff(454,plain,
% 0.20/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c8), multiply(sk_c5, sk_c6)) = multiply(sk_c6, multiply(sk_c8, multiply(sk_c5, sk_c6))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(455,plain,
% 0.20/0.55 (multiply(multiply(sk_c6, sk_c8), multiply(sk_c5, sk_c6)) = multiply(sk_c6, multiply(sk_c8, multiply(sk_c5, sk_c6)))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[454, 38])).
% 0.20/0.55 tff(456,plain,
% 0.20/0.55 (multiply(sk_c6, multiply(sk_c8, multiply(sk_c5, sk_c6))) = multiply(multiply(sk_c6, sk_c8), multiply(sk_c5, sk_c6))),
% 0.20/0.55 inference(symmetry,[status(thm)],[455])).
% 0.20/0.55 tff(457,plain,
% 0.20/0.55 (multiply(multiply(sk_c8, sk_c5), sk_c6) = multiply(sk_c7, sk_c6)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[362])).
% 0.20/0.55 tff(458,plain,
% 0.20/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c5), sk_c6) = multiply(sk_c8, multiply(sk_c5, sk_c6)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(459,plain,
% 0.20/0.55 (multiply(multiply(sk_c8, sk_c5), sk_c6) = multiply(sk_c8, multiply(sk_c5, sk_c6))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[458, 38])).
% 0.20/0.55 tff(460,plain,
% 0.20/0.55 (multiply(sk_c8, multiply(sk_c5, sk_c6)) = multiply(multiply(sk_c8, sk_c5), sk_c6)),
% 0.20/0.55 inference(symmetry,[status(thm)],[459])).
% 0.20/0.55 tff(461,plain,
% 0.20/0.55 (multiply(sk_c8, multiply(sk_c5, sk_c6)) = sk_c8),
% 0.20/0.55 inference(transitivity,[status(thm)],[460, 457, 397])).
% 0.20/0.55 tff(462,plain,
% 0.20/0.55 (multiply(sk_c6, multiply(sk_c8, multiply(sk_c5, sk_c6))) = multiply(inverse(sk_c8), sk_c8)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[222, 461])).
% 0.20/0.55 tff(463,plain,
% 0.20/0.55 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c6, multiply(sk_c8, multiply(sk_c5, sk_c6)))),
% 0.20/0.55 inference(symmetry,[status(thm)],[462])).
% 0.20/0.55 tff(464,plain,
% 0.20/0.55 (identity = multiply(sk_c5, sk_c6)),
% 0.20/0.55 inference(transitivity,[status(thm)],[163, 463, 456, 453, 451, 449])).
% 0.20/0.55 tff(465,plain,
% 0.20/0.55 (multiply(identity, sk_c8) = multiply(multiply(sk_c5, sk_c6), sk_c8)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[464])).
% 0.20/0.55 tff(466,plain,
% 0.20/0.55 (sk_c8 = multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))),
% 0.20/0.55 inference(transitivity,[status(thm)],[186, 465, 441, 439, 437])).
% 0.20/0.55 tff(467,plain,
% 0.20/0.55 (multiply(sk_c8, multiply(multiply(sk_c5, sk_c8), sk_c7)) = multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c5, multiply(sk_c8, sk_c7)))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[466, 415])).
% 0.20/0.55 tff(468,plain,
% 0.20/0.55 (multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c5, multiply(sk_c8, sk_c7))) = multiply(sk_c8, multiply(multiply(sk_c5, sk_c8), sk_c7))),
% 0.20/0.55 inference(symmetry,[status(thm)],[467])).
% 0.20/0.55 tff(469,plain,
% 0.20/0.55 (multiply(multiply(sk_c5, sk_c6), sk_c8) = multiply(identity, sk_c8)),
% 0.20/0.55 inference(symmetry,[status(thm)],[465])).
% 0.20/0.55 tff(470,plain,
% 0.20/0.55 (multiply(sk_c5, multiply(sk_c6, sk_c8)) = multiply(multiply(sk_c5, sk_c6), sk_c8)),
% 0.20/0.55 inference(symmetry,[status(thm)],[441])).
% 0.20/0.55 tff(471,plain,
% 0.20/0.55 (multiply(sk_c5, identity) = multiply(sk_c5, multiply(sk_c6, sk_c8))),
% 0.20/0.55 inference(symmetry,[status(thm)],[439])).
% 0.20/0.55 tff(472,plain,
% 0.20/0.55 (multiply(sk_c7, multiply(sk_c8, sk_c8)) = multiply(multiply(sk_c8, sk_c5), multiply(sk_c8, sk_c8))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[363])).
% 0.20/0.55 tff(473,plain,
% 0.20/0.55 (inverse(sk_c8) = multiply(sk_c7, sk_c8)),
% 0.20/0.55 inference(transitivity,[status(thm)],[221, 392])).
% 0.20/0.55 tff(474,plain,
% 0.20/0.55 (multiply(inverse(sk_c8), sk_c8) = multiply(multiply(sk_c7, sk_c8), sk_c8)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[473])).
% 0.20/0.55 tff(475,plain,
% 0.20/0.55 (identity = multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))),
% 0.20/0.55 inference(transitivity,[status(thm)],[163, 474, 432, 472, 428, 426, 417])).
% 0.20/0.55 tff(476,plain,
% 0.20/0.55 (multiply(sk_c5, identity) = multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[475])).
% 0.20/0.55 tff(477,plain,
% 0.20/0.55 (multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))) = multiply(sk_c5, identity)),
% 0.20/0.55 inference(symmetry,[status(thm)],[476])).
% 0.20/0.55 tff(478,plain,
% 0.20/0.55 (multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))) = sk_c8),
% 0.20/0.55 inference(transitivity,[status(thm)],[477, 471, 470, 469, 10])).
% 0.20/0.55 tff(479,plain,
% 0.20/0.55 (inverse(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = inverse(sk_c8)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[478])).
% 0.20/0.55 tff(480,plain,
% 0.20/0.55 ((inverse(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = sk_c7) <=> (inverse(sk_c8) = sk_c7)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[479])).
% 0.20/0.55 tff(481,plain,
% 0.20/0.55 ((inverse(sk_c8) = sk_c7) <=> (inverse(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = sk_c7)),
% 0.20/0.55 inference(symmetry,[status(thm)],[480])).
% 0.20/0.55 tff(482,plain,
% 0.20/0.55 (multiply(identity, sk_c7) = multiply(multiply(sk_c5, sk_c6), sk_c7)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[464])).
% 0.20/0.55 tff(483,plain,
% 0.20/0.55 (multiply(multiply(sk_c5, sk_c6), sk_c7) = multiply(identity, sk_c7)),
% 0.20/0.55 inference(symmetry,[status(thm)],[482])).
% 0.20/0.55 tff(484,plain,
% 0.20/0.55 (multiply(multiply(sk_c5, sk_c6), sk_c7) = multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c8, sk_c5))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[448, 363])).
% 0.20/0.55 tff(485,plain,
% 0.20/0.55 (multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c8, sk_c5)) = multiply(multiply(sk_c5, sk_c6), sk_c7)),
% 0.20/0.55 inference(symmetry,[status(thm)],[484])).
% 0.20/0.55 tff(486,plain,
% 0.20/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), sk_c8), sk_c5) = multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c8, sk_c5)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(487,plain,
% 0.20/0.55 (multiply(multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), sk_c8), sk_c5) = multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c8, sk_c5))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[486, 38])).
% 0.20/0.55 tff(488,plain,
% 0.20/0.55 (multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), sk_c8) = multiply(multiply(sk_c5, sk_c6), sk_c8)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[449])).
% 0.20/0.55 tff(489,plain,
% 0.20/0.55 (multiply(multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), sk_c8), sk_c5) = multiply(multiply(multiply(sk_c5, sk_c6), sk_c8), sk_c5)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[488])).
% 0.20/0.55 tff(490,plain,
% 0.20/0.55 (multiply(multiply(multiply(sk_c5, sk_c6), sk_c8), sk_c5) = multiply(multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), sk_c8), sk_c5)),
% 0.20/0.55 inference(symmetry,[status(thm)],[489])).
% 0.20/0.55 tff(491,plain,
% 0.20/0.55 (multiply(multiply(sk_c5, sk_c6), sk_c8) = multiply(sk_c5, identity)),
% 0.20/0.55 inference(transitivity,[status(thm)],[441, 439])).
% 0.20/0.55 tff(492,plain,
% 0.20/0.55 (multiply(multiply(multiply(sk_c5, sk_c6), sk_c8), sk_c5) = multiply(multiply(sk_c5, identity), sk_c5)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[491])).
% 0.20/0.55 tff(493,plain,
% 0.20/0.55 (multiply(multiply(sk_c5, identity), sk_c5) = multiply(multiply(multiply(sk_c5, sk_c6), sk_c8), sk_c5)),
% 0.20/0.55 inference(symmetry,[status(thm)],[492])).
% 0.20/0.55 tff(494,plain,
% 0.20/0.55 (multiply(sk_c4, multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = multiply(sk_c4, sk_c8)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[478])).
% 0.20/0.55 tff(495,plain,
% 0.20/0.55 (multiply(sk_c4, sk_c8) = multiply(sk_c4, multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))))),
% 0.20/0.56 inference(symmetry,[status(thm)],[494])).
% 0.20/0.56 tff(496,assumption,(~(multiply(sk_c1, sk_c7) = sk_c8)), introduced(assumption)).
% 0.20/0.56 tff(497,plain,
% 0.20/0.56 (((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c5)) <=> ((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c5))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(498,axiom,((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_9')).
% 0.20/0.56 tff(499,plain,
% 0.20/0.56 ((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c5)),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[498, 497])).
% 0.20/0.56 tff(500,plain,
% 0.20/0.56 (multiply(sk_c4, sk_c8) = sk_c5),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[499, 496])).
% 0.20/0.56 tff(501,plain,
% 0.20/0.56 (sk_c5 = multiply(sk_c4, sk_c8)),
% 0.20/0.56 inference(symmetry,[status(thm)],[500])).
% 0.20/0.56 tff(502,plain,
% 0.20/0.56 (sk_c5 = multiply(sk_c4, multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))))),
% 0.20/0.56 inference(transitivity,[status(thm)],[501, 495])).
% 0.20/0.56 tff(503,plain,
% 0.20/0.56 (multiply(multiply(sk_c5, identity), sk_c5) = multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c4, multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[476, 502])).
% 0.20/0.56 tff(504,plain,
% 0.20/0.56 (multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c4, multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))))) = multiply(multiply(sk_c5, identity), sk_c5)),
% 0.20/0.56 inference(symmetry,[status(thm)],[503])).
% 0.20/0.56 tff(505,plain,
% 0.20/0.56 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c4), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c4, multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))))))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(506,plain,
% 0.20/0.56 (multiply(multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c4), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c4, multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[505, 38])).
% 0.20/0.56 tff(507,plain,
% 0.20/0.56 (((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(508,plain,
% 0.20/0.56 (((multiply(sk_c1, sk_c7) = sk_c8) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(509,axiom,((multiply(sk_c1, sk_c7) = sk_c8) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_10')).
% 0.20/0.56 tff(510,plain,
% 0.20/0.56 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8)),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[509, 508])).
% 0.20/0.56 tff(511,plain,
% 0.20/0.56 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8)),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[510, 507])).
% 0.20/0.56 tff(512,plain,
% 0.20/0.56 (inverse(sk_c4) = sk_c8),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[511, 496])).
% 0.20/0.56 tff(513,plain,
% 0.20/0.56 (sk_c8 = inverse(sk_c4)),
% 0.20/0.56 inference(symmetry,[status(thm)],[512])).
% 0.20/0.56 tff(514,plain,
% 0.20/0.56 (multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))) = inverse(sk_c4)),
% 0.20/0.56 inference(transitivity,[status(thm)],[477, 471, 470, 469, 10, 513])).
% 0.20/0.56 tff(515,plain,
% 0.20/0.56 (multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.20/0.56 inference(monotonicity,[status(thm)],[514])).
% 0.20/0.56 tff(516,plain,
% 0.20/0.56 (multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c4) = multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))),
% 0.20/0.56 inference(transitivity,[status(thm)],[515, 79, 163, 463, 456, 453, 451])).
% 0.20/0.56 tff(517,plain,
% 0.20/0.56 (multiply(multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c4), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c5, identity))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[516, 477])).
% 0.20/0.56 tff(518,plain,
% 0.20/0.56 (multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c5, identity)) = multiply(multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c4), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))))),
% 0.20/0.56 inference(symmetry,[status(thm)],[517])).
% 0.20/0.56 tff(519,plain,
% 0.20/0.56 (multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))) = multiply(multiply(sk_c5, sk_c8), multiply(sk_c5, multiply(sk_c8, sk_c8)))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[398])).
% 0.20/0.56 tff(520,plain,
% 0.20/0.56 (multiply(multiply(sk_c5, sk_c8), multiply(sk_c5, multiply(sk_c8, sk_c8))) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))),
% 0.20/0.56 inference(symmetry,[status(thm)],[519])).
% 0.20/0.56 tff(521,plain,
% 0.20/0.56 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, sk_c8), multiply(sk_c5, multiply(sk_c8, sk_c8))) = multiply(sk_c5, multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c8)))))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(522,plain,
% 0.20/0.56 (multiply(multiply(sk_c5, sk_c8), multiply(sk_c5, multiply(sk_c8, sk_c8))) = multiply(sk_c5, multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c8))))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[521, 38])).
% 0.20/0.56 tff(523,plain,
% 0.20/0.56 (multiply(sk_c5, multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c8)))) = multiply(multiply(sk_c5, sk_c8), multiply(sk_c5, multiply(sk_c8, sk_c8)))),
% 0.20/0.56 inference(symmetry,[status(thm)],[522])).
% 0.20/0.56 tff(524,plain,
% 0.20/0.56 (multiply(multiply(sk_c7, sk_c8), sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.20/0.56 inference(symmetry,[status(thm)],[474])).
% 0.20/0.56 tff(525,plain,
% 0.20/0.56 (multiply(sk_c7, multiply(sk_c8, sk_c8)) = multiply(multiply(sk_c7, sk_c8), sk_c8)),
% 0.20/0.56 inference(symmetry,[status(thm)],[432])).
% 0.20/0.56 tff(526,plain,
% 0.20/0.56 (multiply(multiply(sk_c8, sk_c5), multiply(sk_c8, sk_c8)) = multiply(sk_c7, multiply(sk_c8, sk_c8))),
% 0.20/0.56 inference(symmetry,[status(thm)],[472])).
% 0.20/0.56 tff(527,plain,
% 0.20/0.56 (multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c8))) = multiply(multiply(sk_c8, sk_c5), multiply(sk_c8, sk_c8))),
% 0.20/0.56 inference(symmetry,[status(thm)],[428])).
% 0.20/0.56 tff(528,plain,
% 0.20/0.56 (multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c8))) = identity),
% 0.20/0.56 inference(transitivity,[status(thm)],[527, 526, 525, 524, 96])).
% 0.20/0.56 tff(529,plain,
% 0.20/0.56 (multiply(sk_c5, multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c8)))) = multiply(sk_c5, identity)),
% 0.20/0.56 inference(monotonicity,[status(thm)],[528])).
% 0.20/0.56 tff(530,plain,
% 0.20/0.56 (multiply(sk_c5, identity) = multiply(sk_c5, multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c8))))),
% 0.20/0.56 inference(symmetry,[status(thm)],[529])).
% 0.20/0.56 tff(531,plain,
% 0.20/0.56 (multiply(sk_c5, identity) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))),
% 0.20/0.56 inference(transitivity,[status(thm)],[530, 523, 520])).
% 0.20/0.56 tff(532,plain,
% 0.20/0.56 (multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c5, identity)) = multiply(multiply(sk_c5, sk_c6), multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[449, 531])).
% 0.20/0.56 tff(533,plain,
% 0.20/0.56 (multiply(multiply(sk_c5, sk_c6), multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))) = multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c5, identity))),
% 0.20/0.56 inference(symmetry,[status(thm)],[532])).
% 0.20/0.56 tff(534,plain,
% 0.20/0.56 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, sk_c6), multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))) = multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(535,plain,
% 0.20/0.56 (multiply(multiply(sk_c5, sk_c6), multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))) = multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[534, 38])).
% 0.20/0.56 tff(536,plain,
% 0.20/0.56 (multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))) = multiply(multiply(sk_c5, sk_c6), multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))),
% 0.20/0.56 inference(symmetry,[status(thm)],[535])).
% 0.20/0.56 tff(537,plain,
% 0.20/0.56 (sk_c8 = sk_c7),
% 0.20/0.56 inference(transitivity,[status(thm)],[186, 465, 441, 439, 476, 536, 533, 518, 506, 504, 493, 490, 487, 485, 483, 56])).
% 0.20/0.56 tff(538,plain,
% 0.20/0.56 ((inverse(sk_c8) = sk_c8) <=> (inverse(sk_c8) = sk_c7)),
% 0.20/0.56 inference(monotonicity,[status(thm)],[537])).
% 0.20/0.56 tff(539,plain,
% 0.20/0.56 ((inverse(sk_c8) = sk_c8) <=> (inverse(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = sk_c7)),
% 0.20/0.56 inference(transitivity,[status(thm)],[538, 481])).
% 0.20/0.56 tff(540,plain,
% 0.20/0.56 (multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c4, multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))))) = multiply(multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c4), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))))),
% 0.20/0.56 inference(symmetry,[status(thm)],[506])).
% 0.20/0.56 tff(541,plain,
% 0.20/0.56 (multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c8, sk_c5)) = multiply(multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), sk_c8), sk_c5)),
% 0.20/0.56 inference(symmetry,[status(thm)],[487])).
% 0.20/0.56 tff(542,plain,
% 0.20/0.56 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, sk_c6), sk_c7) = multiply(sk_c5, multiply(sk_c6, sk_c7)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(543,plain,
% 0.20/0.56 (multiply(multiply(sk_c5, sk_c6), sk_c7) = multiply(sk_c5, multiply(sk_c6, sk_c7))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[542, 38])).
% 0.20/0.56 tff(544,plain,
% 0.20/0.56 (multiply(sk_c5, multiply(sk_c6, sk_c7)) = multiply(multiply(sk_c5, sk_c6), sk_c7)),
% 0.20/0.56 inference(symmetry,[status(thm)],[543])).
% 0.20/0.56 tff(545,plain,
% 0.20/0.56 (multiply(sk_c6, sk_c7) = multiply(sk_c6, multiply(sk_c8, sk_c5))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[363])).
% 0.20/0.56 tff(546,plain,
% 0.20/0.56 (multiply(sk_c6, multiply(sk_c8, sk_c5)) = multiply(sk_c6, sk_c7)),
% 0.20/0.56 inference(symmetry,[status(thm)],[545])).
% 0.20/0.56 tff(547,plain,
% 0.20/0.56 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c8), sk_c5) = multiply(sk_c6, multiply(sk_c8, sk_c5)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(548,plain,
% 0.20/0.56 (multiply(multiply(sk_c6, sk_c8), sk_c5) = multiply(sk_c6, multiply(sk_c8, sk_c5))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[547, 38])).
% 0.20/0.56 tff(549,plain,
% 0.20/0.56 (multiply(multiply(sk_c6, sk_c8), sk_c5) = multiply(identity, sk_c5)),
% 0.20/0.56 inference(monotonicity,[status(thm)],[438])).
% 0.20/0.56 tff(550,plain,
% 0.20/0.56 (multiply(identity, sk_c5) = multiply(multiply(sk_c6, sk_c8), sk_c5)),
% 0.20/0.56 inference(symmetry,[status(thm)],[549])).
% 0.20/0.56 tff(551,plain,
% 0.20/0.56 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c5) = sk_c5)),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(552,plain,
% 0.20/0.56 (multiply(identity, sk_c5) = sk_c5),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[551, 8])).
% 0.20/0.56 tff(553,plain,
% 0.20/0.56 (sk_c5 = multiply(identity, sk_c5)),
% 0.20/0.56 inference(symmetry,[status(thm)],[552])).
% 0.20/0.56 tff(554,plain,
% 0.20/0.56 (identity = multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))),
% 0.20/0.56 inference(transitivity,[status(thm)],[163, 463, 456, 453, 451])).
% 0.20/0.56 tff(555,plain,
% 0.20/0.56 (multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), identity) = multiply(multiply(sk_c5, identity), multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[477, 554])).
% 0.20/0.56 tff(556,plain,
% 0.20/0.56 (multiply(multiply(sk_c5, identity), multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))) = multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), identity)),
% 0.20/0.56 inference(symmetry,[status(thm)],[555])).
% 0.20/0.56 tff(557,plain,
% 0.20/0.56 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, identity), multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))) = multiply(sk_c5, multiply(identity, multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)))))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(558,plain,
% 0.20/0.56 (multiply(multiply(sk_c5, identity), multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))) = multiply(sk_c5, multiply(identity, multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[557, 38])).
% 0.20/0.56 tff(559,plain,
% 0.20/0.56 (multiply(sk_c5, multiply(identity, multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)))) = multiply(multiply(sk_c5, identity), multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)))),
% 0.20/0.56 inference(symmetry,[status(thm)],[558])).
% 0.20/0.56 tff(560,plain,
% 0.20/0.56 (multiply(identity, multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))) = identity),
% 0.20/0.56 inference(transitivity,[status(thm)],[452, 455, 462, 96])).
% 0.20/0.56 tff(561,plain,
% 0.20/0.56 (multiply(sk_c5, multiply(identity, multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)))) = multiply(sk_c5, identity)),
% 0.20/0.56 inference(monotonicity,[status(thm)],[560])).
% 0.20/0.56 tff(562,plain,
% 0.20/0.56 (multiply(sk_c5, identity) = multiply(sk_c5, multiply(identity, multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))))),
% 0.20/0.56 inference(symmetry,[status(thm)],[561])).
% 0.20/0.56 tff(563,plain,
% 0.20/0.56 (sk_c8 = multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), identity)),
% 0.20/0.56 inference(transitivity,[status(thm)],[186, 465, 441, 439, 562, 559, 556])).
% 0.20/0.56 tff(564,plain,
% 0.20/0.56 (multiply(sk_c4, sk_c8) = multiply(sk_c4, multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), identity))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[563])).
% 0.20/0.56 tff(565,plain,
% 0.20/0.56 (multiply(sk_c4, multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), identity)) = multiply(sk_c4, sk_c8)),
% 0.20/0.56 inference(symmetry,[status(thm)],[564])).
% 0.20/0.56 tff(566,plain,
% 0.20/0.56 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c4, multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))), identity) = multiply(sk_c4, multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), identity)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(567,plain,
% 0.20/0.56 (multiply(multiply(sk_c4, multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))), identity) = multiply(sk_c4, multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), identity))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[566, 38])).
% 0.20/0.56 tff(568,plain,
% 0.20/0.56 (multiply(sk_c4, multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = sk_c5),
% 0.20/0.56 inference(transitivity,[status(thm)],[494, 500])).
% 0.20/0.56 tff(569,plain,
% 0.20/0.56 (multiply(multiply(sk_c4, multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))), identity) = multiply(sk_c5, identity)),
% 0.20/0.56 inference(monotonicity,[status(thm)],[568])).
% 0.20/0.56 tff(570,plain,
% 0.20/0.56 (multiply(sk_c5, identity) = multiply(multiply(sk_c4, multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))), identity)),
% 0.20/0.56 inference(symmetry,[status(thm)],[569])).
% 0.20/0.56 tff(571,plain,
% 0.20/0.56 (multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))) = multiply(sk_c6, sk_c7)),
% 0.20/0.56 inference(transitivity,[status(thm)],[477, 570, 567, 565, 500, 553, 550, 548, 546])).
% 0.20/0.56 tff(572,plain,
% 0.20/0.56 (multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))) = sk_c5),
% 0.20/0.56 inference(transitivity,[status(thm)],[477, 570, 567, 565, 500])).
% 0.20/0.56 tff(573,plain,
% 0.20/0.56 (multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = multiply(sk_c5, multiply(sk_c6, sk_c7))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[572, 571])).
% 0.20/0.56 tff(574,plain,
% 0.20/0.56 (sk_c8 = multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))),
% 0.20/0.56 inference(transitivity,[status(thm)],[186, 465, 441, 439, 476])).
% 0.20/0.56 tff(575,plain,
% 0.20/0.56 (sk_c7 = multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))),
% 0.20/0.56 inference(transitivity,[status(thm)],[132, 482, 484, 541, 489, 492, 503, 540, 517, 532, 535])).
% 0.20/0.56 tff(576,plain,
% 0.20/0.56 (multiply(sk_c7, sk_c8) = multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[575, 574])).
% 0.20/0.56 tff(577,plain,
% 0.20/0.56 (inverse(sk_c8) = sk_c8),
% 0.20/0.56 inference(transitivity,[status(thm)],[221, 392, 576, 573, 544, 484, 541, 489, 492, 503, 540, 517, 532, 535, 477, 471, 470, 469, 10])).
% 0.20/0.56 tff(578,plain,
% 0.20/0.56 (inverse(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = sk_c7),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[577, 539])).
% 0.20/0.56 tff(579,plain,
% 0.20/0.56 (sk_c8 = multiply(sk_c5, identity)),
% 0.20/0.56 inference(transitivity,[status(thm)],[186, 465, 441, 439])).
% 0.20/0.56 tff(580,plain,
% 0.20/0.56 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = multiply(multiply(sk_c5, identity), sk_c5)),
% 0.20/0.56 inference(monotonicity,[status(thm)],[579, 500])).
% 0.20/0.57 tff(581,plain,
% 0.20/0.57 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7),
% 0.20/0.57 inference(transitivity,[status(thm)],[580, 493, 490, 487, 485, 483, 56])).
% 0.20/0.57 tff(582,plain,
% 0.20/0.57 (multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c7) = multiply(sk_c8, sk_c7)),
% 0.20/0.57 inference(monotonicity,[status(thm)],[478])).
% 0.20/0.57 tff(583,plain,
% 0.20/0.57 ((multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c7) = sk_c8) <=> (multiply(sk_c8, sk_c7) = sk_c8)),
% 0.20/0.57 inference(monotonicity,[status(thm)],[582])).
% 0.20/0.57 tff(584,plain,
% 0.20/0.57 ((multiply(sk_c8, sk_c7) = sk_c8) <=> (multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c7) = sk_c8)),
% 0.20/0.57 inference(symmetry,[status(thm)],[583])).
% 0.20/0.57 tff(585,plain,
% 0.20/0.57 (multiply(sk_c4, multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), identity)) = multiply(multiply(sk_c4, multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))), identity)),
% 0.20/0.57 inference(symmetry,[status(thm)],[567])).
% 0.20/0.57 tff(586,plain,
% 0.20/0.57 (multiply(sk_c6, multiply(sk_c8, sk_c5)) = multiply(multiply(sk_c6, sk_c8), sk_c5)),
% 0.20/0.57 inference(symmetry,[status(thm)],[548])).
% 0.20/0.57 tff(587,plain,
% 0.20/0.57 (multiply(sk_c6, sk_c7) = sk_c8),
% 0.20/0.57 inference(transitivity,[status(thm)],[545, 586, 549, 552, 501, 564, 585, 569, 471, 470, 469, 10])).
% 0.20/0.57 tff(588,plain,
% 0.20/0.57 (multiply(sk_c7, multiply(sk_c6, sk_c7)) = multiply(sk_c7, sk_c8)),
% 0.20/0.57 inference(monotonicity,[status(thm)],[587])).
% 0.20/0.57 tff(589,plain,
% 0.20/0.57 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c6), sk_c7) = multiply(sk_c7, multiply(sk_c6, sk_c7)))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(590,plain,
% 0.20/0.57 (multiply(multiply(sk_c7, sk_c6), sk_c7) = multiply(sk_c7, multiply(sk_c6, sk_c7))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[589, 38])).
% 0.20/0.57 tff(591,plain,
% 0.20/0.57 (sk_c8 = multiply(sk_c7, sk_c6)),
% 0.20/0.57 inference(symmetry,[status(thm)],[397])).
% 0.20/0.57 tff(592,plain,
% 0.20/0.57 (multiply(sk_c8, sk_c7) = multiply(multiply(sk_c7, sk_c6), sk_c7)),
% 0.20/0.57 inference(monotonicity,[status(thm)],[591])).
% 0.20/0.57 tff(593,plain,
% 0.20/0.57 (multiply(sk_c8, sk_c7) = inverse(sk_c8)),
% 0.20/0.57 inference(transitivity,[status(thm)],[592, 590, 588, 391, 222])).
% 0.20/0.57 tff(594,plain,
% 0.20/0.57 ((multiply(sk_c8, sk_c7) = sk_c8) <=> (inverse(sk_c8) = sk_c8)),
% 0.20/0.57 inference(monotonicity,[status(thm)],[593])).
% 0.20/0.57 tff(595,plain,
% 0.20/0.57 ((inverse(sk_c8) = sk_c8) <=> (multiply(sk_c8, sk_c7) = sk_c8)),
% 0.20/0.57 inference(symmetry,[status(thm)],[594])).
% 0.20/0.57 tff(596,plain,
% 0.20/0.57 ((inverse(sk_c8) = sk_c8) <=> (multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c7) = sk_c8)),
% 0.20/0.57 inference(transitivity,[status(thm)],[595, 584])).
% 0.20/0.57 tff(597,plain,
% 0.20/0.57 (multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c7) = sk_c8),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[577, 596])).
% 0.20/0.57 tff(598,plain,
% 0.20/0.57 (((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c7) = sk_c8)) | (~(inverse(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = sk_c7)))) <=> ((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c7) = sk_c8)) | (~(inverse(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = sk_c7)))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(599,plain,
% 0.20/0.57 (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c7) = sk_c8)) | (~(inverse(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = sk_c7)))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(600,plain,
% 0.20/0.57 (((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = sk_c7)))) <=> ((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c7) = sk_c8)) | (~(inverse(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = sk_c7))))),
% 0.20/0.57 inference(monotonicity,[status(thm)],[599])).
% 0.20/0.57 tff(601,plain,
% 0.20/0.57 (((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = sk_c7)))) <=> ((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c7) = sk_c8)) | (~(inverse(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = sk_c7)))),
% 0.20/0.57 inference(transitivity,[status(thm)],[600, 598])).
% 0.20/0.57 tff(602,plain,
% 0.20/0.57 ((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = sk_c7)))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(603,plain,
% 0.20/0.57 ((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c7) = sk_c8)) | (~(inverse(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = sk_c7))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[602, 601])).
% 0.20/0.57 tff(604,plain,
% 0.20/0.57 ((~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c7) = sk_c8)) | (~(inverse(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = sk_c7))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[603, 391, 397, 221, 512, 352])).
% 0.20/0.57 tff(605,plain,
% 0.20/0.57 ($false),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[604, 597, 581, 578])).
% 0.20/0.57 tff(606,plain,(multiply(sk_c1, sk_c7) = sk_c8), inference(lemma,lemma(discharge,[]))).
% 0.20/0.57 tff(607,plain,
% 0.20/0.57 (sk_c8 = multiply(sk_c1, sk_c7)),
% 0.20/0.57 inference(symmetry,[status(thm)],[606])).
% 0.20/0.57 tff(608,plain,
% 0.20/0.57 (multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))) = multiply(sk_c5, identity)),
% 0.20/0.57 inference(symmetry,[status(thm)],[437])).
% 0.20/0.57 tff(609,plain,
% 0.20/0.57 (multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))) = multiply(sk_c1, sk_c7)),
% 0.20/0.57 inference(transitivity,[status(thm)],[608, 471, 470, 469, 10, 607])).
% 0.20/0.57 tff(610,plain,
% 0.20/0.57 (multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c5, multiply(sk_c8, sk_c7))) = multiply(multiply(sk_c1, sk_c7), multiply(sk_c5, multiply(sk_c8, sk_c7)))),
% 0.20/0.57 inference(monotonicity,[status(thm)],[609])).
% 0.20/0.57 tff(611,plain,
% 0.20/0.57 (multiply(multiply(sk_c1, sk_c7), multiply(sk_c5, multiply(sk_c8, sk_c7))) = multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c5, multiply(sk_c8, sk_c7)))),
% 0.20/0.57 inference(symmetry,[status(thm)],[610])).
% 0.20/0.57 tff(612,plain,
% 0.20/0.57 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c7), multiply(sk_c5, multiply(sk_c8, sk_c7))) = multiply(sk_c1, multiply(sk_c7, multiply(sk_c5, multiply(sk_c8, sk_c7)))))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(613,plain,
% 0.20/0.57 (multiply(multiply(sk_c1, sk_c7), multiply(sk_c5, multiply(sk_c8, sk_c7))) = multiply(sk_c1, multiply(sk_c7, multiply(sk_c5, multiply(sk_c8, sk_c7))))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[612, 38])).
% 0.20/0.57 tff(614,plain,
% 0.20/0.57 (multiply(sk_c1, multiply(sk_c7, multiply(sk_c5, multiply(sk_c8, sk_c7)))) = multiply(multiply(sk_c1, sk_c7), multiply(sk_c5, multiply(sk_c8, sk_c7)))),
% 0.20/0.57 inference(symmetry,[status(thm)],[613])).
% 0.20/0.57 tff(615,plain,
% 0.20/0.57 (multiply(multiply(sk_c7, sk_c6), sk_c5) = multiply(sk_c8, sk_c5)),
% 0.20/0.57 inference(monotonicity,[status(thm)],[397])).
% 0.20/0.57 tff(616,plain,
% 0.20/0.57 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c6), sk_c5) = multiply(sk_c7, multiply(sk_c6, sk_c5)))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(617,plain,
% 0.20/0.57 (multiply(multiply(sk_c7, sk_c6), sk_c5) = multiply(sk_c7, multiply(sk_c6, sk_c5))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[616, 38])).
% 0.20/0.57 tff(618,plain,
% 0.20/0.57 (multiply(sk_c7, multiply(sk_c6, sk_c5)) = multiply(multiply(sk_c7, sk_c6), sk_c5)),
% 0.20/0.57 inference(symmetry,[status(thm)],[617])).
% 0.20/0.57 tff(619,plain,
% 0.20/0.57 (multiply(multiply(sk_c7, sk_c8), sk_c5) = multiply(sk_c6, sk_c5)),
% 0.20/0.57 inference(monotonicity,[status(thm)],[391])).
% 0.20/0.57 tff(620,plain,
% 0.20/0.57 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c8), sk_c5) = multiply(sk_c7, multiply(sk_c8, sk_c5)))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(621,plain,
% 0.20/0.57 (multiply(multiply(sk_c7, sk_c8), sk_c5) = multiply(sk_c7, multiply(sk_c8, sk_c5))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[620, 38])).
% 0.20/0.57 tff(622,plain,
% 0.20/0.57 (multiply(sk_c7, multiply(sk_c8, sk_c5)) = multiply(multiply(sk_c7, sk_c8), sk_c5)),
% 0.20/0.57 inference(symmetry,[status(thm)],[621])).
% 0.20/0.57 tff(623,plain,
% 0.20/0.57 (multiply(sk_c7, sk_c7) = multiply(sk_c7, multiply(sk_c8, sk_c5))),
% 0.20/0.57 inference(monotonicity,[status(thm)],[363])).
% 0.20/0.57 tff(624,plain,
% 0.20/0.57 (multiply(sk_c7, sk_c7) = multiply(sk_c6, sk_c5)),
% 0.20/0.57 inference(transitivity,[status(thm)],[623, 622, 619])).
% 0.20/0.57 tff(625,plain,
% 0.20/0.57 (multiply(sk_c7, multiply(sk_c7, sk_c7)) = multiply(sk_c7, multiply(sk_c6, sk_c5))),
% 0.20/0.57 inference(monotonicity,[status(thm)],[624])).
% 0.20/0.57 tff(626,plain,
% 0.20/0.57 (multiply(sk_c7, multiply(sk_c8, sk_c5)) = multiply(sk_c7, sk_c7)),
% 0.20/0.58 inference(symmetry,[status(thm)],[623])).
% 0.20/0.58 tff(627,plain,
% 0.20/0.58 (multiply(sk_c6, sk_c5) = multiply(multiply(sk_c7, sk_c8), sk_c5)),
% 0.20/0.58 inference(symmetry,[status(thm)],[619])).
% 0.20/0.58 tff(628,plain,
% 0.20/0.58 (multiply(sk_c5, multiply(sk_c8, sk_c7)) = multiply(multiply(sk_c5, sk_c8), sk_c7)),
% 0.20/0.58 inference(symmetry,[status(thm)],[415])).
% 0.20/0.58 tff(629,plain,
% 0.20/0.58 (multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c7))) = multiply(sk_c8, multiply(multiply(sk_c5, sk_c8), sk_c7))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[628])).
% 0.20/0.58 tff(630,plain,
% 0.20/0.58 (multiply(sk_c8, multiply(multiply(sk_c5, sk_c8), sk_c7)) = multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c7)))),
% 0.20/0.58 inference(symmetry,[status(thm)],[629])).
% 0.20/0.58 tff(631,plain,
% 0.20/0.58 (multiply(sk_c6, multiply(sk_c8, sk_c5)) = multiply(sk_c6, sk_c7)),
% 0.20/0.58 inference(monotonicity,[status(thm)],[362])).
% 0.20/0.58 tff(632,plain,
% 0.20/0.58 (multiply(identity, sk_c5) = multiply(multiply(sk_c6, sk_c8), sk_c5)),
% 0.20/0.58 inference(monotonicity,[status(thm)],[233])).
% 0.20/0.58 tff(633,plain,
% 0.20/0.58 (sk_c5 = multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c7)))),
% 0.20/0.58 inference(transitivity,[status(thm)],[553, 632, 548, 631, 406, 409, 412, 630])).
% 0.20/0.58 tff(634,plain,
% 0.20/0.58 (multiply(sk_c6, sk_c5) = multiply(sk_c6, multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c7))))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[633])).
% 0.20/0.58 tff(635,plain,
% 0.20/0.58 (multiply(sk_c6, multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c7)))) = multiply(sk_c6, sk_c5)),
% 0.20/0.58 inference(symmetry,[status(thm)],[634])).
% 0.20/0.58 tff(636,plain,
% 0.20/0.58 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c8), multiply(sk_c5, multiply(sk_c8, sk_c7))) = multiply(sk_c6, multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c7)))))),
% 0.20/0.58 inference(quant_inst,[status(thm)],[])).
% 0.20/0.58 tff(637,plain,
% 0.20/0.58 (multiply(multiply(sk_c6, sk_c8), multiply(sk_c5, multiply(sk_c8, sk_c7))) = multiply(sk_c6, multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c7))))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[636, 38])).
% 0.20/0.58 tff(638,plain,
% 0.20/0.58 (multiply(sk_c6, sk_c8) = multiply(sk_c5, sk_c6)),
% 0.20/0.58 inference(transitivity,[status(thm)],[231, 463, 456, 453, 451, 449])).
% 0.20/0.58 tff(639,plain,
% 0.20/0.58 (multiply(multiply(sk_c6, sk_c8), multiply(sk_c5, multiply(sk_c8, sk_c7))) = multiply(multiply(sk_c5, sk_c6), multiply(sk_c5, multiply(sk_c8, sk_c7)))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[638])).
% 0.20/0.58 tff(640,plain,
% 0.20/0.58 (multiply(multiply(sk_c5, sk_c6), multiply(sk_c5, multiply(sk_c8, sk_c7))) = multiply(multiply(sk_c6, sk_c8), multiply(sk_c5, multiply(sk_c8, sk_c7)))),
% 0.20/0.58 inference(symmetry,[status(thm)],[639])).
% 0.20/0.58 tff(641,plain,
% 0.20/0.58 (multiply(multiply(sk_c5, sk_c8), sk_c7) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c7)),
% 0.20/0.58 inference(symmetry,[status(thm)],[411])).
% 0.20/0.58 tff(642,plain,
% 0.20/0.58 (multiply(sk_c5, multiply(sk_c8, sk_c7)) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c7)),
% 0.20/0.58 inference(transitivity,[status(thm)],[628, 641])).
% 0.20/0.58 tff(643,plain,
% 0.20/0.58 (multiply(multiply(sk_c5, sk_c6), multiply(sk_c5, multiply(sk_c8, sk_c7))) = multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c7))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[448, 642])).
% 0.20/0.58 tff(644,plain,
% 0.20/0.58 (multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c7)) = multiply(multiply(sk_c5, sk_c6), multiply(sk_c5, multiply(sk_c8, sk_c7)))),
% 0.20/0.58 inference(symmetry,[status(thm)],[643])).
% 0.20/0.58 tff(645,plain,
% 0.20/0.58 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c5, multiply(sk_c7, sk_c6))), sk_c7) = multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c7)))),
% 0.20/0.58 inference(quant_inst,[status(thm)],[])).
% 0.20/0.58 tff(646,plain,
% 0.20/0.58 (multiply(multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c5, multiply(sk_c7, sk_c6))), sk_c7) = multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c7))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[645, 38])).
% 0.20/0.58 tff(647,plain,
% 0.20/0.58 (multiply(sk_c5, multiply(sk_c6, multiply(sk_c5, multiply(sk_c7, sk_c6)))) = multiply(sk_c5, sk_c8)),
% 0.20/0.58 inference(monotonicity,[status(thm)],[424])).
% 0.20/0.58 tff(648,plain,
% 0.20/0.58 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, sk_c6), multiply(sk_c5, multiply(sk_c7, sk_c6))) = multiply(sk_c5, multiply(sk_c6, multiply(sk_c5, multiply(sk_c7, sk_c6)))))),
% 0.20/0.58 inference(quant_inst,[status(thm)],[])).
% 0.20/0.58 tff(649,plain,
% 0.20/0.58 (multiply(multiply(sk_c5, sk_c6), multiply(sk_c5, multiply(sk_c7, sk_c6))) = multiply(sk_c5, multiply(sk_c6, multiply(sk_c5, multiply(sk_c7, sk_c6))))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[648, 38])).
% 0.20/0.58 tff(650,plain,
% 0.20/0.58 (multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c5, multiply(sk_c7, sk_c6))) = multiply(multiply(sk_c5, sk_c6), multiply(sk_c5, multiply(sk_c7, sk_c6)))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[449])).
% 0.20/0.58 tff(651,plain,
% 0.20/0.58 (multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c5, multiply(sk_c7, sk_c6))) = multiply(sk_c5, sk_c8)),
% 0.20/0.58 inference(transitivity,[status(thm)],[650, 649, 647])).
% 0.20/0.58 tff(652,plain,
% 0.20/0.58 (multiply(multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c5, multiply(sk_c7, sk_c6))), sk_c7) = multiply(multiply(sk_c5, sk_c8), sk_c7)),
% 0.20/0.58 inference(monotonicity,[status(thm)],[651])).
% 0.20/0.58 tff(653,plain,
% 0.20/0.58 (multiply(multiply(sk_c5, sk_c8), sk_c7) = multiply(multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c5, multiply(sk_c7, sk_c6))), sk_c7)),
% 0.20/0.58 inference(symmetry,[status(thm)],[652])).
% 0.20/0.58 tff(654,plain,
% 0.20/0.58 (multiply(sk_c5, multiply(sk_c8, sk_c7)) = multiply(sk_c7, sk_c7)),
% 0.20/0.58 inference(transitivity,[status(thm)],[628, 653, 646, 644, 640, 637, 635, 627, 621, 626])).
% 0.20/0.58 tff(655,plain,
% 0.20/0.58 (multiply(sk_c7, multiply(sk_c5, multiply(sk_c8, sk_c7))) = multiply(sk_c7, multiply(sk_c7, sk_c7))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[654])).
% 0.20/0.58 tff(656,plain,
% 0.20/0.58 (multiply(sk_c7, multiply(sk_c5, multiply(sk_c8, sk_c7))) = sk_c7),
% 0.20/0.58 inference(transitivity,[status(thm)],[655, 625, 618, 615, 362])).
% 0.20/0.58 tff(657,plain,
% 0.20/0.58 (multiply(sk_c1, multiply(sk_c7, multiply(sk_c5, multiply(sk_c8, sk_c7)))) = multiply(sk_c1, sk_c7)),
% 0.20/0.58 inference(monotonicity,[status(thm)],[656])).
% 0.20/0.58 tff(658,plain,
% 0.20/0.58 (multiply(sk_c1, sk_c7) = multiply(sk_c1, multiply(sk_c7, multiply(sk_c5, multiply(sk_c8, sk_c7))))),
% 0.20/0.58 inference(symmetry,[status(thm)],[657])).
% 0.20/0.58 tff(659,plain,
% 0.20/0.58 (multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))) = multiply(sk_c6, sk_c7)),
% 0.20/0.58 inference(transitivity,[status(thm)],[608, 471, 470, 469, 10, 607, 658, 614, 611, 468, 413, 410, 407])).
% 0.20/0.58 tff(660,plain,
% 0.20/0.58 (multiply(multiply(sk_c6, sk_c8), sk_c5) = multiply(identity, sk_c5)),
% 0.20/0.58 inference(symmetry,[status(thm)],[632])).
% 0.20/0.58 tff(661,plain,
% 0.20/0.58 (multiply(sk_c6, sk_c7) = multiply(sk_c6, multiply(sk_c8, sk_c5))),
% 0.20/0.58 inference(symmetry,[status(thm)],[631])).
% 0.20/0.58 tff(662,plain,
% 0.20/0.58 (multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))) = sk_c5),
% 0.20/0.58 inference(transitivity,[status(thm)],[608, 471, 470, 469, 10, 607, 658, 614, 611, 468, 413, 410, 407, 661, 586, 660, 552])).
% 0.20/0.58 tff(663,plain,
% 0.20/0.58 (multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = multiply(sk_c5, multiply(sk_c6, sk_c7))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[662, 659])).
% 0.20/0.58 tff(664,plain,
% 0.20/0.58 (multiply(sk_c5, multiply(sk_c6, sk_c7)) = multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))))),
% 0.20/0.58 inference(symmetry,[status(thm)],[663])).
% 0.20/0.58 tff(665,plain,
% 0.20/0.58 (sk_c7 = multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))))),
% 0.20/0.58 inference(transitivity,[status(thm)],[132, 482, 543, 664])).
% 0.20/0.58 tff(666,plain,
% 0.20/0.58 (multiply(sk_c4, sk_c7) = multiply(sk_c4, multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[665])).
% 0.20/0.58 tff(667,plain,
% 0.20/0.58 (multiply(sk_c4, multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))))) = multiply(sk_c4, sk_c7)),
% 0.20/0.58 inference(symmetry,[status(thm)],[666])).
% 0.20/0.58 tff(668,plain,
% 0.20/0.58 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c4, multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = multiply(sk_c4, multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))))))),
% 0.20/0.58 inference(quant_inst,[status(thm)],[])).
% 0.20/0.58 tff(669,plain,
% 0.20/0.58 (multiply(multiply(sk_c4, multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = multiply(sk_c4, multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[668, 38])).
% 0.20/0.58 tff(670,assumption,(~(multiply(sk_c4, sk_c8) = sk_c5)), introduced(assumption)).
% 0.20/0.58 tff(671,plain,
% 0.20/0.58 (((inverse(sk_c1) = sk_c7) | (multiply(sk_c4, sk_c8) = sk_c5)) <=> ((inverse(sk_c1) = sk_c7) | (multiply(sk_c4, sk_c8) = sk_c5))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(672,axiom,((inverse(sk_c1) = sk_c7) | (multiply(sk_c4, sk_c8) = sk_c5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_14')).
% 0.20/0.58 tff(673,plain,
% 0.20/0.58 ((inverse(sk_c1) = sk_c7) | (multiply(sk_c4, sk_c8) = sk_c5)),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[672, 671])).
% 0.20/0.58 tff(674,plain,
% 0.20/0.58 (inverse(sk_c1) = sk_c7),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[673, 670])).
% 0.20/0.58 tff(675,plain,
% 0.20/0.58 (inverse(multiply(identity, sk_c1)) = inverse(sk_c1)),
% 0.20/0.58 inference(monotonicity,[status(thm)],[134])).
% 0.20/0.58 tff(676,plain,
% 0.20/0.58 (inverse(multiply(identity, sk_c1)) = sk_c7),
% 0.20/0.58 inference(transitivity,[status(thm)],[675, 674])).
% 0.20/0.58 tff(677,plain,
% 0.20/0.58 (multiply(sk_c7, sk_c6) = multiply(multiply(sk_c8, sk_c5), sk_c6)),
% 0.20/0.58 inference(symmetry,[status(thm)],[457])).
% 0.20/0.58 tff(678,plain,
% 0.20/0.58 (sk_c8 = multiply(sk_c8, multiply(sk_c5, sk_c6))),
% 0.20/0.58 inference(transitivity,[status(thm)],[591, 677, 459])).
% 0.20/0.58 tff(679,plain,
% 0.20/0.58 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c6, multiply(sk_c8, multiply(sk_c5, sk_c6)))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[221, 678])).
% 0.20/0.58 tff(680,plain,
% 0.20/0.58 (multiply(sk_c6, multiply(sk_c8, multiply(sk_c5, sk_c6))) = multiply(inverse(sk_c8), sk_c8)),
% 0.20/0.58 inference(symmetry,[status(thm)],[679])).
% 0.20/0.58 tff(681,plain,
% 0.20/0.58 (multiply(multiply(sk_c7, sk_c7), sk_c6) = sk_c6),
% 0.20/0.58 inference(transitivity,[status(thm)],[443, 445, 391])).
% 0.20/0.58 tff(682,plain,
% 0.20/0.58 (multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)) = multiply(sk_c5, sk_c6)),
% 0.20/0.58 inference(monotonicity,[status(thm)],[681])).
% 0.20/0.58 tff(683,plain,
% 0.20/0.58 (multiply(sk_c5, sk_c6) = multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))),
% 0.20/0.58 inference(symmetry,[status(thm)],[682])).
% 0.20/0.58 tff(684,plain,
% 0.20/0.58 (multiply(multiply(sk_c6, sk_c8), multiply(sk_c5, sk_c6)) = multiply(identity, multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[438, 683])).
% 0.20/0.58 tff(685,plain,
% 0.20/0.58 (multiply(identity, multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))) = multiply(multiply(sk_c6, sk_c8), multiply(sk_c5, sk_c6))),
% 0.20/0.58 inference(symmetry,[status(thm)],[684])).
% 0.20/0.58 tff(686,plain,
% 0.20/0.58 (multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)) = multiply(identity, multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)))),
% 0.20/0.58 inference(symmetry,[status(thm)],[451])).
% 0.20/0.58 tff(687,plain,
% 0.20/0.58 (multiply(sk_c5, sk_c6) = identity),
% 0.20/0.58 inference(transitivity,[status(thm)],[683, 686, 685, 455, 680, 96])).
% 0.20/0.58 tff(688,plain,
% 0.20/0.58 (multiply(multiply(sk_c5, sk_c6), sk_c7) = multiply(identity, sk_c7)),
% 0.20/0.58 inference(monotonicity,[status(thm)],[687])).
% 0.20/0.58 tff(689,plain,
% 0.20/0.58 (identity = multiply(sk_c5, sk_c6)),
% 0.20/0.58 inference(transitivity,[status(thm)],[163, 679, 456, 684, 451, 682])).
% 0.20/0.58 tff(690,plain,
% 0.20/0.58 (multiply(identity, sk_c8) = multiply(multiply(sk_c5, sk_c6), sk_c8)),
% 0.20/0.58 inference(monotonicity,[status(thm)],[689])).
% 0.20/0.58 tff(691,plain,
% 0.20/0.58 (sk_c8 = multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))),
% 0.20/0.58 inference(transitivity,[status(thm)],[186, 690, 441, 439, 437])).
% 0.20/0.58 tff(692,plain,
% 0.20/0.58 (multiply(sk_c8, multiply(multiply(sk_c5, sk_c8), sk_c7)) = multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c5, multiply(sk_c8, sk_c7)))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[691, 415])).
% 0.20/0.58 tff(693,plain,
% 0.20/0.58 (multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c5, multiply(sk_c8, sk_c7))) = multiply(sk_c8, multiply(multiply(sk_c5, sk_c8), sk_c7))),
% 0.20/0.58 inference(symmetry,[status(thm)],[692])).
% 0.20/0.58 tff(694,plain,
% 0.20/0.58 (multiply(multiply(sk_c5, sk_c6), sk_c8) = multiply(identity, sk_c8)),
% 0.20/0.58 inference(symmetry,[status(thm)],[690])).
% 0.20/0.58 tff(695,plain,
% 0.20/0.58 (multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))) = multiply(sk_c1, sk_c7)),
% 0.20/0.58 inference(transitivity,[status(thm)],[608, 471, 470, 694, 10, 607])).
% 0.20/0.58 tff(696,plain,
% 0.20/0.58 (multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c5, multiply(sk_c8, sk_c7))) = multiply(multiply(sk_c1, sk_c7), multiply(sk_c5, multiply(sk_c8, sk_c7)))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[695])).
% 0.20/0.58 tff(697,plain,
% 0.20/0.58 (multiply(multiply(sk_c1, sk_c7), multiply(sk_c5, multiply(sk_c8, sk_c7))) = multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c5, multiply(sk_c8, sk_c7)))),
% 0.20/0.58 inference(symmetry,[status(thm)],[696])).
% 0.20/0.58 tff(698,plain,
% 0.20/0.58 (multiply(sk_c6, sk_c8) = multiply(sk_c5, sk_c6)),
% 0.20/0.58 inference(transitivity,[status(thm)],[231, 679, 456, 684, 451, 682])).
% 0.20/0.58 tff(699,plain,
% 0.20/0.58 (multiply(multiply(sk_c6, sk_c8), multiply(sk_c5, multiply(sk_c8, sk_c7))) = multiply(multiply(sk_c5, sk_c6), multiply(sk_c5, multiply(sk_c8, sk_c7)))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[698])).
% 0.20/0.58 tff(700,plain,
% 0.20/0.58 (multiply(multiply(sk_c5, sk_c6), multiply(sk_c5, multiply(sk_c8, sk_c7))) = multiply(multiply(sk_c6, sk_c8), multiply(sk_c5, multiply(sk_c8, sk_c7)))),
% 0.20/0.58 inference(symmetry,[status(thm)],[699])).
% 0.20/0.58 tff(701,plain,
% 0.20/0.58 (multiply(multiply(sk_c5, sk_c6), multiply(sk_c5, multiply(sk_c8, sk_c7))) = multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c7))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[683, 642])).
% 0.20/0.58 tff(702,plain,
% 0.20/0.58 (multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c7)) = multiply(multiply(sk_c5, sk_c6), multiply(sk_c5, multiply(sk_c8, sk_c7)))),
% 0.20/0.58 inference(symmetry,[status(thm)],[701])).
% 0.20/0.58 tff(703,plain,
% 0.20/0.58 (multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c5, multiply(sk_c7, sk_c6))) = multiply(multiply(sk_c5, sk_c6), multiply(sk_c5, multiply(sk_c7, sk_c6)))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[682])).
% 0.20/0.58 tff(704,plain,
% 0.20/0.58 (multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c5, multiply(sk_c7, sk_c6))) = multiply(sk_c5, sk_c8)),
% 0.20/0.58 inference(transitivity,[status(thm)],[703, 649, 647])).
% 0.20/0.58 tff(705,plain,
% 0.20/0.58 (multiply(multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c5, multiply(sk_c7, sk_c6))), sk_c7) = multiply(multiply(sk_c5, sk_c8), sk_c7)),
% 0.20/0.58 inference(monotonicity,[status(thm)],[704])).
% 0.20/0.58 tff(706,plain,
% 0.20/0.58 (multiply(multiply(sk_c5, sk_c8), sk_c7) = multiply(multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c5, multiply(sk_c7, sk_c6))), sk_c7)),
% 0.20/0.58 inference(symmetry,[status(thm)],[705])).
% 0.20/0.58 tff(707,plain,
% 0.20/0.58 (multiply(sk_c5, multiply(sk_c8, sk_c7)) = multiply(sk_c7, sk_c7)),
% 0.20/0.58 inference(transitivity,[status(thm)],[628, 706, 646, 702, 700, 637, 635, 627, 621, 626])).
% 0.20/0.58 tff(708,plain,
% 0.20/0.58 (multiply(sk_c7, multiply(sk_c5, multiply(sk_c8, sk_c7))) = multiply(sk_c7, multiply(sk_c7, sk_c7))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[707])).
% 0.20/0.58 tff(709,plain,
% 0.20/0.58 (multiply(sk_c7, multiply(sk_c5, multiply(sk_c8, sk_c7))) = sk_c7),
% 0.20/0.58 inference(transitivity,[status(thm)],[708, 625, 618, 615, 362])).
% 0.20/0.58 tff(710,plain,
% 0.20/0.58 (multiply(sk_c1, multiply(sk_c7, multiply(sk_c5, multiply(sk_c8, sk_c7)))) = multiply(sk_c1, sk_c7)),
% 0.20/0.58 inference(monotonicity,[status(thm)],[709])).
% 0.20/0.58 tff(711,plain,
% 0.20/0.58 (multiply(sk_c1, sk_c7) = multiply(sk_c1, multiply(sk_c7, multiply(sk_c5, multiply(sk_c8, sk_c7))))),
% 0.20/0.58 inference(symmetry,[status(thm)],[710])).
% 0.20/0.58 tff(712,plain,
% 0.20/0.58 (multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))) = multiply(sk_c6, sk_c7)),
% 0.20/0.58 inference(transitivity,[status(thm)],[608, 471, 470, 694, 10, 607, 711, 614, 697, 693, 413, 410, 407])).
% 0.20/0.58 tff(713,plain,
% 0.20/0.58 (multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))) = sk_c5),
% 0.20/0.58 inference(transitivity,[status(thm)],[608, 471, 470, 694, 10, 607, 711, 614, 697, 693, 413, 410, 407, 661, 586, 660, 552])).
% 0.20/0.58 tff(714,plain,
% 0.20/0.58 (multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = multiply(sk_c5, multiply(sk_c6, sk_c7))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[713, 712])).
% 0.20/0.58 tff(715,plain,
% 0.20/0.58 (multiply(multiply(sk_c8, multiply(sk_c5, sk_c6)), sk_c5) = multiply(sk_c8, sk_c5)),
% 0.20/0.58 inference(monotonicity,[status(thm)],[461])).
% 0.20/0.58 tff(716,plain,
% 0.20/0.58 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, multiply(sk_c5, sk_c6)), sk_c5) = multiply(sk_c8, multiply(multiply(sk_c5, sk_c6), sk_c5)))),
% 0.20/0.58 inference(quant_inst,[status(thm)],[])).
% 0.20/0.58 tff(717,plain,
% 0.20/0.58 (multiply(multiply(sk_c8, multiply(sk_c5, sk_c6)), sk_c5) = multiply(sk_c8, multiply(multiply(sk_c5, sk_c6), sk_c5))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[716, 38])).
% 0.20/0.58 tff(718,plain,
% 0.20/0.58 (multiply(sk_c8, multiply(multiply(sk_c5, sk_c6), sk_c5)) = multiply(multiply(sk_c8, multiply(sk_c5, sk_c6)), sk_c5)),
% 0.20/0.58 inference(symmetry,[status(thm)],[717])).
% 0.20/0.58 tff(719,plain,
% 0.20/0.58 (multiply(sk_c8, multiply(multiply(sk_c5, sk_c6), sk_c5)) = sk_c7),
% 0.20/0.58 inference(transitivity,[status(thm)],[718, 715, 362])).
% 0.20/0.58 tff(720,plain,
% 0.20/0.58 (multiply(sk_c6, multiply(sk_c8, multiply(multiply(sk_c5, sk_c6), sk_c5))) = multiply(sk_c6, sk_c7)),
% 0.20/0.58 inference(monotonicity,[status(thm)],[719])).
% 0.20/0.58 tff(721,plain,
% 0.20/0.58 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c8), multiply(multiply(sk_c5, sk_c6), sk_c5)) = multiply(sk_c6, multiply(sk_c8, multiply(multiply(sk_c5, sk_c6), sk_c5))))),
% 0.20/0.58 inference(quant_inst,[status(thm)],[])).
% 0.20/0.58 tff(722,plain,
% 0.20/0.58 (multiply(multiply(sk_c6, sk_c8), multiply(multiply(sk_c5, sk_c6), sk_c5)) = multiply(sk_c6, multiply(sk_c8, multiply(multiply(sk_c5, sk_c6), sk_c5)))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[721, 38])).
% 0.20/0.58 tff(723,plain,
% 0.20/0.58 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, sk_c6), sk_c5) = multiply(sk_c5, multiply(sk_c6, sk_c5)))),
% 0.20/0.58 inference(quant_inst,[status(thm)],[])).
% 0.20/0.58 tff(724,plain,
% 0.20/0.58 (multiply(multiply(sk_c5, sk_c6), sk_c5) = multiply(sk_c5, multiply(sk_c6, sk_c5))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[723, 38])).
% 0.20/0.58 tff(725,plain,
% 0.20/0.58 (multiply(sk_c5, multiply(sk_c6, sk_c5)) = multiply(multiply(sk_c5, sk_c6), sk_c5)),
% 0.20/0.58 inference(symmetry,[status(thm)],[724])).
% 0.20/0.58 tff(726,plain,
% 0.20/0.58 (multiply(sk_c6, sk_c5) = multiply(sk_c7, sk_c7)),
% 0.20/0.58 inference(transitivity,[status(thm)],[627, 621, 626])).
% 0.20/0.58 tff(727,plain,
% 0.20/0.58 (multiply(sk_c5, multiply(sk_c6, sk_c5)) = multiply(sk_c5, multiply(sk_c7, sk_c7))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[726])).
% 0.20/0.58 tff(728,plain,
% 0.20/0.58 (multiply(sk_c5, multiply(sk_c7, sk_c7)) = multiply(sk_c5, multiply(sk_c6, sk_c5))),
% 0.20/0.58 inference(symmetry,[status(thm)],[727])).
% 0.20/0.58 tff(729,plain,
% 0.20/0.58 (multiply(sk_c5, multiply(sk_c7, sk_c7)) = multiply(multiply(sk_c5, sk_c6), sk_c5)),
% 0.20/0.58 inference(transitivity,[status(thm)],[728, 725])).
% 0.20/0.58 tff(730,plain,
% 0.20/0.58 (multiply(identity, multiply(sk_c5, multiply(sk_c7, sk_c7))) = multiply(multiply(sk_c6, sk_c8), multiply(multiply(sk_c5, sk_c6), sk_c5))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[233, 729])).
% 0.20/0.58 tff(731,plain,
% 0.20/0.58 (multiply(sk_c7, multiply(sk_c6, sk_c5)) = sk_c7),
% 0.20/0.58 inference(transitivity,[status(thm)],[618, 615, 362])).
% 0.20/0.58 tff(732,plain,
% 0.20/0.58 (multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5))) = multiply(sk_c7, sk_c7)),
% 0.20/0.58 inference(monotonicity,[status(thm)],[731])).
% 0.20/0.58 tff(733,plain,
% 0.20/0.58 (multiply(sk_c5, multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5)))) = multiply(sk_c5, multiply(sk_c7, sk_c7))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[732])).
% 0.20/0.58 tff(734,plain,
% 0.20/0.58 (multiply(identity, multiply(sk_c5, multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5))))) = multiply(identity, multiply(sk_c5, multiply(sk_c7, sk_c7)))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[733])).
% 0.20/0.58 tff(735,plain,
% 0.20/0.58 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, sk_c5), multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5)))) = multiply(identity, multiply(sk_c5, multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5))))))),
% 0.20/0.58 inference(quant_inst,[status(thm)],[])).
% 0.20/0.58 tff(736,plain,
% 0.20/0.58 (multiply(multiply(identity, sk_c5), multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5)))) = multiply(identity, multiply(sk_c5, multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5)))))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[735, 38])).
% 0.20/0.58 tff(737,plain,
% 0.20/0.58 (multiply(sk_c7, sk_c7) = multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5)))),
% 0.20/0.58 inference(symmetry,[status(thm)],[732])).
% 0.20/0.58 tff(738,plain,
% 0.20/0.58 (multiply(sk_c5, multiply(sk_c7, sk_c7)) = multiply(multiply(identity, sk_c5), multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5))))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[553, 737])).
% 0.20/0.58 tff(739,plain,
% 0.20/0.58 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, sk_c7), sk_c7) = multiply(sk_c5, multiply(sk_c7, sk_c7)))),
% 0.20/0.58 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(740,plain,
% 0.20/0.59 (multiply(multiply(sk_c5, sk_c7), sk_c7) = multiply(sk_c5, multiply(sk_c7, sk_c7))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[739, 38])).
% 0.20/0.59 tff(741,plain,
% 0.20/0.59 (multiply(sk_c5, sk_c7) = multiply(sk_c5, multiply(sk_c8, sk_c5))),
% 0.20/0.59 inference(monotonicity,[status(thm)],[363])).
% 0.20/0.59 tff(742,plain,
% 0.20/0.59 (multiply(sk_c5, multiply(sk_c8, sk_c5)) = multiply(sk_c5, sk_c7)),
% 0.20/0.59 inference(symmetry,[status(thm)],[741])).
% 0.20/0.59 tff(743,plain,
% 0.20/0.59 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, sk_c8), sk_c5) = multiply(sk_c5, multiply(sk_c8, sk_c5)))),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(744,plain,
% 0.20/0.59 (multiply(multiply(sk_c5, sk_c8), sk_c5) = multiply(sk_c5, multiply(sk_c8, sk_c5))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[743, 38])).
% 0.20/0.59 tff(745,plain,
% 0.20/0.59 (multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c5) = multiply(multiply(sk_c5, sk_c8), sk_c5)),
% 0.20/0.59 inference(monotonicity,[status(thm)],[398])).
% 0.20/0.59 tff(746,plain,
% 0.20/0.59 (multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c5) = multiply(sk_c5, sk_c7)),
% 0.20/0.59 inference(transitivity,[status(thm)],[745, 744, 742])).
% 0.20/0.59 tff(747,plain,
% 0.20/0.59 (multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c5), sk_c7) = multiply(multiply(sk_c5, sk_c7), sk_c7)),
% 0.20/0.59 inference(monotonicity,[status(thm)],[746])).
% 0.20/0.59 tff(748,plain,
% 0.20/0.59 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c5), sk_c7) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, sk_c7)))),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(749,plain,
% 0.20/0.59 (multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c5), sk_c7) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, sk_c7))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[748, 38])).
% 0.20/0.59 tff(750,plain,
% 0.20/0.59 (multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, sk_c7)) = multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c5), sk_c7)),
% 0.20/0.59 inference(symmetry,[status(thm)],[749])).
% 0.20/0.59 tff(751,plain,
% 0.20/0.59 (multiply(sk_c5, multiply(sk_c7, multiply(sk_c6, sk_c5))) = multiply(sk_c5, sk_c7)),
% 0.20/0.59 inference(monotonicity,[status(thm)],[731])).
% 0.20/0.59 tff(752,plain,
% 0.20/0.59 (multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c7, multiply(sk_c6, sk_c5)))) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, sk_c7))),
% 0.20/0.59 inference(monotonicity,[status(thm)],[751])).
% 0.20/0.59 tff(753,plain,
% 0.20/0.59 (multiply(sk_c5, sk_c7) = multiply(sk_c5, multiply(sk_c7, multiply(sk_c6, sk_c5)))),
% 0.20/0.59 inference(symmetry,[status(thm)],[751])).
% 0.20/0.59 tff(754,plain,
% 0.20/0.59 (multiply(multiply(identity, sk_c5), sk_c7) = multiply(sk_c5, sk_c7)),
% 0.20/0.59 inference(monotonicity,[status(thm)],[552])).
% 0.20/0.59 tff(755,plain,
% 0.20/0.59 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, sk_c5), sk_c7) = multiply(identity, multiply(sk_c5, sk_c7)))),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(756,plain,
% 0.20/0.59 (multiply(multiply(identity, sk_c5), sk_c7) = multiply(identity, multiply(sk_c5, sk_c7))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[755, 38])).
% 0.20/0.59 tff(757,plain,
% 0.20/0.59 (multiply(identity, multiply(sk_c5, sk_c7)) = multiply(multiply(identity, sk_c5), sk_c7)),
% 0.20/0.59 inference(symmetry,[status(thm)],[756])).
% 0.20/0.59 tff(758,plain,
% 0.20/0.59 (multiply(multiply(sk_c6, sk_c8), multiply(sk_c5, multiply(sk_c7, multiply(sk_c6, sk_c5)))) = multiply(identity, multiply(sk_c5, sk_c7))),
% 0.20/0.59 inference(monotonicity,[status(thm)],[438, 751])).
% 0.20/0.59 tff(759,plain,
% 0.20/0.59 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c8), multiply(sk_c5, multiply(sk_c7, multiply(sk_c6, sk_c5)))) = multiply(sk_c6, multiply(sk_c8, multiply(sk_c5, multiply(sk_c7, multiply(sk_c6, sk_c5))))))),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(760,plain,
% 0.20/0.59 (multiply(multiply(sk_c6, sk_c8), multiply(sk_c5, multiply(sk_c7, multiply(sk_c6, sk_c5)))) = multiply(sk_c6, multiply(sk_c8, multiply(sk_c5, multiply(sk_c7, multiply(sk_c6, sk_c5)))))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[759, 38])).
% 0.20/0.59 tff(761,plain,
% 0.20/0.59 (multiply(sk_c6, multiply(sk_c8, multiply(sk_c5, multiply(sk_c7, multiply(sk_c6, sk_c5))))) = multiply(multiply(sk_c6, sk_c8), multiply(sk_c5, multiply(sk_c7, multiply(sk_c6, sk_c5))))),
% 0.20/0.59 inference(symmetry,[status(thm)],[760])).
% 0.20/0.59 tff(762,plain,
% 0.20/0.59 (multiply(sk_c8, multiply(sk_c5, multiply(sk_c7, multiply(sk_c6, sk_c5)))) = multiply(sk_c8, multiply(sk_c5, sk_c7))),
% 0.20/0.59 inference(monotonicity,[status(thm)],[751])).
% 0.20/0.59 tff(763,plain,
% 0.20/0.59 (multiply(sk_c8, multiply(sk_c5, sk_c7)) = multiply(sk_c8, multiply(sk_c5, multiply(sk_c7, multiply(sk_c6, sk_c5))))),
% 0.20/0.59 inference(symmetry,[status(thm)],[762])).
% 0.20/0.59 tff(764,plain,
% 0.20/0.59 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c5), sk_c7) = multiply(sk_c8, multiply(sk_c5, sk_c7)))),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(765,plain,
% 0.20/0.59 (multiply(multiply(sk_c8, sk_c5), sk_c7) = multiply(sk_c8, multiply(sk_c5, sk_c7))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[764, 38])).
% 0.20/0.59 tff(766,plain,
% 0.20/0.59 (multiply(multiply(sk_c8, sk_c5), sk_c7) = multiply(sk_c7, sk_c7)),
% 0.20/0.59 inference(monotonicity,[status(thm)],[362])).
% 0.20/0.59 tff(767,plain,
% 0.20/0.59 (multiply(sk_c7, sk_c7) = multiply(multiply(sk_c8, sk_c5), sk_c7)),
% 0.20/0.59 inference(symmetry,[status(thm)],[766])).
% 0.20/0.59 tff(768,plain,
% 0.20/0.59 (multiply(sk_c7, sk_c7) = multiply(sk_c8, multiply(sk_c5, multiply(sk_c7, multiply(sk_c6, sk_c5))))),
% 0.20/0.59 inference(transitivity,[status(thm)],[767, 765, 763])).
% 0.20/0.59 tff(769,plain,
% 0.20/0.59 (multiply(sk_c6, multiply(sk_c7, sk_c7)) = multiply(sk_c6, multiply(sk_c8, multiply(sk_c5, multiply(sk_c7, multiply(sk_c6, sk_c5)))))),
% 0.20/0.59 inference(monotonicity,[status(thm)],[768])).
% 0.20/0.59 tff(770,plain,
% 0.20/0.59 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c7), sk_c7) = multiply(sk_c6, multiply(sk_c7, sk_c7)))),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(771,plain,
% 0.20/0.59 (multiply(multiply(sk_c6, sk_c7), sk_c7) = multiply(sk_c6, multiply(sk_c7, sk_c7))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[770, 38])).
% 0.20/0.59 tff(772,plain,
% 0.20/0.59 (multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c7))) = multiply(sk_c6, sk_c7)),
% 0.20/0.59 inference(transitivity,[status(thm)],[629, 413, 410, 407])).
% 0.20/0.59 tff(773,plain,
% 0.20/0.59 (multiply(multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c7))), sk_c7) = multiply(multiply(sk_c6, sk_c7), sk_c7)),
% 0.20/0.59 inference(monotonicity,[status(thm)],[772])).
% 0.20/0.59 tff(774,plain,
% 0.20/0.59 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c7))), sk_c7) = multiply(sk_c8, multiply(multiply(sk_c5, multiply(sk_c8, sk_c7)), sk_c7)))),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(775,plain,
% 0.20/0.59 (multiply(multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c7))), sk_c7) = multiply(sk_c8, multiply(multiply(sk_c5, multiply(sk_c8, sk_c7)), sk_c7))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[774, 38])).
% 0.20/0.59 tff(776,plain,
% 0.20/0.59 (multiply(sk_c8, multiply(multiply(sk_c5, multiply(sk_c8, sk_c7)), sk_c7)) = multiply(multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c7))), sk_c7)),
% 0.20/0.59 inference(symmetry,[status(thm)],[775])).
% 0.20/0.59 tff(777,plain,
% 0.20/0.59 (multiply(multiply(sk_c5, multiply(sk_c8, sk_c7)), sk_c7) = multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c7)),
% 0.20/0.59 inference(monotonicity,[status(thm)],[628])).
% 0.20/0.59 tff(778,plain,
% 0.20/0.59 (multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c7) = multiply(multiply(sk_c5, multiply(sk_c8, sk_c7)), sk_c7)),
% 0.20/0.59 inference(symmetry,[status(thm)],[777])).
% 0.20/0.59 tff(779,plain,
% 0.20/0.59 (multiply(sk_c8, multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c7)) = multiply(sk_c8, multiply(multiply(sk_c5, multiply(sk_c8, sk_c7)), sk_c7))),
% 0.20/0.59 inference(monotonicity,[status(thm)],[778])).
% 0.20/0.59 tff(780,plain,
% 0.20/0.59 (multiply(sk_c8, multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c7)) = multiply(sk_c5, multiply(sk_c7, multiply(sk_c6, sk_c5)))),
% 0.20/0.59 inference(transitivity,[status(thm)],[779, 776, 773, 771, 769, 761, 758, 757, 754, 753])).
% 0.20/0.59 tff(781,plain,
% 0.20/0.59 (multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c8, multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c7))) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c7, multiply(sk_c6, sk_c5))))),
% 0.20/0.59 inference(monotonicity,[status(thm)],[780])).
% 0.20/0.59 tff(782,plain,
% 0.20/0.59 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c8), multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c7)) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c8, multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c7))))),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(783,plain,
% 0.20/0.59 (multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c8), multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c7)) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c8, multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c7)))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[782, 38])).
% 0.20/0.59 tff(784,plain,
% 0.20/0.59 (multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c7) = multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c7), sk_c7)),
% 0.20/0.59 inference(monotonicity,[status(thm)],[641])).
% 0.20/0.59 tff(785,plain,
% 0.20/0.59 (multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c7), sk_c7) = multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c7)),
% 0.20/0.59 inference(symmetry,[status(thm)],[784])).
% 0.20/0.59 tff(786,plain,
% 0.20/0.59 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c7), sk_c7) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c7, sk_c7)))),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(787,plain,
% 0.20/0.59 (multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c7), sk_c7) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c7, sk_c7))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[786, 38])).
% 0.20/0.59 tff(788,plain,
% 0.20/0.59 (multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c7, sk_c7)) = multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c7), sk_c7)),
% 0.20/0.59 inference(symmetry,[status(thm)],[787])).
% 0.20/0.59 tff(789,plain,
% 0.20/0.59 (multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, sk_c6))),
% 0.20/0.59 inference(monotonicity,[status(thm)],[682])).
% 0.20/0.59 tff(790,plain,
% 0.20/0.59 (multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, sk_c6)) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)))),
% 0.20/0.59 inference(symmetry,[status(thm)],[789])).
% 0.20/0.59 tff(791,plain,
% 0.20/0.59 (multiply(sk_c5, sk_c8) = multiply(sk_c5, multiply(sk_c7, sk_c6))),
% 0.20/0.59 inference(symmetry,[status(thm)],[398])).
% 0.20/0.59 tff(792,plain,
% 0.20/0.59 (multiply(multiply(sk_c5, sk_c8), multiply(sk_c5, sk_c6)) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, sk_c6))),
% 0.20/0.59 inference(monotonicity,[status(thm)],[791])).
% 0.20/0.59 tff(793,plain,
% 0.20/0.59 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, sk_c8), multiply(sk_c5, sk_c6)) = multiply(sk_c5, multiply(sk_c8, multiply(sk_c5, sk_c6))))),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(794,plain,
% 0.20/0.59 (multiply(multiply(sk_c5, sk_c8), multiply(sk_c5, sk_c6)) = multiply(sk_c5, multiply(sk_c8, multiply(sk_c5, sk_c6)))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[793, 38])).
% 0.20/0.59 tff(795,plain,
% 0.20/0.59 (multiply(sk_c5, multiply(sk_c8, multiply(sk_c5, sk_c6))) = multiply(multiply(sk_c5, sk_c8), multiply(sk_c5, sk_c6))),
% 0.20/0.59 inference(symmetry,[status(thm)],[794])).
% 0.20/0.59 tff(796,plain,
% 0.20/0.59 (multiply(sk_c5, sk_c8) = multiply(sk_c5, multiply(sk_c8, multiply(sk_c5, sk_c6)))),
% 0.20/0.59 inference(monotonicity,[status(thm)],[678])).
% 0.20/0.59 tff(797,plain,
% 0.20/0.59 (multiply(sk_c5, multiply(sk_c7, sk_c6)) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)))),
% 0.20/0.59 inference(transitivity,[status(thm)],[398, 796, 795, 792, 790])).
% 0.20/0.59 tff(798,plain,
% 0.20/0.59 (multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c7, sk_c7)) = multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))), multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5))))),
% 0.20/0.59 inference(monotonicity,[status(thm)],[797, 737])).
% 0.20/0.59 tff(799,plain,
% 0.20/0.59 (multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))), multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5)))) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c7, sk_c7))),
% 0.20/0.59 inference(symmetry,[status(thm)],[798])).
% 0.20/0.59 tff(800,plain,
% 0.20/0.59 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))), multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5)))) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5))))))),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(801,plain,
% 0.20/0.59 (multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))), multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5)))) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5)))))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[800, 38])).
% 0.20/0.59 tff(802,plain,
% 0.20/0.59 (multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5))))) = multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))), multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5))))),
% 0.20/0.59 inference(symmetry,[status(thm)],[801])).
% 0.20/0.59 tff(803,plain,
% 0.20/0.59 (multiply(sk_c6, sk_c6) = multiply(sk_c6, multiply(sk_c8, multiply(sk_c5, multiply(sk_c7, sk_c6))))),
% 0.20/0.59 inference(monotonicity,[status(thm)],[405])).
% 0.20/0.59 tff(804,plain,
% 0.20/0.59 (multiply(sk_c6, multiply(sk_c8, multiply(sk_c5, multiply(sk_c7, sk_c6)))) = multiply(sk_c6, sk_c6)),
% 0.20/0.59 inference(symmetry,[status(thm)],[803])).
% 0.20/0.59 tff(805,plain,
% 0.20/0.59 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c8), multiply(sk_c5, multiply(sk_c7, sk_c6))) = multiply(sk_c6, multiply(sk_c8, multiply(sk_c5, multiply(sk_c7, sk_c6)))))),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(806,plain,
% 0.20/0.59 (multiply(multiply(sk_c6, sk_c8), multiply(sk_c5, multiply(sk_c7, sk_c6))) = multiply(sk_c6, multiply(sk_c8, multiply(sk_c5, multiply(sk_c7, sk_c6))))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[805, 38])).
% 0.20/0.59 tff(807,plain,
% 0.20/0.59 (multiply(multiply(sk_c6, sk_c8), multiply(sk_c5, multiply(sk_c7, sk_c6))) = multiply(identity, multiply(sk_c5, sk_c8))),
% 0.20/0.59 inference(monotonicity,[status(thm)],[438, 398])).
% 0.20/0.59 tff(808,plain,
% 0.20/0.59 (multiply(identity, multiply(sk_c5, sk_c8)) = multiply(multiply(sk_c6, sk_c8), multiply(sk_c5, multiply(sk_c7, sk_c6)))),
% 0.20/0.59 inference(symmetry,[status(thm)],[807])).
% 0.20/0.59 tff(809,plain,
% 0.20/0.59 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, sk_c5), sk_c8) = multiply(identity, multiply(sk_c5, sk_c8)))),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(810,plain,
% 0.20/0.59 (multiply(multiply(identity, sk_c5), sk_c8) = multiply(identity, multiply(sk_c5, sk_c8))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[809, 38])).
% 0.20/0.59 tff(811,plain,
% 0.20/0.59 (multiply(multiply(identity, sk_c5), sk_c8) = multiply(sk_c5, sk_c8)),
% 0.20/0.59 inference(monotonicity,[status(thm)],[552])).
% 0.20/0.59 tff(812,plain,
% 0.20/0.59 (multiply(sk_c5, sk_c8) = multiply(multiply(identity, sk_c5), sk_c8)),
% 0.20/0.59 inference(symmetry,[status(thm)],[811])).
% 0.20/0.59 tff(813,plain,
% 0.20/0.59 (multiply(sk_c5, multiply(sk_c7, sk_c6)) = multiply(sk_c6, sk_c6)),
% 0.20/0.59 inference(transitivity,[status(thm)],[398, 812, 810, 808, 806, 804])).
% 0.20/0.59 tff(814,plain,
% 0.20/0.59 (multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5))))) = multiply(multiply(sk_c6, sk_c6), multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5)))))),
% 0.20/0.59 inference(monotonicity,[status(thm)],[813])).
% 0.20/0.59 tff(815,plain,
% 0.20/0.59 (multiply(multiply(sk_c6, sk_c6), multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5))))) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5)))))),
% 0.20/0.59 inference(symmetry,[status(thm)],[814])).
% 0.20/0.59 tff(816,plain,
% 0.20/0.59 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c6), multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5))))) = multiply(sk_c6, multiply(sk_c6, multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5)))))))),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(817,plain,
% 0.20/0.59 (multiply(multiply(sk_c6, sk_c6), multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5))))) = multiply(sk_c6, multiply(sk_c6, multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5))))))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[816, 38])).
% 0.20/0.59 tff(818,plain,
% 0.20/0.59 (multiply(sk_c6, multiply(sk_c6, multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5)))))) = multiply(multiply(sk_c6, sk_c6), multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5)))))),
% 0.20/0.59 inference(symmetry,[status(thm)],[817])).
% 0.20/0.59 tff(819,plain,
% 0.20/0.59 (multiply(sk_c7, multiply(sk_c8, multiply(sk_c5, sk_c6))) = multiply(sk_c7, sk_c8)),
% 0.20/0.59 inference(monotonicity,[status(thm)],[461])).
% 0.20/0.59 tff(820,plain,
% 0.20/0.59 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c8), multiply(sk_c5, sk_c6)) = multiply(sk_c7, multiply(sk_c8, multiply(sk_c5, sk_c6))))),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(821,plain,
% 0.20/0.59 (multiply(multiply(sk_c7, sk_c8), multiply(sk_c5, sk_c6)) = multiply(sk_c7, multiply(sk_c8, multiply(sk_c5, sk_c6)))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[820, 38])).
% 0.20/0.59 tff(822,plain,
% 0.20/0.59 (multiply(sk_c6, multiply(sk_c5, sk_c6)) = multiply(multiply(sk_c7, sk_c8), multiply(sk_c5, sk_c6))),
% 0.20/0.59 inference(monotonicity,[status(thm)],[392])).
% 0.20/0.59 tff(823,plain,
% 0.20/0.59 (multiply(sk_c6, multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))) = multiply(sk_c6, multiply(sk_c5, sk_c6))),
% 0.20/0.59 inference(monotonicity,[status(thm)],[682])).
% 0.20/0.59 tff(824,plain,
% 0.20/0.59 (multiply(sk_c6, multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))) = sk_c6),
% 0.20/0.59 inference(transitivity,[status(thm)],[823, 822, 821, 819, 391])).
% 0.20/0.59 tff(825,plain,
% 0.20/0.59 (multiply(multiply(sk_c6, multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))), multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5)))) = multiply(sk_c6, multiply(sk_c7, sk_c7))),
% 0.20/0.59 inference(monotonicity,[status(thm)],[824, 732])).
% 0.20/0.59 tff(826,plain,
% 0.20/0.59 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))), multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5)))) = multiply(sk_c6, multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5))))))),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(827,plain,
% 0.20/0.59 (multiply(multiply(sk_c6, multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))), multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5)))) = multiply(sk_c6, multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5)))))),
% 0.20/0.60 inference(unit_resolution,[status(thm)],[826, 38])).
% 0.20/0.60 tff(828,plain,
% 0.20/0.60 (multiply(sk_c6, multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5))))) = multiply(multiply(sk_c6, multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))), multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5))))),
% 0.20/0.60 inference(symmetry,[status(thm)],[827])).
% 0.20/0.60 tff(829,plain,
% 0.20/0.60 (multiply(sk_c6, multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5))))) = multiply(sk_c5, sk_c7)),
% 0.20/0.60 inference(transitivity,[status(thm)],[828, 825, 769, 761, 758, 757, 754])).
% 0.20/0.60 tff(830,plain,
% 0.20/0.60 (multiply(sk_c6, multiply(sk_c6, multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5)))))) = multiply(sk_c6, multiply(sk_c5, sk_c7))),
% 0.20/0.60 inference(monotonicity,[status(thm)],[829])).
% 0.20/0.60 tff(831,plain,
% 0.20/0.60 (multiply(sk_c6, multiply(sk_c5, sk_c7)) = multiply(sk_c6, multiply(sk_c6, multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c7, multiply(sk_c7, multiply(sk_c6, sk_c5))))))),
% 0.20/0.60 inference(symmetry,[status(thm)],[830])).
% 0.20/0.60 tff(832,plain,
% 0.20/0.60 (multiply(multiply(sk_c5, sk_c8), sk_c5) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c5)),
% 0.20/0.60 inference(symmetry,[status(thm)],[745])).
% 0.20/0.60 tff(833,plain,
% 0.20/0.60 (multiply(sk_c5, multiply(sk_c8, sk_c5)) = multiply(multiply(sk_c5, sk_c8), sk_c5)),
% 0.20/0.60 inference(symmetry,[status(thm)],[744])).
% 0.20/0.60 tff(834,plain,
% 0.20/0.60 (multiply(sk_c5, sk_c7) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c5)),
% 0.20/0.60 inference(transitivity,[status(thm)],[741, 833, 832])).
% 0.20/0.60 tff(835,plain,
% 0.20/0.60 (multiply(sk_c6, multiply(sk_c5, sk_c7)) = multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c5))),
% 0.20/0.60 inference(monotonicity,[status(thm)],[834])).
% 0.20/0.60 tff(836,plain,
% 0.20/0.60 (multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c5)) = multiply(sk_c6, multiply(sk_c5, sk_c7))),
% 0.20/0.60 inference(symmetry,[status(thm)],[835])).
% 0.20/0.60 tff(837,plain,
% 0.20/0.60 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, multiply(sk_c5, multiply(sk_c7, sk_c6))), sk_c5) = multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c5)))),
% 0.20/0.60 inference(quant_inst,[status(thm)],[])).
% 0.20/0.60 tff(838,plain,
% 0.20/0.60 (multiply(multiply(sk_c6, multiply(sk_c5, multiply(sk_c7, sk_c6))), sk_c5) = multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c5))),
% 0.20/0.60 inference(unit_resolution,[status(thm)],[837, 38])).
% 0.20/0.60 tff(839,plain,
% 0.20/0.60 (multiply(multiply(sk_c6, multiply(sk_c5, multiply(sk_c7, sk_c6))), sk_c5) = multiply(sk_c8, sk_c5)),
% 0.20/0.60 inference(monotonicity,[status(thm)],[424])).
% 0.20/0.60 tff(840,plain,
% 0.20/0.60 (multiply(sk_c8, sk_c5) = multiply(multiply(sk_c6, multiply(sk_c5, multiply(sk_c7, sk_c6))), sk_c5)),
% 0.20/0.60 inference(symmetry,[status(thm)],[839])).
% 0.20/0.60 tff(841,plain,
% 0.20/0.60 (sk_c7 = multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c7)),
% 0.20/0.60 inference(transitivity,[status(thm)],[363, 840, 838, 836, 831, 818, 815, 802, 799, 788, 785])).
% 0.20/0.60 tff(842,plain,
% 0.20/0.60 (multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c8) = multiply(multiply(sk_c5, sk_c8), sk_c8)),
% 0.20/0.60 inference(monotonicity,[status(thm)],[398])).
% 0.20/0.60 tff(843,plain,
% 0.20/0.60 (multiply(multiply(sk_c5, sk_c8), sk_c8) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c8)),
% 0.20/0.60 inference(symmetry,[status(thm)],[842])).
% 0.20/0.60 tff(844,plain,
% 0.20/0.60 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, sk_c8), sk_c8) = multiply(sk_c5, multiply(sk_c8, sk_c8)))),
% 0.20/0.60 inference(quant_inst,[status(thm)],[])).
% 0.20/0.60 tff(845,plain,
% 0.20/0.60 (multiply(multiply(sk_c5, sk_c8), sk_c8) = multiply(sk_c5, multiply(sk_c8, sk_c8))),
% 0.20/0.60 inference(unit_resolution,[status(thm)],[844, 38])).
% 0.20/0.60 tff(846,plain,
% 0.20/0.60 (multiply(sk_c5, multiply(sk_c8, sk_c8)) = multiply(multiply(sk_c5, sk_c8), sk_c8)),
% 0.20/0.60 inference(symmetry,[status(thm)],[845])).
% 0.20/0.60 tff(847,plain,
% 0.20/0.60 (multiply(sk_c5, multiply(sk_c8, sk_c8)) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c8)),
% 0.20/0.60 inference(transitivity,[status(thm)],[846, 843])).
% 0.20/0.60 tff(848,plain,
% 0.20/0.60 (multiply(multiply(sk_c5, multiply(sk_c8, sk_c8)), sk_c7) = multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c8), multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c7))),
% 0.20/0.60 inference(monotonicity,[status(thm)],[847, 841])).
% 0.20/0.60 tff(849,assumption,(~(multiply(sk_c8, sk_c3) = sk_c7)), introduced(assumption)).
% 0.20/0.60 tff(850,plain,
% 0.20/0.60 (((multiply(sk_c4, sk_c8) = sk_c5) | (multiply(sk_c8, sk_c3) = sk_c7)) <=> ((multiply(sk_c4, sk_c8) = sk_c5) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.20/0.60 inference(rewrite,[status(thm)],[])).
% 0.20/0.60 tff(851,plain,
% 0.20/0.60 (((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c4, sk_c8) = sk_c5)) <=> ((multiply(sk_c4, sk_c8) = sk_c5) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.20/0.60 inference(rewrite,[status(thm)],[])).
% 0.20/0.60 tff(852,axiom,((multiply(sk_c8, sk_c3) = sk_c7) | (multiply(sk_c4, sk_c8) = sk_c5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_19')).
% 0.20/0.60 tff(853,plain,
% 0.20/0.60 ((multiply(sk_c4, sk_c8) = sk_c5) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.20/0.60 inference(modus_ponens,[status(thm)],[852, 851])).
% 0.20/0.60 tff(854,plain,
% 0.20/0.60 ((multiply(sk_c4, sk_c8) = sk_c5) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.20/0.60 inference(modus_ponens,[status(thm)],[853, 850])).
% 0.20/0.60 tff(855,plain,
% 0.20/0.60 (multiply(sk_c4, sk_c8) = sk_c5),
% 0.20/0.60 inference(unit_resolution,[status(thm)],[854, 849])).
% 0.20/0.60 tff(856,plain,
% 0.20/0.60 (sk_c5 = multiply(sk_c4, sk_c8)),
% 0.20/0.60 inference(symmetry,[status(thm)],[855])).
% 0.20/0.60 tff(857,plain,
% 0.20/0.60 (sk_c5 = multiply(sk_c4, multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))))),
% 0.20/0.60 inference(transitivity,[status(thm)],[856, 495])).
% 0.20/0.60 tff(858,plain,
% 0.20/0.60 (multiply(multiply(sk_c5, identity), sk_c5) = multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c4, multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))))),
% 0.20/0.60 inference(monotonicity,[status(thm)],[476, 857])).
% 0.20/0.60 tff(859,plain,
% 0.20/0.60 (multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c4, multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))))) = multiply(multiply(sk_c5, identity), sk_c5)),
% 0.20/0.60 inference(symmetry,[status(thm)],[858])).
% 0.20/0.60 tff(860,plain,
% 0.20/0.60 (((inverse(sk_c4) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.20/0.60 inference(rewrite,[status(thm)],[])).
% 0.20/0.60 tff(861,plain,
% 0.20/0.60 (((multiply(sk_c8, sk_c3) = sk_c7) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7))),
% 0.20/0.60 inference(rewrite,[status(thm)],[])).
% 0.20/0.60 tff(862,axiom,((multiply(sk_c8, sk_c3) = sk_c7) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_20')).
% 0.20/0.60 tff(863,plain,
% 0.20/0.60 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.20/0.60 inference(modus_ponens,[status(thm)],[862, 861])).
% 0.20/0.60 tff(864,plain,
% 0.20/0.60 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c8, sk_c3) = sk_c7)),
% 0.20/0.60 inference(modus_ponens,[status(thm)],[863, 860])).
% 0.20/0.60 tff(865,plain,
% 0.20/0.60 (inverse(sk_c4) = sk_c8),
% 0.20/0.60 inference(unit_resolution,[status(thm)],[864, 849])).
% 0.20/0.60 tff(866,plain,
% 0.20/0.60 (sk_c8 = inverse(sk_c4)),
% 0.20/0.60 inference(symmetry,[status(thm)],[865])).
% 0.20/0.60 tff(867,plain,
% 0.20/0.60 (multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))) = inverse(sk_c4)),
% 0.20/0.60 inference(transitivity,[status(thm)],[477, 471, 470, 469, 10, 866])).
% 0.20/0.60 tff(868,plain,
% 0.20/0.60 (multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.20/0.60 inference(monotonicity,[status(thm)],[867])).
% 0.20/0.60 tff(869,plain,
% 0.20/0.60 (multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c4) = multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))),
% 0.20/0.60 inference(transitivity,[status(thm)],[868, 79, 163, 463, 456, 453, 451])).
% 0.20/0.60 tff(870,plain,
% 0.20/0.60 (multiply(multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c4), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c5, identity))),
% 0.20/0.60 inference(monotonicity,[status(thm)],[869, 477])).
% 0.20/0.60 tff(871,plain,
% 0.20/0.60 (multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c5, identity)) = multiply(multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c4), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))))),
% 0.20/0.60 inference(symmetry,[status(thm)],[870])).
% 0.20/0.60 tff(872,plain,
% 0.20/0.60 (sk_c8 = sk_c7),
% 0.20/0.60 inference(transitivity,[status(thm)],[186, 465, 441, 439, 476, 536, 533, 871, 506, 859, 493, 490, 487, 485, 483, 56])).
% 0.20/0.60 tff(873,plain,
% 0.20/0.60 ((inverse(sk_c8) = sk_c8) <=> (inverse(sk_c8) = sk_c7)),
% 0.20/0.60 inference(monotonicity,[status(thm)],[872])).
% 0.20/0.60 tff(874,plain,
% 0.20/0.60 ((inverse(sk_c8) = sk_c8) <=> (inverse(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = sk_c7)),
% 0.20/0.60 inference(transitivity,[status(thm)],[873, 481])).
% 0.20/0.60 tff(875,plain,
% 0.20/0.60 (multiply(sk_c4, multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = sk_c5),
% 0.20/0.60 inference(transitivity,[status(thm)],[494, 855])).
% 0.20/0.60 tff(876,plain,
% 0.20/0.60 (multiply(multiply(sk_c4, multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))), identity) = multiply(sk_c5, identity)),
% 0.20/0.60 inference(monotonicity,[status(thm)],[875])).
% 0.20/0.60 tff(877,plain,
% 0.20/0.60 (multiply(sk_c5, identity) = multiply(multiply(sk_c4, multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))), identity)),
% 0.20/0.60 inference(symmetry,[status(thm)],[876])).
% 0.20/0.60 tff(878,plain,
% 0.20/0.60 (multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))) = multiply(sk_c6, sk_c7)),
% 0.20/0.60 inference(transitivity,[status(thm)],[477, 877, 567, 565, 855, 553, 550, 548, 546])).
% 0.20/0.60 tff(879,plain,
% 0.20/0.60 (multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))) = sk_c5),
% 0.20/0.60 inference(transitivity,[status(thm)],[477, 877, 567, 565, 855])).
% 0.20/0.60 tff(880,plain,
% 0.20/0.60 (multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = multiply(sk_c5, multiply(sk_c6, sk_c7))),
% 0.20/0.60 inference(monotonicity,[status(thm)],[879, 878])).
% 0.20/0.60 tff(881,plain,
% 0.20/0.60 (sk_c7 = multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))),
% 0.20/0.60 inference(transitivity,[status(thm)],[132, 482, 484, 541, 489, 492, 858, 540, 870, 532, 535])).
% 0.20/0.60 tff(882,plain,
% 0.20/0.60 (multiply(sk_c7, sk_c8) = multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))))),
% 0.20/0.60 inference(monotonicity,[status(thm)],[881, 574])).
% 0.20/0.60 tff(883,plain,
% 0.20/0.60 (inverse(sk_c8) = sk_c8),
% 0.20/0.60 inference(transitivity,[status(thm)],[221, 392, 882, 880, 544, 484, 541, 489, 492, 858, 540, 870, 532, 535, 477, 471, 470, 469, 10])).
% 0.20/0.60 tff(884,plain,
% 0.20/0.60 (inverse(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = sk_c7),
% 0.20/0.60 inference(modus_ponens,[status(thm)],[883, 874])).
% 0.20/0.60 tff(885,plain,
% 0.20/0.60 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = multiply(multiply(sk_c5, identity), sk_c5)),
% 0.20/0.60 inference(monotonicity,[status(thm)],[579, 855])).
% 0.20/0.60 tff(886,plain,
% 0.20/0.60 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7),
% 0.20/0.60 inference(transitivity,[status(thm)],[885, 493, 490, 487, 485, 483, 56])).
% 0.20/0.60 tff(887,plain,
% 0.20/0.60 (multiply(sk_c6, sk_c7) = sk_c8),
% 0.20/0.60 inference(transitivity,[status(thm)],[545, 586, 549, 552, 856, 564, 585, 876, 471, 470, 469, 10])).
% 0.20/0.60 tff(888,plain,
% 0.20/0.60 (multiply(sk_c7, multiply(sk_c6, sk_c7)) = multiply(sk_c7, sk_c8)),
% 0.20/0.60 inference(monotonicity,[status(thm)],[887])).
% 0.20/0.60 tff(889,plain,
% 0.20/0.60 (multiply(sk_c8, sk_c7) = inverse(sk_c8)),
% 0.20/0.60 inference(transitivity,[status(thm)],[592, 590, 888, 391, 222])).
% 0.20/0.60 tff(890,plain,
% 0.20/0.60 ((multiply(sk_c8, sk_c7) = sk_c8) <=> (inverse(sk_c8) = sk_c8)),
% 0.20/0.60 inference(monotonicity,[status(thm)],[889])).
% 0.20/0.60 tff(891,plain,
% 0.20/0.60 ((inverse(sk_c8) = sk_c8) <=> (multiply(sk_c8, sk_c7) = sk_c8)),
% 0.20/0.60 inference(symmetry,[status(thm)],[890])).
% 0.20/0.60 tff(892,plain,
% 0.20/0.60 ((inverse(sk_c8) = sk_c8) <=> (multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c7) = sk_c8)),
% 0.20/0.60 inference(transitivity,[status(thm)],[891, 584])).
% 0.20/0.60 tff(893,plain,
% 0.20/0.60 (multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c7) = sk_c8),
% 0.20/0.60 inference(modus_ponens,[status(thm)],[883, 892])).
% 0.20/0.60 tff(894,plain,
% 0.20/0.60 ((~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c7) = sk_c8)) | (~(inverse(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = sk_c7))),
% 0.20/0.60 inference(unit_resolution,[status(thm)],[603, 391, 397, 221, 865, 352])).
% 0.20/0.60 tff(895,plain,
% 0.20/0.60 ($false),
% 0.20/0.60 inference(unit_resolution,[status(thm)],[894, 893, 886, 884])).
% 0.20/0.60 tff(896,plain,(multiply(sk_c8, sk_c3) = sk_c7), inference(lemma,lemma(discharge,[]))).
% 0.20/0.60 tff(897,plain,
% 0.20/0.60 (multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))) = sk_c8),
% 0.20/0.60 inference(transitivity,[status(thm)],[608, 471, 470, 694, 10])).
% 0.20/0.60 tff(898,plain,
% 0.20/0.60 (multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c3) = multiply(sk_c8, sk_c3)),
% 0.20/0.60 inference(monotonicity,[status(thm)],[897])).
% 0.20/0.60 tff(899,plain,
% 0.20/0.60 (multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c3) = sk_c7),
% 0.20/0.60 inference(transitivity,[status(thm)],[898, 896])).
% 0.20/0.60 tff(900,plain,
% 0.20/0.60 (multiply(multiply(sk_c5, multiply(sk_c8, sk_c8)), multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c3)) = multiply(multiply(sk_c5, multiply(sk_c8, sk_c8)), sk_c7)),
% 0.20/0.60 inference(monotonicity,[status(thm)],[899])).
% 0.20/0.60 tff(901,plain,
% 0.20/0.60 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c5, multiply(sk_c8, sk_c8)), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))), sk_c3) = multiply(multiply(sk_c5, multiply(sk_c8, sk_c8)), multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c3)))),
% 0.44/0.60 inference(quant_inst,[status(thm)],[])).
% 0.44/0.60 tff(902,plain,
% 0.44/0.60 (multiply(multiply(multiply(sk_c5, multiply(sk_c8, sk_c8)), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))), sk_c3) = multiply(multiply(sk_c5, multiply(sk_c8, sk_c8)), multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c3))),
% 0.44/0.60 inference(unit_resolution,[status(thm)],[901, 38])).
% 0.44/0.60 tff(903,plain,
% 0.44/0.60 (multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c8) = multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c7), sk_c8)),
% 0.44/0.60 inference(monotonicity,[status(thm)],[641])).
% 0.44/0.60 tff(904,plain,
% 0.44/0.60 (multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c7), sk_c8) = multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c8)),
% 0.44/0.60 inference(symmetry,[status(thm)],[903])).
% 0.44/0.60 tff(905,plain,
% 0.44/0.60 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c7), sk_c8) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c7, sk_c8)))),
% 0.44/0.60 inference(quant_inst,[status(thm)],[])).
% 0.44/0.60 tff(906,plain,
% 0.44/0.60 (multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c7), sk_c8) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c7, sk_c8))),
% 0.44/0.60 inference(unit_resolution,[status(thm)],[905, 38])).
% 0.44/0.60 tff(907,plain,
% 0.44/0.60 (multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c7, sk_c8)) = multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c7), sk_c8)),
% 0.44/0.60 inference(symmetry,[status(thm)],[906])).
% 0.44/0.60 tff(908,plain,
% 0.44/0.60 (multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c7, sk_c8)) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c6)),
% 0.44/0.60 inference(monotonicity,[status(thm)],[391])).
% 0.44/0.60 tff(909,plain,
% 0.44/0.60 (multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c6) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c7, sk_c8))),
% 0.44/0.60 inference(symmetry,[status(thm)],[908])).
% 0.44/0.60 tff(910,plain,
% 0.44/0.60 (multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c6) = multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))), sk_c6)),
% 0.44/0.60 inference(monotonicity,[status(thm)],[797])).
% 0.44/0.60 tff(911,plain,
% 0.44/0.60 (multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))), sk_c6) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c6)),
% 0.44/0.60 inference(symmetry,[status(thm)],[910])).
% 0.44/0.60 tff(912,plain,
% 0.44/0.60 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))), sk_c6) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), sk_c6)))),
% 0.44/0.60 inference(quant_inst,[status(thm)],[])).
% 0.44/0.60 tff(913,plain,
% 0.44/0.60 (multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))), sk_c6) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), sk_c6))),
% 0.44/0.60 inference(unit_resolution,[status(thm)],[912, 38])).
% 0.44/0.60 tff(914,plain,
% 0.44/0.60 (multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), sk_c6)) = multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))), sk_c6)),
% 0.44/0.60 inference(symmetry,[status(thm)],[913])).
% 0.44/0.60 tff(915,plain,
% 0.44/0.60 (multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), sk_c6)) = multiply(multiply(sk_c6, sk_c6), multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), sk_c6))),
% 0.44/0.60 inference(monotonicity,[status(thm)],[813])).
% 0.44/0.60 tff(916,plain,
% 0.44/0.60 (multiply(multiply(sk_c6, sk_c6), multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), sk_c6)) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), sk_c6))),
% 0.44/0.61 inference(symmetry,[status(thm)],[915])).
% 0.44/0.61 tff(917,plain,
% 0.44/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c6), multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), sk_c6)) = multiply(sk_c6, multiply(sk_c6, multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), sk_c6))))),
% 0.44/0.61 inference(quant_inst,[status(thm)],[])).
% 0.44/0.61 tff(918,plain,
% 0.44/0.61 (multiply(multiply(sk_c6, sk_c6), multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), sk_c6)) = multiply(sk_c6, multiply(sk_c6, multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), sk_c6)))),
% 0.44/0.61 inference(unit_resolution,[status(thm)],[917, 38])).
% 0.44/0.61 tff(919,plain,
% 0.44/0.61 (multiply(sk_c6, multiply(sk_c6, multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), sk_c6))) = multiply(multiply(sk_c6, sk_c6), multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), sk_c6))),
% 0.44/0.61 inference(symmetry,[status(thm)],[918])).
% 0.44/0.61 tff(920,plain,
% 0.44/0.61 (multiply(identity, multiply(sk_c5, sk_c8)) = multiply(multiply(identity, sk_c5), sk_c8)),
% 0.44/0.61 inference(symmetry,[status(thm)],[810])).
% 0.44/0.61 tff(921,plain,
% 0.44/0.61 (multiply(sk_c6, multiply(sk_c8, multiply(sk_c5, multiply(sk_c7, sk_c6)))) = multiply(multiply(sk_c6, sk_c8), multiply(sk_c5, multiply(sk_c7, sk_c6)))),
% 0.44/0.61 inference(symmetry,[status(thm)],[806])).
% 0.44/0.61 tff(922,plain,
% 0.44/0.61 (multiply(multiply(sk_c6, multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))), sk_c6) = multiply(sk_c6, sk_c6)),
% 0.44/0.61 inference(monotonicity,[status(thm)],[824])).
% 0.44/0.61 tff(923,plain,
% 0.44/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))), sk_c6) = multiply(sk_c6, multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), sk_c6)))),
% 0.44/0.61 inference(quant_inst,[status(thm)],[])).
% 0.44/0.61 tff(924,plain,
% 0.44/0.61 (multiply(multiply(sk_c6, multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))), sk_c6) = multiply(sk_c6, multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), sk_c6))),
% 0.44/0.61 inference(unit_resolution,[status(thm)],[923, 38])).
% 0.44/0.61 tff(925,plain,
% 0.44/0.61 (multiply(sk_c6, multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), sk_c6)) = multiply(multiply(sk_c6, multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))), sk_c6)),
% 0.44/0.61 inference(symmetry,[status(thm)],[924])).
% 0.44/0.61 tff(926,plain,
% 0.44/0.61 (multiply(sk_c6, multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), sk_c6)) = multiply(sk_c5, sk_c8)),
% 0.44/0.61 inference(transitivity,[status(thm)],[925, 922, 803, 921, 807, 920, 811])).
% 0.44/0.61 tff(927,plain,
% 0.44/0.61 (multiply(sk_c6, multiply(sk_c6, multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), sk_c6))) = multiply(multiply(sk_c7, sk_c8), multiply(sk_c5, sk_c8))),
% 0.44/0.61 inference(monotonicity,[status(thm)],[392, 926])).
% 0.44/0.61 tff(928,plain,
% 0.44/0.61 (multiply(multiply(sk_c7, sk_c8), multiply(sk_c5, sk_c8)) = multiply(sk_c6, multiply(sk_c6, multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), sk_c6)))),
% 0.44/0.61 inference(symmetry,[status(thm)],[927])).
% 0.44/0.61 tff(929,plain,
% 0.44/0.61 (multiply(sk_c7, multiply(sk_c8, multiply(sk_c5, sk_c8))) = multiply(multiply(sk_c7, sk_c8), multiply(sk_c5, sk_c8))),
% 0.44/0.61 inference(symmetry,[status(thm)],[422])).
% 0.44/0.61 tff(930,plain,
% 0.44/0.61 (multiply(sk_c7, sk_c6) = multiply(sk_c7, multiply(sk_c8, multiply(sk_c5, sk_c8)))),
% 0.44/0.61 inference(symmetry,[status(thm)],[420])).
% 0.44/0.61 tff(931,plain,
% 0.44/0.61 (multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))) = multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c8)),
% 0.44/0.61 inference(transitivity,[status(thm)],[608, 471, 470, 694, 10, 591, 930, 929, 928, 919, 916, 914, 911, 909, 907, 904])).
% 0.44/0.61 tff(932,plain,
% 0.44/0.61 (multiply(multiply(sk_c5, multiply(sk_c8, sk_c8)), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = multiply(multiply(sk_c5, multiply(sk_c8, sk_c8)), multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c8))),
% 0.44/0.61 inference(monotonicity,[status(thm)],[931])).
% 0.44/0.61 tff(933,plain,
% 0.44/0.61 (multiply(multiply(sk_c5, multiply(sk_c8, sk_c8)), multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c8)) = multiply(multiply(sk_c5, multiply(sk_c8, sk_c8)), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))))),
% 0.44/0.61 inference(symmetry,[status(thm)],[932])).
% 0.44/0.61 tff(934,plain,
% 0.44/0.61 (multiply(multiply(sk_c5, multiply(sk_c8, sk_c8)), multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c8)) = multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c8), multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c8))),
% 0.44/0.61 inference(monotonicity,[status(thm)],[847])).
% 0.44/0.61 tff(935,plain,
% 0.44/0.61 (multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c8), multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c8)) = multiply(multiply(sk_c5, multiply(sk_c8, sk_c8)), multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c8))),
% 0.44/0.61 inference(symmetry,[status(thm)],[934])).
% 0.44/0.61 tff(936,plain,
% 0.44/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c8), multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c8)) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c8, multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c8))))),
% 0.44/0.61 inference(quant_inst,[status(thm)],[])).
% 0.44/0.61 tff(937,plain,
% 0.44/0.61 (multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c8), multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c8)) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c8, multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c8)))),
% 0.44/0.61 inference(unit_resolution,[status(thm)],[936, 38])).
% 0.44/0.61 tff(938,plain,
% 0.44/0.61 (multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c8, multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c8))) = multiply(multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), sk_c8), multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c8))),
% 0.44/0.61 inference(symmetry,[status(thm)],[937])).
% 0.44/0.61 tff(939,plain,
% 0.44/0.61 (multiply(sk_c6, multiply(sk_c7, sk_c8)) = multiply(sk_c6, sk_c6)),
% 0.44/0.61 inference(monotonicity,[status(thm)],[391])).
% 0.44/0.61 tff(940,plain,
% 0.44/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c7), sk_c8) = multiply(sk_c6, multiply(sk_c7, sk_c8)))),
% 0.44/0.61 inference(quant_inst,[status(thm)],[])).
% 0.44/0.61 tff(941,plain,
% 0.44/0.61 (multiply(multiply(sk_c6, sk_c7), sk_c8) = multiply(sk_c6, multiply(sk_c7, sk_c8))),
% 0.44/0.61 inference(unit_resolution,[status(thm)],[940, 38])).
% 0.44/0.61 tff(942,plain,
% 0.44/0.61 (multiply(multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c7))), sk_c8) = multiply(multiply(sk_c6, sk_c7), sk_c8)),
% 0.44/0.61 inference(monotonicity,[status(thm)],[772])).
% 0.44/0.61 tff(943,plain,
% 0.44/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c7))), sk_c8) = multiply(sk_c8, multiply(multiply(sk_c5, multiply(sk_c8, sk_c7)), sk_c8)))),
% 0.44/0.61 inference(quant_inst,[status(thm)],[])).
% 0.44/0.61 tff(944,plain,
% 0.44/0.61 (multiply(multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c7))), sk_c8) = multiply(sk_c8, multiply(multiply(sk_c5, multiply(sk_c8, sk_c7)), sk_c8))),
% 0.44/0.61 inference(unit_resolution,[status(thm)],[943, 38])).
% 0.44/0.61 tff(945,plain,
% 0.44/0.61 (multiply(sk_c8, multiply(multiply(sk_c5, multiply(sk_c8, sk_c7)), sk_c8)) = multiply(multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c7))), sk_c8)),
% 0.44/0.61 inference(symmetry,[status(thm)],[944])).
% 0.44/0.61 tff(946,plain,
% 0.44/0.61 (multiply(multiply(sk_c5, multiply(sk_c8, sk_c7)), sk_c8) = multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c8)),
% 0.44/0.61 inference(monotonicity,[status(thm)],[628])).
% 0.44/0.61 tff(947,plain,
% 0.44/0.61 (multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c8) = multiply(multiply(sk_c5, multiply(sk_c8, sk_c7)), sk_c8)),
% 0.44/0.61 inference(symmetry,[status(thm)],[946])).
% 0.44/0.61 tff(948,plain,
% 0.44/0.61 (multiply(sk_c8, multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c8)) = multiply(sk_c8, multiply(multiply(sk_c5, multiply(sk_c8, sk_c7)), sk_c8))),
% 0.44/0.61 inference(monotonicity,[status(thm)],[947])).
% 0.44/0.61 tff(949,plain,
% 0.44/0.61 (multiply(sk_c8, multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c8)) = multiply(sk_c5, multiply(sk_c7, sk_c6))),
% 0.44/0.61 inference(transitivity,[status(thm)],[948, 945, 942, 941, 939, 803, 921, 807, 920, 811, 791])).
% 0.44/0.61 tff(950,plain,
% 0.44/0.61 (multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c8, multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c8))) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c7, sk_c6)))),
% 0.44/0.61 inference(monotonicity,[status(thm)],[949])).
% 0.44/0.61 tff(951,plain,
% 0.44/0.61 (multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c7, sk_c6))) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c8, multiply(multiply(multiply(sk_c5, sk_c8), sk_c7), sk_c8)))),
% 0.44/0.61 inference(symmetry,[status(thm)],[950])).
% 0.44/0.61 tff(952,plain,
% 0.44/0.61 (multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c7, sk_c6))) = multiply(multiply(sk_c5, sk_c8), multiply(sk_c5, multiply(sk_c7, sk_c6)))),
% 0.44/0.61 inference(monotonicity,[status(thm)],[398])).
% 0.44/0.61 tff(953,plain,
% 0.44/0.61 (multiply(multiply(sk_c5, sk_c8), multiply(sk_c5, multiply(sk_c7, sk_c6))) = multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c7, sk_c6)))),
% 0.44/0.61 inference(symmetry,[status(thm)],[952])).
% 0.44/0.61 tff(954,plain,
% 0.44/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c5, sk_c8), multiply(sk_c5, multiply(sk_c7, sk_c6))) = multiply(sk_c5, multiply(sk_c8, multiply(sk_c5, multiply(sk_c7, sk_c6)))))),
% 0.44/0.61 inference(quant_inst,[status(thm)],[])).
% 0.44/0.61 tff(955,plain,
% 0.44/0.61 (multiply(multiply(sk_c5, sk_c8), multiply(sk_c5, multiply(sk_c7, sk_c6))) = multiply(sk_c5, multiply(sk_c8, multiply(sk_c5, multiply(sk_c7, sk_c6))))),
% 0.44/0.61 inference(unit_resolution,[status(thm)],[954, 38])).
% 0.44/0.61 tff(956,plain,
% 0.44/0.61 (multiply(sk_c5, multiply(sk_c8, multiply(sk_c5, multiply(sk_c7, sk_c6)))) = multiply(multiply(sk_c5, sk_c8), multiply(sk_c5, multiply(sk_c7, sk_c6)))),
% 0.44/0.61 inference(symmetry,[status(thm)],[955])).
% 0.44/0.61 tff(957,plain,
% 0.44/0.61 (multiply(sk_c8, multiply(sk_c5, multiply(sk_c7, sk_c6))) = sk_c6),
% 0.44/0.61 inference(transitivity,[status(thm)],[399, 418, 403, 391])).
% 0.44/0.61 tff(958,plain,
% 0.44/0.61 (multiply(sk_c5, multiply(sk_c8, multiply(sk_c5, multiply(sk_c7, sk_c6)))) = multiply(sk_c5, sk_c6)),
% 0.44/0.61 inference(monotonicity,[status(thm)],[957])).
% 0.44/0.61 tff(959,plain,
% 0.44/0.61 (multiply(sk_c5, sk_c6) = multiply(sk_c5, multiply(sk_c8, multiply(sk_c5, multiply(sk_c7, sk_c6))))),
% 0.44/0.61 inference(symmetry,[status(thm)],[958])).
% 0.44/0.61 tff(960,plain,
% 0.44/0.61 (identity = multiply(multiply(sk_c5, multiply(sk_c8, sk_c8)), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))))),
% 0.44/0.61 inference(transitivity,[status(thm)],[163, 679, 456, 684, 451, 682, 959, 956, 953, 951, 938, 935, 933])).
% 0.44/0.61 tff(961,plain,
% 0.44/0.61 (multiply(identity, sk_c3) = multiply(multiply(multiply(sk_c5, multiply(sk_c8, sk_c8)), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))), sk_c3)),
% 0.44/0.61 inference(monotonicity,[status(thm)],[960])).
% 0.44/0.61 tff(962,plain,
% 0.44/0.61 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c3) = sk_c3)),
% 0.44/0.61 inference(quant_inst,[status(thm)],[])).
% 0.44/0.61 tff(963,plain,
% 0.44/0.61 (multiply(identity, sk_c3) = sk_c3),
% 0.44/0.61 inference(unit_resolution,[status(thm)],[962, 8])).
% 0.44/0.61 tff(964,plain,
% 0.44/0.61 (sk_c3 = multiply(identity, sk_c3)),
% 0.44/0.61 inference(symmetry,[status(thm)],[963])).
% 0.44/0.61 tff(965,plain,
% 0.44/0.61 (((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c4, sk_c8) = sk_c5)) <=> ((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c4, sk_c8) = sk_c5))),
% 0.44/0.61 inference(rewrite,[status(thm)],[])).
% 0.44/0.61 tff(966,axiom,((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c4, sk_c8) = sk_c5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_24')).
% 0.44/0.61 tff(967,plain,
% 0.44/0.61 ((multiply(sk_c2, sk_c8) = sk_c3) | (multiply(sk_c4, sk_c8) = sk_c5)),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[966, 965])).
% 0.44/0.61 tff(968,plain,
% 0.44/0.61 (multiply(sk_c2, sk_c8) = sk_c3),
% 0.44/0.61 inference(unit_resolution,[status(thm)],[967, 670])).
% 0.44/0.61 tff(969,plain,
% 0.44/0.61 (multiply(sk_c2, sk_c8) = multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))),
% 0.44/0.61 inference(transitivity,[status(thm)],[968, 964, 961, 902, 900, 848, 783, 781, 752, 750, 747, 740, 738, 736, 734, 730, 722, 720, 406, 409, 412, 692, 696, 613, 710, 606, 186, 690, 441, 439, 437])).
% 0.44/0.61 tff(970,plain,
% 0.44/0.61 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))))),
% 0.44/0.61 inference(monotonicity,[status(thm)],[691, 969])).
% 0.44/0.61 tff(971,plain,
% 0.44/0.61 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7),
% 0.44/0.61 inference(transitivity,[status(thm)],[970, 714, 544, 688, 56])).
% 0.44/0.61 tff(972,plain,
% 0.44/0.61 (multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c8))) = identity),
% 0.44/0.61 inference(transitivity,[status(thm)],[527, 429, 525, 434, 96])).
% 0.44/0.61 tff(973,plain,
% 0.44/0.61 (multiply(sk_c5, multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c8)))) = multiply(sk_c5, identity)),
% 0.44/0.61 inference(monotonicity,[status(thm)],[972])).
% 0.44/0.61 tff(974,plain,
% 0.44/0.61 (multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))) = multiply(sk_c5, identity)),
% 0.44/0.61 inference(transitivity,[status(thm)],[519, 522, 973])).
% 0.44/0.61 tff(975,plain,
% 0.44/0.61 (multiply(multiply(sk_c5, sk_c6), multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))) = multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c5, identity))),
% 0.44/0.61 inference(monotonicity,[status(thm)],[683, 974])).
% 0.44/0.61 tff(976,plain,
% 0.44/0.61 (multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c5, identity)) = multiply(multiply(sk_c5, sk_c6), multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))),
% 0.44/0.61 inference(symmetry,[status(thm)],[975])).
% 0.44/0.61 tff(977,plain,
% 0.44/0.61 (multiply(sk_c1, sk_c7) = multiply(sk_c5, identity)),
% 0.44/0.61 inference(transitivity,[status(thm)],[606, 186, 690, 441, 439])).
% 0.44/0.61 tff(978,plain,
% 0.44/0.61 (identity = multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6))),
% 0.44/0.61 inference(transitivity,[status(thm)],[163, 679, 456, 684, 451])).
% 0.44/0.61 tff(979,plain,
% 0.44/0.61 (multiply(identity, multiply(sk_c1, sk_c7)) = multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c5, identity))),
% 0.44/0.61 inference(monotonicity,[status(thm)],[978, 977])).
% 0.44/0.61 tff(980,plain,
% 0.44/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, sk_c1), sk_c7) = multiply(identity, multiply(sk_c1, sk_c7)))),
% 0.44/0.61 inference(quant_inst,[status(thm)],[])).
% 0.44/0.61 tff(981,plain,
% 0.44/0.61 (multiply(multiply(identity, sk_c1), sk_c7) = multiply(identity, multiply(sk_c1, sk_c7))),
% 0.44/0.61 inference(unit_resolution,[status(thm)],[980, 38])).
% 0.44/0.61 tff(982,plain,
% 0.44/0.61 (multiply(multiply(identity, sk_c1), sk_c7) = sk_c8),
% 0.44/0.61 inference(transitivity,[status(thm)],[981, 979, 976, 535, 608, 471, 470, 694, 10])).
% 0.44/0.61 tff(983,plain,
% 0.44/0.61 (((inverse(sk_c2) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c5)) <=> ((inverse(sk_c2) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c5))),
% 0.44/0.61 inference(rewrite,[status(thm)],[])).
% 0.44/0.61 tff(984,axiom,((inverse(sk_c2) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_29')).
% 0.44/0.61 tff(985,plain,
% 0.44/0.61 ((inverse(sk_c2) = sk_c8) | (multiply(sk_c4, sk_c8) = sk_c5)),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[984, 983])).
% 0.44/0.61 tff(986,plain,
% 0.44/0.61 (inverse(sk_c2) = sk_c8),
% 0.44/0.61 inference(unit_resolution,[status(thm)],[985, 670])).
% 0.44/0.61 tff(987,plain,
% 0.44/0.61 (((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(multiply(identity, sk_c1), sk_c7) = sk_c8)) | (~(inverse(multiply(identity, sk_c1)) = sk_c7)))) <=> ((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(multiply(identity, sk_c1), sk_c7) = sk_c8)) | (~(inverse(multiply(identity, sk_c1)) = sk_c7)))),
% 0.44/0.61 inference(rewrite,[status(thm)],[])).
% 0.44/0.61 tff(988,plain,
% 0.44/0.61 (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(multiply(identity, sk_c1), sk_c7) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(inverse(multiply(identity, sk_c1)) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(multiply(identity, sk_c1), sk_c7) = sk_c8)) | (~(inverse(multiply(identity, sk_c1)) = sk_c7)))),
% 0.44/0.61 inference(rewrite,[status(thm)],[])).
% 0.44/0.61 tff(989,plain,
% 0.44/0.61 (((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(multiply(identity, sk_c1), sk_c7) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(inverse(multiply(identity, sk_c1)) = sk_c7)))) <=> ((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(multiply(identity, sk_c1), sk_c7) = sk_c8)) | (~(inverse(multiply(identity, sk_c1)) = sk_c7))))),
% 0.44/0.61 inference(monotonicity,[status(thm)],[988])).
% 0.44/0.61 tff(990,plain,
% 0.44/0.61 (((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(multiply(identity, sk_c1), sk_c7) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(inverse(multiply(identity, sk_c1)) = sk_c7)))) <=> ((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(multiply(identity, sk_c1), sk_c7) = sk_c8)) | (~(inverse(multiply(identity, sk_c1)) = sk_c7)))),
% 0.44/0.62 inference(transitivity,[status(thm)],[989, 987])).
% 0.44/0.62 tff(991,plain,
% 0.44/0.62 ((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(multiply(identity, sk_c1), sk_c7) = sk_c8)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(inverse(multiply(identity, sk_c1)) = sk_c7)))),
% 0.44/0.62 inference(quant_inst,[status(thm)],[])).
% 0.44/0.62 tff(992,plain,
% 0.44/0.62 ((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(multiply(identity, sk_c1), sk_c7) = sk_c8)) | (~(inverse(multiply(identity, sk_c1)) = sk_c7))),
% 0.44/0.62 inference(modus_ponens,[status(thm)],[991, 990])).
% 0.44/0.62 tff(993,plain,
% 0.44/0.62 ((~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(inverse(multiply(identity, sk_c1)) = sk_c7))),
% 0.44/0.62 inference(unit_resolution,[status(thm)],[992, 391, 397, 221, 986, 352, 982])).
% 0.44/0.62 tff(994,plain,
% 0.44/0.62 ($false),
% 0.44/0.62 inference(unit_resolution,[status(thm)],[993, 971, 676])).
% 0.44/0.62 tff(995,plain,(multiply(sk_c4, sk_c8) = sk_c5), inference(lemma,lemma(discharge,[]))).
% 0.44/0.62 tff(996,plain,
% 0.44/0.62 (multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))) = sk_c8),
% 0.44/0.62 inference(transitivity,[status(thm)],[608, 471, 470, 469, 10])).
% 0.44/0.62 tff(997,plain,
% 0.44/0.62 (multiply(sk_c4, multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = multiply(sk_c4, sk_c8)),
% 0.44/0.62 inference(monotonicity,[status(thm)],[996])).
% 0.44/0.62 tff(998,plain,
% 0.44/0.62 (multiply(sk_c4, multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))),
% 0.44/0.62 inference(transitivity,[status(thm)],[997, 995, 553, 632, 548, 631, 406, 409, 412, 467, 610, 613, 657, 606, 186, 465, 441, 439, 437])).
% 0.44/0.62 tff(999,plain,
% 0.44/0.62 (multiply(multiply(sk_c4, multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))))),
% 0.46/0.62 inference(monotonicity,[status(thm)],[998])).
% 0.46/0.62 tff(1000,plain,
% 0.46/0.62 (multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = multiply(multiply(sk_c4, multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))))),
% 0.46/0.62 inference(symmetry,[status(thm)],[999])).
% 0.46/0.62 tff(1001,plain,
% 0.46/0.62 (sk_c7 = multiply(sk_c4, sk_c7)),
% 0.46/0.62 inference(transitivity,[status(thm)],[132, 482, 543, 664, 1000, 669, 667])).
% 0.46/0.62 tff(1002,assumption,(inverse(sk_c4) = sk_c8), introduced(assumption)).
% 0.46/0.62 tff(1003,plain,
% 0.46/0.62 ((inverse(sk_c4) = sk_c7) <=> (sk_c8 = multiply(sk_c4, sk_c7))),
% 0.46/0.62 inference(monotonicity,[status(thm)],[1002, 1001])).
% 0.46/0.62 tff(1004,plain,
% 0.46/0.62 ((inverse(sk_c4) = sk_c7) <=> (multiply(sk_c4, sk_c7) = sk_c8)),
% 0.46/0.62 inference(transitivity,[status(thm)],[1003, 1])).
% 0.46/0.62 tff(1005,plain,
% 0.46/0.62 ((~(inverse(sk_c4) = sk_c7)) <=> (~(multiply(sk_c4, sk_c7) = sk_c8))),
% 0.46/0.62 inference(monotonicity,[status(thm)],[1004])).
% 0.46/0.62 tff(1006,plain,
% 0.46/0.62 (multiply(sk_c4, sk_c8) = multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))),
% 0.46/0.62 inference(transitivity,[status(thm)],[995, 553, 632, 548, 631, 406, 409, 412, 467, 610, 613, 657, 606, 186, 465, 441, 439, 437])).
% 0.46/0.62 tff(1007,plain,
% 0.46/0.62 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))))),
% 0.46/0.62 inference(monotonicity,[status(thm)],[466, 1006])).
% 0.46/0.62 tff(1008,plain,
% 0.46/0.62 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7),
% 0.46/0.62 inference(transitivity,[status(thm)],[1007, 663, 544, 483, 56])).
% 0.46/0.62 tff(1009,plain,
% 0.46/0.62 (multiply(multiply(sk_c5, sk_c6), multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))) = multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c5, identity))),
% 0.46/0.62 inference(monotonicity,[status(thm)],[448, 974])).
% 0.46/0.62 tff(1010,plain,
% 0.46/0.62 (multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c5, identity)) = multiply(multiply(sk_c5, sk_c6), multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))),
% 0.46/0.62 inference(symmetry,[status(thm)],[1009])).
% 0.46/0.62 tff(1011,plain,
% 0.46/0.62 (sk_c8 = inverse(sk_c4)),
% 0.46/0.62 inference(symmetry,[status(thm)],[1002])).
% 0.46/0.62 tff(1012,plain,
% 0.46/0.62 (multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))) = inverse(sk_c4)),
% 0.46/0.62 inference(transitivity,[status(thm)],[608, 471, 470, 469, 10, 1011])).
% 0.46/0.62 tff(1013,plain,
% 0.46/0.62 (multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.46/0.62 inference(monotonicity,[status(thm)],[1012])).
% 0.46/0.62 tff(1014,plain,
% 0.46/0.62 (multiply(inverse(sk_c4), sk_c4) = multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c4)),
% 0.46/0.62 inference(symmetry,[status(thm)],[1013])).
% 0.46/0.62 tff(1015,plain,
% 0.46/0.62 (multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)) = multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c4)),
% 0.46/0.62 inference(transitivity,[status(thm)],[686, 452, 455, 462, 96, 94, 1014])).
% 0.46/0.62 tff(1016,plain,
% 0.46/0.62 (multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c5, identity)) = multiply(multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c4), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))))),
% 0.46/0.62 inference(monotonicity,[status(thm)],[1015, 437])).
% 0.46/0.62 tff(1017,plain,
% 0.46/0.62 (multiply(multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), sk_c4), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = multiply(multiply(sk_c5, multiply(multiply(sk_c7, sk_c7), sk_c6)), multiply(sk_c5, identity))),
% 0.46/0.62 inference(symmetry,[status(thm)],[1016])).
% 0.46/0.62 tff(1018,plain,
% 0.46/0.62 (multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c4, multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))))) = multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))))),
% 0.46/0.62 inference(monotonicity,[status(thm)],[998])).
% 0.46/0.62 tff(1019,plain,
% 0.46/0.62 (multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))) = multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c4, multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))))),
% 0.46/0.62 inference(symmetry,[status(thm)],[1018])).
% 0.46/0.62 tff(1020,plain,
% 0.46/0.62 (multiply(sk_c4, multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))))) = multiply(multiply(sk_c4, multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))))),
% 0.46/0.62 inference(symmetry,[status(thm)],[669])).
% 0.46/0.62 tff(1021,plain,
% 0.46/0.62 (multiply(sk_c4, sk_c7) = sk_c8),
% 0.46/0.62 inference(transitivity,[status(thm)],[666, 1020, 999, 1019, 540, 1017, 1010, 535, 608, 471, 470, 469, 10])).
% 0.46/0.62 tff(1022,plain,
% 0.46/0.62 (((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)))) <=> ((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)))),
% 0.46/0.62 inference(rewrite,[status(thm)],[])).
% 0.46/0.62 tff(1023,plain,
% 0.46/0.62 (((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c7))) <=> ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)))),
% 0.46/0.62 inference(rewrite,[status(thm)],[])).
% 0.46/0.62 tff(1024,plain,
% 0.46/0.62 (((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c7)))) <=> ((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7))))),
% 0.46/0.62 inference(monotonicity,[status(thm)],[1023])).
% 0.46/0.62 tff(1025,plain,
% 0.46/0.62 (((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c7)))) <=> ((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)))),
% 0.46/0.62 inference(transitivity,[status(thm)],[1024, 1022])).
% 0.46/0.62 tff(1026,plain,
% 0.46/0.62 ((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c7)))),
% 0.46/0.63 inference(quant_inst,[status(thm)],[])).
% 0.46/0.63 tff(1027,plain,
% 0.46/0.63 ((~![X3: $i, X2: $i, X5: $i] : ((~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(inverse(X2) = sk_c8)) | (~(multiply(sk_c8, multiply(X2, sk_c8)) = sk_c7)) | (~(multiply(X3, sk_c7) = sk_c8)) | (~(inverse(X5) = sk_c8)) | (~(multiply(sk_c8, multiply(X5, sk_c8)) = sk_c7)) | (~(inverse(X3) = sk_c7)))) | (~(multiply(sk_c7, sk_c8) = sk_c6)) | (~(multiply(sk_c7, sk_c6) = sk_c8)) | (~(inverse(sk_c8) = sk_c6)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7))),
% 0.46/0.63 inference(modus_ponens,[status(thm)],[1026, 1025])).
% 0.46/0.63 tff(1028,plain,
% 0.46/0.63 ((~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7))),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[1027, 391, 397, 221, 1002, 352])).
% 0.46/0.63 tff(1029,plain,
% 0.46/0.63 (~(inverse(sk_c4) = sk_c7)),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[1028, 1021, 1008])).
% 0.46/0.63 tff(1030,plain,
% 0.46/0.63 (~(multiply(sk_c4, sk_c7) = sk_c8)),
% 0.46/0.63 inference(modus_ponens,[status(thm)],[1029, 1005])).
% 0.46/0.63 tff(1031,plain,
% 0.46/0.63 ($false),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[1021, 1030])).
% 0.46/0.63 tff(1032,plain,(~(inverse(sk_c4) = sk_c8)), inference(lemma,lemma(discharge,[]))).
% 0.46/0.63 tff(1033,plain,
% 0.46/0.63 (((inverse(sk_c1) = sk_c7) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c1) = sk_c7) | (inverse(sk_c4) = sk_c8))),
% 0.46/0.63 inference(rewrite,[status(thm)],[])).
% 0.46/0.63 tff(1034,axiom,((inverse(sk_c1) = sk_c7) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_15')).
% 0.46/0.63 tff(1035,plain,
% 0.46/0.63 ((inverse(sk_c1) = sk_c7) | (inverse(sk_c4) = sk_c8)),
% 0.46/0.63 inference(modus_ponens,[status(thm)],[1034, 1033])).
% 0.46/0.63 tff(1036,plain,
% 0.46/0.63 (inverse(sk_c1) = sk_c7),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[1035, 1032])).
% 0.46/0.63 tff(1037,plain,
% 0.46/0.63 (inverse(multiply(identity, sk_c1)) = sk_c7),
% 0.46/0.63 inference(transitivity,[status(thm)],[675, 1036])).
% 0.46/0.63 tff(1038,plain,
% 0.46/0.63 (((inverse(sk_c4) = sk_c8) | (multiply(sk_c2, sk_c8) = sk_c3)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c2, sk_c8) = sk_c3))),
% 0.46/0.63 inference(rewrite,[status(thm)],[])).
% 0.46/0.63 tff(1039,plain,
% 0.46/0.63 (((multiply(sk_c2, sk_c8) = sk_c3) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c2, sk_c8) = sk_c3))),
% 0.46/0.63 inference(rewrite,[status(thm)],[])).
% 0.46/0.63 tff(1040,axiom,((multiply(sk_c2, sk_c8) = sk_c3) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_25')).
% 0.46/0.63 tff(1041,plain,
% 0.46/0.63 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c2, sk_c8) = sk_c3)),
% 0.46/0.63 inference(modus_ponens,[status(thm)],[1040, 1039])).
% 0.46/0.63 tff(1042,plain,
% 0.46/0.63 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c2, sk_c8) = sk_c3)),
% 0.46/0.63 inference(modus_ponens,[status(thm)],[1041, 1038])).
% 0.46/0.63 tff(1043,plain,
% 0.46/0.63 (multiply(sk_c2, sk_c8) = sk_c3),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[1042, 1032])).
% 0.46/0.63 tff(1044,plain,
% 0.46/0.63 (multiply(sk_c2, sk_c8) = multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8)))))),
% 0.46/0.63 inference(transitivity,[status(thm)],[1043, 964, 961, 902, 900, 848, 783, 781, 752, 750, 747, 740, 738, 736, 734, 730, 722, 720, 406, 409, 412, 692, 696, 613, 710, 606, 186, 690, 441, 439, 437])).
% 0.46/0.63 tff(1045,plain,
% 0.46/0.63 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = multiply(multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))), multiply(sk_c5, multiply(sk_c6, multiply(multiply(sk_c5, multiply(sk_c7, sk_c6)), multiply(sk_c5, multiply(sk_c8, sk_c8))))))),
% 0.46/0.63 inference(monotonicity,[status(thm)],[691, 1044])).
% 0.46/0.63 tff(1046,plain,
% 0.46/0.63 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7),
% 0.46/0.63 inference(transitivity,[status(thm)],[1045, 714, 544, 688, 56])).
% 0.46/0.63 tff(1047,plain,
% 0.46/0.63 (((inverse(sk_c2) = sk_c8) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c2) = sk_c8) | (inverse(sk_c4) = sk_c8))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(1048,axiom,((inverse(sk_c2) = sk_c8) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_30')).
% 0.47/0.63 tff(1049,plain,
% 0.47/0.63 ((inverse(sk_c2) = sk_c8) | (inverse(sk_c4) = sk_c8)),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[1048, 1047])).
% 0.47/0.63 tff(1050,plain,
% 0.47/0.63 (inverse(sk_c2) = sk_c8),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[1049, 1032])).
% 0.47/0.63 tff(1051,plain,
% 0.47/0.63 ((~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(inverse(multiply(identity, sk_c1)) = sk_c7))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[992, 391, 397, 221, 1050, 352, 982])).
% 0.47/0.63 tff(1052,plain,
% 0.47/0.63 ($false),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[1051, 1046, 1037])).
% 0.47/0.63 % SZS output end Proof
% 0.47/0.63 % E exiting
%------------------------------------------------------------------------------