%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP236-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:07:30 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.54s
% Output : Proof 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP236-1 : TPTP v9.0.0. Released v2.5.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 15:50:09 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.54 % SZS status Unsatisfiable
% 0.21/0.54 % SZS output start Proof
% 0.21/0.54 tff(sk_c7_type, type, (
% 0.21/0.54 sk_c7: $i)).
% 0.21/0.54 tff(multiply_type, type, (
% 0.21/0.54 multiply: ( $i * $i ) > $i)).
% 0.21/0.54 tff(inverse_type, type, (
% 0.21/0.54 inverse: $i > $i)).
% 0.21/0.54 tff(sk_c1_type, type, (
% 0.21/0.54 sk_c1: $i)).
% 0.21/0.54 tff(sk_c3_type, type, (
% 0.21/0.54 sk_c3: $i)).
% 0.21/0.54 tff(identity_type, type, (
% 0.21/0.54 identity: $i)).
% 0.21/0.54 tff(sk_c8_type, type, (
% 0.21/0.54 sk_c8: $i)).
% 0.21/0.54 tff(sk_c4_type, type, (
% 0.21/0.54 sk_c4: $i)).
% 0.21/0.54 tff(sk_c6_type, type, (
% 0.21/0.54 sk_c6: $i)).
% 0.21/0.54 tff(sk_c5_type, type, (
% 0.21/0.54 sk_c5: $i)).
% 0.21/0.54 tff(sk_c2_type, type, (
% 0.21/0.54 sk_c2: $i)).
% 0.21/0.54 tff(1,plain,
% 0.21/0.54 (^[X: $i] : refl((multiply(identity, X) = X) <=> (multiply(identity, X) = X))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(2,plain,
% 0.21/0.54 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.21/0.54 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.54 tff(3,plain,
% 0.21/0.54 (![X: $i] : (multiply(identity, X) = X) <=> ![X: $i] : (multiply(identity, X) = X)),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(4,axiom,(![X: $i] : (multiply(identity, X) = X)), file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax','left_identity')).
% 0.21/0.54 tff(5,plain,
% 0.21/0.54 (![X: $i] : (multiply(identity, X) = X)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.54 tff(6,plain,(
% 0.21/0.54 ![X: $i] : (multiply(identity, X) = X)),
% 0.21/0.54 inference(skolemize,[status(sab)],[5])).
% 0.21/0.54 tff(7,plain,
% 0.21/0.54 (![X: $i] : (multiply(identity, X) = X)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.54 tff(8,plain,
% 0.21/0.54 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c7) = sk_c7)),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(9,plain,
% 0.21/0.54 (multiply(identity, sk_c7) = sk_c7),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.54 tff(10,plain,
% 0.21/0.54 (^[X: $i] : refl((multiply(inverse(X), X) = identity) <=> (multiply(inverse(X), X) = identity))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(11,plain,
% 0.21/0.54 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.21/0.54 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.54 tff(12,plain,
% 0.21/0.54 (![X: $i] : (multiply(inverse(X), X) = identity) <=> ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(13,axiom,(![X: $i] : (multiply(inverse(X), X) = identity)), file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax','left_inverse')).
% 0.21/0.54 tff(14,plain,
% 0.21/0.54 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.21/0.54 tff(15,plain,(
% 0.21/0.54 ![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.21/0.54 inference(skolemize,[status(sab)],[14])).
% 0.21/0.54 tff(16,plain,
% 0.21/0.54 (![X: $i] : (multiply(inverse(X), X) = identity)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.21/0.54 tff(17,plain,
% 0.21/0.54 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c1), sk_c1) = identity)),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(18,plain,
% 0.21/0.54 (multiply(inverse(sk_c1), sk_c1) = identity),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.21/0.54 tff(19,assumption,(~(multiply(sk_c8, sk_c6) = sk_c7)), introduced(assumption)).
% 0.21/0.54 tff(20,plain,
% 0.21/0.54 (((inverse(sk_c1) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7)) <=> ((inverse(sk_c1) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(21,axiom,((inverse(sk_c1) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_4')).
% 0.21/0.54 tff(22,plain,
% 0.21/0.54 ((inverse(sk_c1) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.54 tff(23,plain,
% 0.21/0.54 (inverse(sk_c1) = sk_c8),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[22, 19])).
% 0.21/0.54 tff(24,plain,
% 0.21/0.54 (sk_c8 = inverse(sk_c1)),
% 0.21/0.54 inference(symmetry,[status(thm)],[23])).
% 0.21/0.54 tff(25,plain,
% 0.21/0.54 (multiply(sk_c8, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.21/0.54 inference(monotonicity,[status(thm)],[24])).
% 0.21/0.54 tff(26,plain,
% 0.21/0.54 (multiply(sk_c8, sk_c1) = identity),
% 0.21/0.54 inference(transitivity,[status(thm)],[25, 18])).
% 0.21/0.54 tff(27,plain,
% 0.21/0.54 (multiply(multiply(sk_c8, sk_c1), sk_c7) = multiply(identity, sk_c7)),
% 0.21/0.54 inference(monotonicity,[status(thm)],[26])).
% 0.21/0.54 tff(28,plain,
% 0.21/0.54 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c8, sk_c1)),
% 0.21/0.55 inference(symmetry,[status(thm)],[25])).
% 0.21/0.55 tff(29,plain,
% 0.21/0.55 (identity = multiply(inverse(sk_c1), sk_c1)),
% 0.21/0.55 inference(symmetry,[status(thm)],[18])).
% 0.21/0.55 tff(30,plain,
% 0.21/0.55 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c8), sk_c8) = identity)),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(31,plain,
% 0.21/0.55 (multiply(inverse(sk_c8), sk_c8) = identity),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[30, 16])).
% 0.21/0.55 tff(32,plain,
% 0.21/0.55 (((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7)) <=> ((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(33,axiom,((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_9')).
% 0.21/0.55 tff(34,plain,
% 0.21/0.55 ((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c8, sk_c6) = sk_c7)),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.21/0.55 tff(35,plain,
% 0.21/0.55 (multiply(sk_c1, sk_c7) = sk_c8),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[34, 19])).
% 0.21/0.55 tff(36,plain,
% 0.21/0.55 ((inverse(sk_c8) = sk_c7) <=> (inverse(sk_c8) = sk_c7)),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(37,axiom,(inverse(sk_c8) = sk_c7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_1')).
% 0.21/0.55 tff(38,plain,
% 0.21/0.55 (inverse(sk_c8) = sk_c7),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.21/0.55 tff(39,plain,
% 0.21/0.55 (sk_c7 = inverse(sk_c8)),
% 0.21/0.55 inference(symmetry,[status(thm)],[38])).
% 0.21/0.55 tff(40,plain,
% 0.21/0.55 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(inverse(sk_c8), sk_c8)),
% 0.21/0.55 inference(monotonicity,[status(thm)],[39, 35])).
% 0.21/0.55 tff(41,plain,
% 0.21/0.55 (^[Z: $i, Y: $i, X: $i] : refl((multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))) <=> (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))))),
% 0.21/0.55 inference(bind,[status(th)],[])).
% 0.21/0.55 tff(42,plain,
% 0.21/0.55 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.21/0.55 inference(quant_intro,[status(thm)],[41])).
% 0.21/0.55 tff(43,plain,
% 0.21/0.55 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(44,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')).
% 0.21/0.55 tff(45,plain,
% 0.21/0.55 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.21/0.55 tff(46,plain,(
% 0.21/0.55 ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.21/0.55 inference(skolemize,[status(sab)],[45])).
% 0.21/0.55 tff(47,plain,
% 0.21/0.55 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.21/0.55 tff(48,plain,
% 0.21/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(sk_c7, multiply(sk_c1, sk_c7)))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(49,plain,
% 0.21/0.55 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.21/0.55 tff(50,plain,
% 0.21/0.55 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(sk_c8, sk_c1)),
% 0.21/0.55 inference(transitivity,[status(thm)],[49, 40, 31, 29, 28])).
% 0.21/0.55 tff(51,plain,
% 0.21/0.55 (multiply(multiply(multiply(sk_c7, sk_c1), sk_c7), sk_c7) = multiply(multiply(sk_c8, sk_c1), sk_c7)),
% 0.21/0.55 inference(monotonicity,[status(thm)],[50])).
% 0.21/0.55 tff(52,plain,
% 0.21/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c7, sk_c1), sk_c7), sk_c7) = multiply(multiply(sk_c7, sk_c1), multiply(sk_c7, sk_c7)))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(53,plain,
% 0.21/0.55 (multiply(multiply(multiply(sk_c7, sk_c1), sk_c7), sk_c7) = multiply(multiply(sk_c7, sk_c1), multiply(sk_c7, sk_c7))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[52, 47])).
% 0.21/0.55 tff(54,plain,
% 0.21/0.55 (multiply(multiply(sk_c7, sk_c1), multiply(sk_c7, sk_c7)) = multiply(multiply(multiply(sk_c7, sk_c1), sk_c7), sk_c7)),
% 0.21/0.55 inference(symmetry,[status(thm)],[53])).
% 0.21/0.55 tff(55,assumption,(~(multiply(sk_c3, sk_c8) = sk_c7)), introduced(assumption)).
% 0.21/0.55 tff(56,plain,
% 0.21/0.55 (((multiply(sk_c3, sk_c8) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7)) <=> ((multiply(sk_c3, sk_c8) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(57,axiom,((multiply(sk_c3, sk_c8) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_24')).
% 0.21/0.55 tff(58,plain,
% 0.21/0.55 ((multiply(sk_c3, sk_c8) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7)),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.21/0.55 tff(59,plain,
% 0.21/0.55 (multiply(sk_c8, sk_c6) = sk_c7),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[58, 55])).
% 0.21/0.55 tff(60,plain,
% 0.21/0.55 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c8) = sk_c8)),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(61,plain,
% 0.21/0.55 (multiply(identity, sk_c8) = sk_c8),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[60, 7])).
% 0.21/0.55 tff(62,plain,
% 0.21/0.55 (multiply(multiply(identity, sk_c8), sk_c6) = multiply(sk_c8, sk_c6)),
% 0.21/0.55 inference(monotonicity,[status(thm)],[61])).
% 0.21/0.55 tff(63,plain,
% 0.21/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, sk_c8), sk_c6) = multiply(identity, multiply(sk_c8, sk_c6)))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(64,plain,
% 0.21/0.55 (multiply(multiply(identity, sk_c8), sk_c6) = multiply(identity, multiply(sk_c8, sk_c6))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[63, 47])).
% 0.21/0.55 tff(65,plain,
% 0.21/0.55 (multiply(identity, multiply(sk_c8, sk_c6)) = multiply(multiply(identity, sk_c8), sk_c6)),
% 0.21/0.55 inference(symmetry,[status(thm)],[64])).
% 0.21/0.55 tff(66,plain,
% 0.21/0.55 (((multiply(sk_c3, sk_c8) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6)) <=> ((multiply(sk_c3, sk_c8) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(67,axiom,((multiply(sk_c3, sk_c8) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_25')).
% 0.21/0.55 tff(68,plain,
% 0.21/0.55 ((multiply(sk_c3, sk_c8) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6)),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.21/0.55 tff(69,plain,
% 0.21/0.55 (multiply(sk_c5, sk_c8) = sk_c6),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[68, 55])).
% 0.21/0.55 tff(70,plain,
% 0.21/0.55 (multiply(sk_c8, multiply(sk_c5, sk_c8)) = multiply(sk_c8, sk_c6)),
% 0.21/0.55 inference(monotonicity,[status(thm)],[69])).
% 0.21/0.55 tff(71,plain,
% 0.21/0.55 ((~![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)))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(72,plain,
% 0.21/0.55 (multiply(multiply(sk_c8, sk_c5), sk_c8) = multiply(sk_c8, multiply(sk_c5, sk_c8))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[71, 47])).
% 0.21/0.55 tff(73,plain,
% 0.21/0.55 (((inverse(sk_c5) = sk_c8) | (multiply(sk_c3, sk_c8) = sk_c7)) <=> ((inverse(sk_c5) = sk_c8) | (multiply(sk_c3, sk_c8) = sk_c7))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(74,plain,
% 0.21/0.55 (((multiply(sk_c3, sk_c8) = sk_c7) | (inverse(sk_c5) = sk_c8)) <=> ((inverse(sk_c5) = sk_c8) | (multiply(sk_c3, sk_c8) = sk_c7))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(75,axiom,((multiply(sk_c3, sk_c8) = sk_c7) | (inverse(sk_c5) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_26')).
% 0.21/0.55 tff(76,plain,
% 0.21/0.55 ((inverse(sk_c5) = sk_c8) | (multiply(sk_c3, sk_c8) = sk_c7)),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.21/0.55 tff(77,plain,
% 0.21/0.55 ((inverse(sk_c5) = sk_c8) | (multiply(sk_c3, sk_c8) = sk_c7)),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[76, 73])).
% 0.21/0.55 tff(78,plain,
% 0.21/0.55 (inverse(sk_c5) = sk_c8),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[77, 55])).
% 0.21/0.55 tff(79,plain,
% 0.21/0.55 (sk_c8 = inverse(sk_c5)),
% 0.21/0.55 inference(symmetry,[status(thm)],[78])).
% 0.21/0.55 tff(80,plain,
% 0.21/0.55 (multiply(sk_c8, sk_c5) = multiply(inverse(sk_c5), sk_c5)),
% 0.21/0.55 inference(monotonicity,[status(thm)],[79])).
% 0.21/0.55 tff(81,plain,
% 0.21/0.55 (multiply(inverse(sk_c5), sk_c5) = multiply(sk_c8, sk_c5)),
% 0.21/0.55 inference(symmetry,[status(thm)],[80])).
% 0.21/0.55 tff(82,plain,
% 0.21/0.55 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c5), sk_c5) = identity)),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(83,plain,
% 0.21/0.55 (multiply(inverse(sk_c5), sk_c5) = identity),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[82, 16])).
% 0.21/0.55 tff(84,plain,
% 0.21/0.55 (identity = multiply(inverse(sk_c5), sk_c5)),
% 0.21/0.55 inference(symmetry,[status(thm)],[83])).
% 0.21/0.55 tff(85,plain,
% 0.21/0.55 (identity = multiply(sk_c8, sk_c5)),
% 0.21/0.55 inference(transitivity,[status(thm)],[84, 81])).
% 0.21/0.55 tff(86,plain,
% 0.21/0.55 (multiply(identity, sk_c8) = multiply(multiply(sk_c8, sk_c5), sk_c8)),
% 0.21/0.55 inference(monotonicity,[status(thm)],[85])).
% 0.21/0.55 tff(87,plain,
% 0.21/0.55 (sk_c8 = multiply(identity, sk_c8)),
% 0.21/0.55 inference(symmetry,[status(thm)],[61])).
% 0.21/0.55 tff(88,plain,
% 0.21/0.55 (sk_c8 = multiply(sk_c8, sk_c6)),
% 0.21/0.55 inference(transitivity,[status(thm)],[87, 86, 72, 70])).
% 0.21/0.55 tff(89,plain,
% 0.21/0.55 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c4), sk_c4) = identity)),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(90,plain,
% 0.21/0.55 (multiply(inverse(sk_c4), sk_c4) = identity),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[89, 16])).
% 0.21/0.55 tff(91,plain,
% 0.21/0.55 (((inverse(sk_c4) = sk_c8) | (multiply(sk_c3, sk_c8) = sk_c7)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c3, sk_c8) = sk_c7))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(92,plain,
% 0.21/0.55 (((multiply(sk_c3, sk_c8) = sk_c7) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c3, sk_c8) = sk_c7))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(93,axiom,((multiply(sk_c3, sk_c8) = sk_c7) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_22')).
% 0.21/0.55 tff(94,plain,
% 0.21/0.55 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c3, sk_c8) = sk_c7)),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.21/0.55 tff(95,plain,
% 0.21/0.55 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c3, sk_c8) = sk_c7)),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[94, 91])).
% 0.21/0.55 tff(96,plain,
% 0.21/0.55 (inverse(sk_c4) = sk_c8),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[95, 55])).
% 0.21/0.55 tff(97,plain,
% 0.21/0.55 (sk_c8 = inverse(sk_c4)),
% 0.21/0.55 inference(symmetry,[status(thm)],[96])).
% 0.21/0.55 tff(98,plain,
% 0.21/0.55 (multiply(sk_c8, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.21/0.55 inference(monotonicity,[status(thm)],[97])).
% 0.21/0.55 tff(99,plain,
% 0.21/0.55 (multiply(sk_c8, sk_c4) = identity),
% 0.21/0.55 inference(transitivity,[status(thm)],[98, 90])).
% 0.21/0.55 tff(100,plain,
% 0.21/0.55 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(identity, multiply(sk_c8, sk_c6))),
% 0.21/0.55 inference(monotonicity,[status(thm)],[99, 88])).
% 0.21/0.55 tff(101,plain,
% 0.21/0.55 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(sk_c8, multiply(sk_c4, sk_c8)))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(102,plain,
% 0.21/0.55 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[101, 47])).
% 0.21/0.55 tff(103,plain,
% 0.21/0.55 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = multiply(multiply(sk_c8, sk_c4), sk_c8)),
% 0.21/0.55 inference(symmetry,[status(thm)],[102])).
% 0.21/0.55 tff(104,plain,
% 0.21/0.55 (multiply(multiply(sk_c8, sk_c5), sk_c8) = multiply(identity, sk_c8)),
% 0.21/0.55 inference(symmetry,[status(thm)],[86])).
% 0.21/0.55 tff(105,plain,
% 0.21/0.55 (multiply(sk_c8, multiply(sk_c5, sk_c8)) = multiply(multiply(sk_c8, sk_c5), sk_c8)),
% 0.21/0.55 inference(symmetry,[status(thm)],[72])).
% 0.21/0.55 tff(106,plain,
% 0.21/0.55 (multiply(sk_c8, sk_c6) = multiply(sk_c8, multiply(sk_c5, sk_c8))),
% 0.21/0.55 inference(symmetry,[status(thm)],[70])).
% 0.21/0.55 tff(107,plain,
% 0.21/0.55 (sk_c7 = multiply(sk_c8, sk_c6)),
% 0.21/0.55 inference(symmetry,[status(thm)],[59])).
% 0.21/0.55 tff(108,plain,
% 0.21/0.55 (sk_c7 = sk_c8),
% 0.21/0.55 inference(transitivity,[status(thm)],[107, 106, 105, 104, 61])).
% 0.21/0.55 tff(109,plain,
% 0.21/0.55 (multiply(sk_c7, multiply(sk_c4, sk_c8)) = multiply(sk_c8, multiply(sk_c4, sk_c8))),
% 0.21/0.55 inference(monotonicity,[status(thm)],[108])).
% 0.21/0.55 tff(110,plain,
% 0.21/0.55 (sk_c8 = sk_c7),
% 0.21/0.55 inference(transitivity,[status(thm)],[87, 86, 72, 70, 59])).
% 0.21/0.55 tff(111,plain,
% 0.21/0.55 (multiply(sk_c4, sk_c8) = multiply(sk_c4, sk_c7)),
% 0.21/0.55 inference(monotonicity,[status(thm)],[110])).
% 0.21/0.55 tff(112,plain,
% 0.21/0.55 (multiply(sk_c4, sk_c7) = multiply(sk_c4, sk_c8)),
% 0.21/0.55 inference(symmetry,[status(thm)],[111])).
% 0.21/0.55 tff(113,plain,
% 0.21/0.55 (((multiply(sk_c3, sk_c8) = sk_c7) | (multiply(sk_c4, sk_c7) = sk_c8)) <=> ((multiply(sk_c3, sk_c8) = sk_c7) | (multiply(sk_c4, sk_c7) = sk_c8))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(114,axiom,((multiply(sk_c3, sk_c8) = sk_c7) | (multiply(sk_c4, sk_c7) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_23')).
% 0.21/0.55 tff(115,plain,
% 0.21/0.55 ((multiply(sk_c3, sk_c8) = sk_c7) | (multiply(sk_c4, sk_c7) = sk_c8)),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.21/0.55 tff(116,plain,
% 0.21/0.55 (multiply(sk_c4, sk_c7) = sk_c8),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[115, 55])).
% 0.21/0.55 tff(117,plain,
% 0.21/0.55 (sk_c8 = multiply(sk_c4, sk_c7)),
% 0.21/0.55 inference(symmetry,[status(thm)],[116])).
% 0.21/0.55 tff(118,plain,
% 0.21/0.55 (sk_c8 = multiply(sk_c4, sk_c8)),
% 0.21/0.55 inference(transitivity,[status(thm)],[117, 112])).
% 0.21/0.55 tff(119,plain,
% 0.21/0.55 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c7, multiply(sk_c4, sk_c8))),
% 0.21/0.55 inference(monotonicity,[status(thm)],[38, 118])).
% 0.21/0.55 tff(120,plain,
% 0.21/0.55 (sk_c8 = inverse(sk_c8)),
% 0.21/0.55 inference(transitivity,[status(thm)],[87, 86, 72, 70, 59, 39])).
% 0.21/0.55 tff(121,plain,
% 0.21/0.55 (multiply(sk_c8, sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.21/0.55 inference(monotonicity,[status(thm)],[120])).
% 0.21/0.55 tff(122,plain,
% 0.21/0.55 (multiply(inverse(sk_c4), sk_c8) = multiply(sk_c8, sk_c8)),
% 0.21/0.55 inference(monotonicity,[status(thm)],[96])).
% 0.21/0.55 tff(123,plain,
% 0.21/0.55 (multiply(inverse(sk_c4), sk_c8) = sk_c7),
% 0.21/0.55 inference(transitivity,[status(thm)],[122, 121, 119, 109, 103, 100, 65, 62, 59])).
% 0.21/0.55 tff(124,plain,
% 0.21/0.55 (multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7),
% 0.21/0.55 inference(transitivity,[status(thm)],[70, 59])).
% 0.21/0.55 tff(125,plain,
% 0.21/0.55 (multiply(sk_c4, inverse(sk_c4)) = multiply(sk_c4, sk_c8)),
% 0.21/0.55 inference(monotonicity,[status(thm)],[96])).
% 0.21/0.55 tff(126,plain,
% 0.21/0.55 (multiply(sk_c4, inverse(sk_c4)) = sk_c7),
% 0.21/0.55 inference(transitivity,[status(thm)],[125, 111, 116, 87, 86, 72, 70, 59])).
% 0.21/0.55 tff(127,plain,
% 0.21/0.55 (^[X4: $i, X3: $i, X5: $i, X1: $i] : refl(((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))))),
% 0.21/0.55 inference(bind,[status(th)],[])).
% 0.21/0.55 tff(128,plain,
% 0.21/0.55 (![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))) <=> ![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))),
% 0.21/0.55 inference(quant_intro,[status(thm)],[127])).
% 0.21/0.55 tff(129,plain,
% 0.21/0.55 (![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))) <=> ![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(130,plain,
% 0.21/0.55 (^[X4: $i, X3: $i, X5: $i, X1: $i] : rewrite(((~(inverse(X4) = sk_c8)) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))))),
% 0.21/0.55 inference(bind,[status(th)],[])).
% 0.21/0.55 tff(131,plain,
% 0.21/0.55 (![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(X4) = sk_c8)) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))) <=> ![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))),
% 0.21/0.55 inference(quant_intro,[status(thm)],[130])).
% 0.21/0.55 tff(132,plain,
% 0.21/0.55 (![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(inverse(X4) = sk_c8)) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8))) <=> ![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(X4) = sk_c8)) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))),
% 0.21/0.55 inference(elim_unused_vars,[status(thm)],[])).
% 0.21/0.55 tff(133,plain,
% 0.21/0.55 (![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X6, sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) <=> ![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(inverse(X4) = sk_c8)) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))),
% 0.21/0.55 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.21/0.55 tff(134,plain,
% 0.21/0.55 (![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X6, sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) <=> ![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(X4) = sk_c8)) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))),
% 0.21/0.55 inference(transitivity,[status(thm)],[133, 132])).
% 0.21/0.55 tff(135,plain,
% 0.21/0.55 (![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X6, sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) <=> ![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))),
% 0.21/0.55 inference(transitivity,[status(thm)],[134, 131])).
% 0.21/0.55 tff(136,plain,
% 0.21/0.55 (^[X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8)))), (((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(X5, X6) = sk_c7))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X5, X6) = sk_c7))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X5, X6) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8)))), (((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(X5, X6) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))))), ((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(X5, X6) = sk_c7))) | (~(inverse(X5) = X6))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(inverse(X5) = X6))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(inverse(X5) = X6))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8)))), ((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(X5, X6) = sk_c7))) | (~(inverse(X5) = X6))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))))), (((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(X5, X6) = sk_c7))) | (~(inverse(X5) = X6))) | (~(multiply(X6, sk_c8) = sk_c7))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X6, sk_c8) = sk_c7))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X6, sk_c8) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X6, sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8)))), (((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(X5, X6) = sk_c7))) | (~(inverse(X5) = X6))) | (~(multiply(X6, sk_c8) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X6, sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))))), ((((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(X5, X6) = sk_c7))) | (~(inverse(X5) = X6))) | (~(multiply(X6, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X6, sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(inverse(X1) = sk_c8))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X6, sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(inverse(X1) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X6, sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8)))), ((((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(X5, X6) = sk_c7))) | (~(inverse(X5) = X6))) | (~(multiply(X6, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X6, sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))))), (((((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(X5, X6) = sk_c7))) | (~(inverse(X5) = X6))) | (~(multiply(X6, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X6, sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X6, sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X6, sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8)))), (((((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(X5, X6) = sk_c7))) | (~(inverse(X5) = X6))) | (~(multiply(X6, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X6, sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))))), ((((((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(X5, X6) = sk_c7))) | (~(inverse(X5) = X6))) | (~(multiply(X6, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X6, sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X6, sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X6, sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8)))), ((((((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(X5, X6) = sk_c7))) | (~(inverse(X5) = X6))) | (~(multiply(X6, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X6, sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))))), (((((((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(X5, X6) = sk_c7))) | (~(inverse(X5) = X6))) | (~(multiply(X6, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X6, sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X3, sk_c8) = X2))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X6, sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X3, sk_c8) = X2))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X6, sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8)))), (((((((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(X5, X6) = sk_c7))) | (~(inverse(X5) = X6))) | (~(multiply(X6, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X6, sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))))), ((((((((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(X5, X6) = sk_c7))) | (~(inverse(X5) = X6))) | (~(multiply(X6, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))) | (~(inverse(X3) = sk_c8))) <=> (((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X6, sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(inverse(X3) = sk_c8))))), rewrite((((~(inverse(sk_c8) = sk_c7)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X6, sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8))) | (~(inverse(X3) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X6, sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8)))), ((((((((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(X5, X6) = sk_c7))) | (~(inverse(X5) = X6))) | (~(multiply(X6, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))) | (~(inverse(X3) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X6, sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8)))))),
% 0.40/0.56 inference(bind,[status(th)],[])).
% 0.40/0.56 tff(137,plain,
% 0.40/0.56 (![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : (((((((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(X5, X6) = sk_c7))) | (~(inverse(X5) = X6))) | (~(multiply(X6, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))) | (~(inverse(X3) = sk_c8))) <=> ![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(X3, sk_c8) = X2)) | (~(multiply(sk_c8, X2) = sk_c7)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(X6, sk_c8) = sk_c7)) | (~(inverse(X5) = X6)) | (~(multiply(X5, X6) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)) | (~(inverse(X4) = sk_c8)))),
% 0.40/0.56 inference(quant_intro,[status(thm)],[136])).
% 0.40/0.56 tff(138,plain,
% 0.40/0.56 (![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : (((((((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(X5, X6) = sk_c7))) | (~(inverse(X5) = X6))) | (~(multiply(X6, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))) | (~(inverse(X3) = sk_c8))) <=> ![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))),
% 0.40/0.56 inference(transitivity,[status(thm)],[137, 135])).
% 0.40/0.56 tff(139,axiom,(![X6: $i, X4: $i, X3: $i, X2: $i, X5: $i, X1: $i] : (((((((((((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8))) | (~(multiply(X4, sk_c7) = sk_c8))) | (~(multiply(X5, X6) = sk_c7))) | (~(inverse(X5) = X6))) | (~(multiply(X6, sk_c8) = sk_c7))) | (~(inverse(X1) = sk_c8))) | (~(multiply(X1, sk_c7) = sk_c8))) | (~(multiply(sk_c8, X2) = sk_c7))) | (~(multiply(X3, sk_c8) = X2))) | (~(inverse(X3) = sk_c8)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_27')).
% 0.40/0.56 tff(140,plain,
% 0.40/0.56 (![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.40/0.56 tff(141,plain,
% 0.40/0.56 (![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[140, 129])).
% 0.40/0.56 tff(142,plain,(
% 0.40/0.56 ![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))),
% 0.40/0.56 inference(skolemize,[status(sab)],[141])).
% 0.40/0.56 tff(143,plain,
% 0.40/0.56 (![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[142, 128])).
% 0.40/0.56 tff(144,plain,
% 0.40/0.56 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(inverse(sk_c4), sk_c8) = sk_c7)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(inverse(sk_c4), sk_c8) = sk_c7)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(145,plain,
% 0.40/0.56 (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(inverse(sk_c4), sk_c8) = sk_c7)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(inverse(sk_c4), sk_c8) = sk_c7)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(146,plain,
% 0.40/0.56 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(inverse(sk_c4), sk_c8) = sk_c7)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(inverse(sk_c4), sk_c8) = sk_c7)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[145])).
% 0.40/0.57 tff(147,plain,
% 0.40/0.57 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(inverse(sk_c4), sk_c8) = sk_c7)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(inverse(sk_c4), sk_c8) = sk_c7)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7)))),
% 0.40/0.57 inference(transitivity,[status(thm)],[146, 144])).
% 0.40/0.57 tff(148,plain,
% 0.40/0.57 ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(inverse(sk_c4), sk_c8) = sk_c7)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c7)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(149,plain,
% 0.40/0.57 ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(inverse(sk_c4), sk_c8) = sk_c7)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c7)) | (~(multiply(sk_c4, sk_c7) = sk_c8)) | (~(inverse(sk_c5) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.40/0.57 tff(150,plain,
% 0.40/0.57 ((~(multiply(inverse(sk_c4), sk_c8) = sk_c7)) | (~(multiply(sk_c4, inverse(sk_c4)) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c5, sk_c8)) = sk_c7))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[149, 38, 96, 116, 78, 143])).
% 0.40/0.57 tff(151,plain,
% 0.40/0.57 (~(multiply(inverse(sk_c4), sk_c8) = sk_c7)),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[150, 126, 124])).
% 0.40/0.57 tff(152,plain,
% 0.40/0.57 ($false),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[151, 123])).
% 0.40/0.57 tff(153,plain,(multiply(sk_c3, sk_c8) = sk_c7), inference(lemma,lemma(discharge,[]))).
% 0.40/0.57 tff(154,plain,
% 0.40/0.57 (sk_c7 = multiply(sk_c3, sk_c8)),
% 0.40/0.57 inference(symmetry,[status(thm)],[153])).
% 0.40/0.57 tff(155,plain,
% 0.40/0.57 (multiply(sk_c7, sk_c1) = multiply(multiply(sk_c3, sk_c8), sk_c1)),
% 0.40/0.57 inference(monotonicity,[status(thm)],[154])).
% 0.40/0.57 tff(156,plain,
% 0.40/0.57 (multiply(multiply(sk_c3, sk_c8), sk_c1) = multiply(sk_c7, sk_c1)),
% 0.40/0.57 inference(symmetry,[status(thm)],[155])).
% 0.40/0.57 tff(157,plain,
% 0.40/0.57 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c3, sk_c8), sk_c1) = multiply(sk_c3, multiply(sk_c8, sk_c1)))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(158,plain,
% 0.40/0.57 (multiply(multiply(sk_c3, sk_c8), sk_c1) = multiply(sk_c3, multiply(sk_c8, sk_c1))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[157, 47])).
% 0.40/0.57 tff(159,plain,
% 0.40/0.57 (multiply(sk_c3, multiply(sk_c8, sk_c1)) = multiply(multiply(sk_c3, sk_c8), sk_c1)),
% 0.40/0.57 inference(symmetry,[status(thm)],[158])).
% 0.40/0.57 tff(160,plain,
% 0.40/0.57 (multiply(sk_c2, sk_c7) = multiply(sk_c2, multiply(sk_c3, sk_c8))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[154])).
% 0.40/0.57 tff(161,plain,
% 0.40/0.57 (multiply(sk_c2, multiply(sk_c3, sk_c8)) = multiply(sk_c2, sk_c7)),
% 0.40/0.57 inference(symmetry,[status(thm)],[160])).
% 0.40/0.57 tff(162,plain,
% 0.40/0.57 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, sk_c3), sk_c8) = multiply(sk_c2, multiply(sk_c3, sk_c8)))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(163,plain,
% 0.40/0.57 (multiply(multiply(sk_c2, sk_c3), sk_c8) = multiply(sk_c2, multiply(sk_c3, sk_c8))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[162, 47])).
% 0.40/0.57 tff(164,plain,
% 0.40/0.57 (((multiply(sk_c2, sk_c3) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7)) <=> ((multiply(sk_c2, sk_c3) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(165,axiom,((multiply(sk_c2, sk_c3) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_14')).
% 0.40/0.57 tff(166,plain,
% 0.40/0.57 ((multiply(sk_c2, sk_c3) = sk_c7) | (multiply(sk_c8, sk_c6) = sk_c7)),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.40/0.57 tff(167,plain,
% 0.40/0.57 (multiply(sk_c2, sk_c3) = sk_c7),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[166, 19])).
% 0.40/0.57 tff(168,plain,
% 0.40/0.57 (multiply(sk_c2, sk_c3) = inverse(sk_c8)),
% 0.40/0.57 inference(transitivity,[status(thm)],[167, 39])).
% 0.40/0.57 tff(169,plain,
% 0.40/0.57 (multiply(multiply(sk_c2, sk_c3), sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.40/0.57 inference(monotonicity,[status(thm)],[168])).
% 0.40/0.57 tff(170,plain,
% 0.40/0.57 (multiply(inverse(sk_c8), sk_c8) = multiply(multiply(sk_c2, sk_c3), sk_c8)),
% 0.40/0.57 inference(symmetry,[status(thm)],[169])).
% 0.40/0.57 tff(171,plain,
% 0.40/0.57 (identity = multiply(inverse(sk_c8), sk_c8)),
% 0.40/0.57 inference(symmetry,[status(thm)],[31])).
% 0.40/0.57 tff(172,plain,
% 0.40/0.57 (multiply(sk_c8, sk_c1) = multiply(sk_c2, sk_c7)),
% 0.40/0.57 inference(transitivity,[status(thm)],[25, 18, 171, 170, 163, 161])).
% 0.40/0.57 tff(173,plain,
% 0.40/0.57 (multiply(sk_c3, multiply(sk_c8, sk_c1)) = multiply(sk_c3, multiply(sk_c2, sk_c7))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[172])).
% 0.40/0.57 tff(174,plain,
% 0.40/0.57 (multiply(sk_c3, multiply(sk_c2, sk_c7)) = multiply(sk_c3, multiply(sk_c8, sk_c1))),
% 0.40/0.57 inference(symmetry,[status(thm)],[173])).
% 0.40/0.57 tff(175,plain,
% 0.40/0.57 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c3, sk_c2), sk_c7) = multiply(sk_c3, multiply(sk_c2, sk_c7)))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(176,plain,
% 0.40/0.57 (multiply(multiply(sk_c3, sk_c2), sk_c7) = multiply(sk_c3, multiply(sk_c2, sk_c7))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[175, 47])).
% 0.40/0.57 tff(177,plain,
% 0.40/0.57 ((~![X: $i] : (multiply(inverse(X), X) = identity)) | (multiply(inverse(sk_c2), sk_c2) = identity)),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(178,plain,
% 0.40/0.57 (multiply(inverse(sk_c2), sk_c2) = identity),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[177, 16])).
% 0.40/0.57 tff(179,plain,
% 0.40/0.57 (((inverse(sk_c2) = sk_c3) | (multiply(sk_c8, sk_c6) = sk_c7)) <=> ((inverse(sk_c2) = sk_c3) | (multiply(sk_c8, sk_c6) = sk_c7))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(180,axiom,((inverse(sk_c2) = sk_c3) | (multiply(sk_c8, sk_c6) = sk_c7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_19')).
% 0.40/0.57 tff(181,plain,
% 0.40/0.57 ((inverse(sk_c2) = sk_c3) | (multiply(sk_c8, sk_c6) = sk_c7)),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.40/0.57 tff(182,plain,
% 0.40/0.57 (inverse(sk_c2) = sk_c3),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[181, 19])).
% 0.40/0.57 tff(183,plain,
% 0.40/0.57 (sk_c3 = inverse(sk_c2)),
% 0.40/0.57 inference(symmetry,[status(thm)],[182])).
% 0.40/0.57 tff(184,plain,
% 0.40/0.57 (multiply(sk_c3, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.40/0.57 inference(monotonicity,[status(thm)],[183])).
% 0.40/0.57 tff(185,plain,
% 0.40/0.57 (multiply(sk_c3, sk_c2) = multiply(sk_c8, sk_c1)),
% 0.40/0.57 inference(transitivity,[status(thm)],[184, 178, 29, 28])).
% 0.40/0.57 tff(186,plain,
% 0.40/0.57 (multiply(multiply(sk_c3, sk_c2), sk_c7) = multiply(multiply(sk_c8, sk_c1), sk_c7)),
% 0.40/0.57 inference(monotonicity,[status(thm)],[185])).
% 0.40/0.57 tff(187,plain,
% 0.40/0.57 (multiply(multiply(sk_c8, sk_c1), sk_c7) = multiply(multiply(sk_c3, sk_c2), sk_c7)),
% 0.40/0.57 inference(symmetry,[status(thm)],[186])).
% 0.40/0.57 tff(188,plain,
% 0.40/0.57 (multiply(identity, sk_c7) = multiply(multiply(sk_c8, sk_c1), sk_c7)),
% 0.40/0.57 inference(symmetry,[status(thm)],[27])).
% 0.40/0.57 tff(189,plain,
% 0.40/0.57 (sk_c7 = multiply(identity, sk_c7)),
% 0.40/0.57 inference(symmetry,[status(thm)],[9])).
% 0.40/0.57 tff(190,plain,
% 0.40/0.57 (sk_c7 = multiply(sk_c7, sk_c1)),
% 0.40/0.57 inference(transitivity,[status(thm)],[189, 188, 187, 176, 174, 159, 156])).
% 0.40/0.57 tff(191,plain,
% 0.40/0.57 (multiply(sk_c7, sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.40/0.57 inference(monotonicity,[status(thm)],[190])).
% 0.40/0.57 tff(192,plain,
% 0.40/0.57 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(sk_c7, sk_c7)),
% 0.40/0.57 inference(symmetry,[status(thm)],[191])).
% 0.40/0.57 tff(193,plain,
% 0.40/0.57 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.40/0.57 inference(symmetry,[status(thm)],[49])).
% 0.40/0.57 tff(194,plain,
% 0.40/0.57 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.40/0.57 inference(symmetry,[status(thm)],[40])).
% 0.40/0.57 tff(195,plain,
% 0.40/0.57 (multiply(sk_c1, sk_c7) = inverse(sk_c1)),
% 0.40/0.57 inference(transitivity,[status(thm)],[35, 24])).
% 0.40/0.57 tff(196,plain,
% 0.40/0.57 (multiply(multiply(sk_c1, sk_c7), sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.40/0.57 inference(monotonicity,[status(thm)],[195])).
% 0.40/0.57 tff(197,plain,
% 0.40/0.57 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c7), sk_c1) = multiply(sk_c1, multiply(sk_c7, sk_c1)))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(198,plain,
% 0.40/0.57 (multiply(multiply(sk_c1, sk_c7), sk_c1) = multiply(sk_c1, multiply(sk_c7, sk_c1))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[197, 47])).
% 0.40/0.57 tff(199,plain,
% 0.40/0.57 (multiply(sk_c1, multiply(sk_c7, sk_c1)) = multiply(multiply(sk_c1, sk_c7), sk_c1)),
% 0.40/0.57 inference(symmetry,[status(thm)],[198])).
% 0.40/0.57 tff(200,plain,
% 0.40/0.57 (multiply(sk_c1, sk_c7) = multiply(sk_c1, multiply(sk_c7, sk_c1))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[190])).
% 0.40/0.57 tff(201,plain,
% 0.40/0.57 (sk_c8 = multiply(sk_c1, sk_c7)),
% 0.40/0.57 inference(symmetry,[status(thm)],[35])).
% 0.40/0.57 tff(202,plain,
% 0.40/0.57 (sk_c8 = multiply(sk_c7, sk_c7)),
% 0.40/0.57 inference(transitivity,[status(thm)],[201, 200, 199, 196, 18, 171, 194, 193, 192])).
% 0.40/0.57 tff(203,plain,
% 0.40/0.57 (inverse(sk_c8) = multiply(sk_c7, sk_c1)),
% 0.40/0.57 inference(transitivity,[status(thm)],[38, 189, 188, 187, 176, 174, 159, 156])).
% 0.40/0.57 tff(204,plain,
% 0.40/0.57 (multiply(inverse(sk_c8), sk_c8) = multiply(multiply(sk_c7, sk_c1), multiply(sk_c7, sk_c7))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[203, 202])).
% 0.40/0.57 tff(205,plain,
% 0.40/0.57 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c1), sk_c7) = multiply(sk_c8, multiply(sk_c1, sk_c7)))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(206,plain,
% 0.40/0.57 (multiply(multiply(sk_c8, sk_c1), sk_c7) = multiply(sk_c8, multiply(sk_c1, sk_c7))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[205, 47])).
% 0.40/0.57 tff(207,plain,
% 0.40/0.57 (multiply(sk_c8, multiply(sk_c1, sk_c7)) = multiply(multiply(sk_c8, sk_c1), sk_c7)),
% 0.40/0.57 inference(symmetry,[status(thm)],[206])).
% 0.40/0.57 tff(208,plain,
% 0.40/0.57 (multiply(sk_c8, sk_c8) = multiply(sk_c8, multiply(sk_c1, sk_c7))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[201])).
% 0.40/0.57 tff(209,plain,
% 0.40/0.57 (multiply(multiply(sk_c1, sk_c7), sk_c8) = multiply(sk_c8, sk_c8)),
% 0.40/0.57 inference(monotonicity,[status(thm)],[35])).
% 0.40/0.57 tff(210,plain,
% 0.40/0.57 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c7), sk_c8) = multiply(sk_c1, multiply(sk_c7, sk_c8)))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(211,plain,
% 0.40/0.57 (multiply(multiply(sk_c1, sk_c7), sk_c8) = multiply(sk_c1, multiply(sk_c7, sk_c8))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[210, 47])).
% 0.40/0.57 tff(212,plain,
% 0.40/0.57 (multiply(sk_c1, multiply(sk_c7, sk_c8)) = multiply(multiply(sk_c1, sk_c7), sk_c8)),
% 0.40/0.57 inference(symmetry,[status(thm)],[211])).
% 0.40/0.57 tff(213,plain,
% 0.40/0.57 (multiply(sk_c7, sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.40/0.57 inference(monotonicity,[status(thm)],[39])).
% 0.40/0.57 tff(214,plain,
% 0.40/0.57 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c7, sk_c8)),
% 0.40/0.57 inference(symmetry,[status(thm)],[213])).
% 0.40/0.57 tff(215,plain,
% 0.40/0.57 (sk_c8 = multiply(sk_c7, sk_c8)),
% 0.40/0.57 inference(transitivity,[status(thm)],[201, 200, 199, 196, 18, 171, 214])).
% 0.40/0.57 tff(216,plain,
% 0.40/0.57 (multiply(sk_c1, sk_c8) = multiply(sk_c1, multiply(sk_c7, sk_c8))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[215])).
% 0.40/0.57 tff(217,plain,
% 0.40/0.57 (multiply(sk_c1, sk_c8) = sk_c7),
% 0.40/0.57 inference(transitivity,[status(thm)],[216, 212, 209, 208, 207, 27, 9])).
% 0.40/0.57 tff(218,plain,
% 0.40/0.57 (sk_c8 = sk_c7),
% 0.40/0.57 inference(transitivity,[status(thm)],[201, 200, 199, 196, 18, 171, 204, 54, 51, 27, 9])).
% 0.40/0.57 tff(219,plain,
% 0.40/0.57 (multiply(sk_c8, multiply(sk_c1, sk_c8)) = multiply(sk_c7, sk_c7)),
% 0.40/0.57 inference(monotonicity,[status(thm)],[218, 217])).
% 0.40/0.57 tff(220,plain,
% 0.40/0.57 (multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7),
% 0.40/0.57 inference(transitivity,[status(thm)],[219, 191, 49, 40, 204, 54, 51, 27, 9])).
% 0.40/0.57 tff(221,plain,
% 0.40/0.57 (multiply(sk_c2, inverse(sk_c2)) = multiply(sk_c2, sk_c3)),
% 0.40/0.57 inference(monotonicity,[status(thm)],[182])).
% 0.40/0.57 tff(222,plain,
% 0.40/0.57 (multiply(sk_c2, inverse(sk_c2)) = sk_c7),
% 0.40/0.57 inference(transitivity,[status(thm)],[221, 167])).
% 0.40/0.57 tff(223,plain,
% 0.40/0.57 (multiply(inverse(sk_c2), sk_c8) = multiply(sk_c3, sk_c8)),
% 0.40/0.57 inference(monotonicity,[status(thm)],[182])).
% 0.40/0.57 tff(224,plain,
% 0.40/0.57 (multiply(inverse(sk_c2), sk_c8) = sk_c7),
% 0.40/0.57 inference(transitivity,[status(thm)],[223, 153])).
% 0.40/0.57 tff(225,plain,
% 0.40/0.57 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(inverse(sk_c2), sk_c8) = sk_c7)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(inverse(sk_c2), sk_c8) = sk_c7)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(226,plain,
% 0.40/0.57 (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(inverse(sk_c2), sk_c8) = sk_c7)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(inverse(sk_c2), sk_c8) = sk_c7)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(227,plain,
% 0.40/0.57 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(inverse(sk_c2), sk_c8) = sk_c7)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(inverse(sk_c2), sk_c8) = sk_c7)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8))))),
% 0.42/0.57 inference(monotonicity,[status(thm)],[226])).
% 0.42/0.57 tff(228,plain,
% 0.42/0.57 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(inverse(sk_c2), sk_c8) = sk_c7)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(inverse(sk_c2), sk_c8) = sk_c7)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)))),
% 0.42/0.57 inference(transitivity,[status(thm)],[227, 225])).
% 0.42/0.57 tff(229,plain,
% 0.42/0.57 ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c1, sk_c7) = sk_c8)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(inverse(sk_c2), sk_c8) = sk_c7)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8)))),
% 0.42/0.57 inference(quant_inst,[status(thm)],[])).
% 0.42/0.57 tff(230,plain,
% 0.42/0.57 ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(inverse(sk_c2), sk_c8) = sk_c7)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c7)) | (~(multiply(sk_c1, sk_c7) = sk_c8))),
% 0.42/0.57 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.42/0.57 tff(231,plain,
% 0.42/0.57 ((~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(inverse(sk_c2), sk_c8) = sk_c7)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c7))),
% 0.42/0.57 inference(unit_resolution,[status(thm)],[230, 38, 23, 35, 143])).
% 0.42/0.57 tff(232,plain,
% 0.42/0.57 (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)),
% 0.42/0.57 inference(unit_resolution,[status(thm)],[231, 224, 222])).
% 0.42/0.57 tff(233,plain,
% 0.42/0.57 ($false),
% 0.42/0.57 inference(unit_resolution,[status(thm)],[232, 220])).
% 0.42/0.57 tff(234,plain,(multiply(sk_c8, sk_c6) = sk_c7), inference(lemma,lemma(discharge,[]))).
% 0.42/0.57 tff(235,assumption,(~(inverse(sk_c1) = sk_c8)), introduced(assumption)).
% 0.42/0.57 tff(236,plain,
% 0.42/0.57 (((inverse(sk_c1) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6)) <=> ((inverse(sk_c1) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6))),
% 0.42/0.57 inference(rewrite,[status(thm)],[])).
% 0.42/0.57 tff(237,axiom,((inverse(sk_c1) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_5')).
% 0.42/0.57 tff(238,plain,
% 0.42/0.57 ((inverse(sk_c1) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6)),
% 0.42/0.57 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.42/0.57 tff(239,plain,
% 0.42/0.57 (multiply(sk_c5, sk_c8) = sk_c6),
% 0.42/0.57 inference(unit_resolution,[status(thm)],[238, 235])).
% 0.42/0.57 tff(240,plain,
% 0.42/0.57 (sk_c6 = multiply(sk_c5, sk_c8)),
% 0.42/0.57 inference(symmetry,[status(thm)],[239])).
% 0.42/0.57 tff(241,plain,
% 0.42/0.57 (multiply(sk_c8, sk_c6) = multiply(sk_c8, multiply(sk_c5, sk_c8))),
% 0.42/0.57 inference(monotonicity,[status(thm)],[240])).
% 0.42/0.57 tff(242,plain,
% 0.42/0.57 (multiply(sk_c8, multiply(sk_c5, sk_c8)) = multiply(sk_c8, sk_c6)),
% 0.42/0.57 inference(symmetry,[status(thm)],[241])).
% 0.42/0.57 tff(243,plain,
% 0.42/0.57 (((inverse(sk_c1) = sk_c8) | (inverse(sk_c5) = sk_c8)) <=> ((inverse(sk_c1) = sk_c8) | (inverse(sk_c5) = sk_c8))),
% 0.42/0.57 inference(rewrite,[status(thm)],[])).
% 0.42/0.57 tff(244,axiom,((inverse(sk_c1) = sk_c8) | (inverse(sk_c5) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_6')).
% 0.42/0.57 tff(245,plain,
% 0.42/0.57 ((inverse(sk_c1) = sk_c8) | (inverse(sk_c5) = sk_c8)),
% 0.42/0.57 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.42/0.57 tff(246,plain,
% 0.42/0.57 (inverse(sk_c5) = sk_c8),
% 0.42/0.57 inference(unit_resolution,[status(thm)],[245, 235])).
% 0.42/0.57 tff(247,plain,
% 0.42/0.57 (sk_c8 = inverse(sk_c5)),
% 0.42/0.57 inference(symmetry,[status(thm)],[246])).
% 0.42/0.57 tff(248,plain,
% 0.42/0.57 (multiply(sk_c8, sk_c5) = multiply(inverse(sk_c5), sk_c5)),
% 0.42/0.57 inference(monotonicity,[status(thm)],[247])).
% 0.42/0.57 tff(249,plain,
% 0.42/0.57 (multiply(inverse(sk_c5), sk_c5) = multiply(sk_c8, sk_c5)),
% 0.42/0.57 inference(symmetry,[status(thm)],[248])).
% 0.42/0.57 tff(250,plain,
% 0.42/0.57 (((inverse(sk_c1) = sk_c8) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c1) = sk_c8) | (inverse(sk_c4) = sk_c8))),
% 0.42/0.57 inference(rewrite,[status(thm)],[])).
% 0.42/0.57 tff(251,axiom,((inverse(sk_c1) = sk_c8) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_2')).
% 0.42/0.57 tff(252,plain,
% 0.42/0.57 ((inverse(sk_c1) = sk_c8) | (inverse(sk_c4) = sk_c8)),
% 0.42/0.57 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.42/0.57 tff(253,plain,
% 0.42/0.57 (inverse(sk_c4) = sk_c8),
% 0.42/0.57 inference(unit_resolution,[status(thm)],[252, 235])).
% 0.42/0.57 tff(254,plain,
% 0.42/0.57 (sk_c8 = inverse(sk_c4)),
% 0.42/0.57 inference(symmetry,[status(thm)],[253])).
% 0.42/0.57 tff(255,plain,
% 0.42/0.57 (multiply(sk_c8, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.42/0.57 inference(monotonicity,[status(thm)],[254])).
% 0.42/0.57 tff(256,plain,
% 0.42/0.57 (multiply(sk_c8, sk_c4) = multiply(sk_c8, sk_c5)),
% 0.42/0.57 inference(transitivity,[status(thm)],[255, 90, 84, 249])).
% 0.42/0.57 tff(257,plain,
% 0.42/0.57 (multiply(multiply(sk_c8, sk_c4), sk_c8) = multiply(multiply(sk_c8, sk_c5), sk_c8)),
% 0.42/0.57 inference(monotonicity,[status(thm)],[256])).
% 0.42/0.57 tff(258,plain,
% 0.42/0.57 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7),
% 0.42/0.57 inference(transitivity,[status(thm)],[103, 257, 72, 242, 234])).
% 0.42/0.57 tff(259,plain,
% 0.42/0.57 (multiply(sk_c8, sk_c5) = identity),
% 0.42/0.57 inference(transitivity,[status(thm)],[248, 83])).
% 0.42/0.57 tff(260,plain,
% 0.42/0.57 (multiply(multiply(sk_c8, sk_c5), sk_c8) = multiply(identity, sk_c8)),
% 0.42/0.57 inference(monotonicity,[status(thm)],[259])).
% 0.42/0.57 tff(261,plain,
% 0.42/0.57 (sk_c7 = multiply(sk_c8, sk_c6)),
% 0.42/0.57 inference(symmetry,[status(thm)],[234])).
% 0.42/0.57 tff(262,plain,
% 0.42/0.57 (sk_c7 = sk_c8),
% 0.42/0.57 inference(transitivity,[status(thm)],[261, 241, 105, 260, 61])).
% 0.42/0.57 tff(263,plain,
% 0.42/0.57 (multiply(sk_c8, inverse(sk_c8)) = multiply(sk_c8, sk_c7)),
% 0.42/0.57 inference(monotonicity,[status(thm)],[38])).
% 0.42/0.57 tff(264,plain,
% 0.42/0.57 ((multiply(sk_c8, inverse(sk_c8)) = sk_c7) <=> (multiply(sk_c8, sk_c7) = sk_c8)),
% 0.42/0.57 inference(monotonicity,[status(thm)],[263, 262])).
% 0.42/0.57 tff(265,plain,
% 0.42/0.58 ((multiply(sk_c8, sk_c7) = sk_c8) <=> (multiply(sk_c8, inverse(sk_c8)) = sk_c7)),
% 0.42/0.58 inference(symmetry,[status(thm)],[264])).
% 0.42/0.58 tff(266,plain,
% 0.42/0.58 (multiply(sk_c8, sk_c4) = identity),
% 0.42/0.58 inference(transitivity,[status(thm)],[255, 90])).
% 0.42/0.58 tff(267,plain,
% 0.42/0.58 (multiply(multiply(sk_c8, sk_c4), sk_c7) = multiply(identity, sk_c7)),
% 0.42/0.58 inference(monotonicity,[status(thm)],[266])).
% 0.42/0.58 tff(268,plain,
% 0.42/0.58 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c4), sk_c7) = multiply(sk_c8, multiply(sk_c4, sk_c7)))),
% 0.42/0.58 inference(quant_inst,[status(thm)],[])).
% 0.42/0.58 tff(269,plain,
% 0.42/0.58 (multiply(multiply(sk_c8, sk_c4), sk_c7) = multiply(sk_c8, multiply(sk_c4, sk_c7))),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[268, 47])).
% 0.42/0.58 tff(270,plain,
% 0.42/0.58 (multiply(sk_c8, multiply(sk_c4, sk_c7)) = multiply(multiply(sk_c8, sk_c4), sk_c7)),
% 0.42/0.58 inference(symmetry,[status(thm)],[269])).
% 0.42/0.58 tff(271,plain,
% 0.42/0.58 (((inverse(sk_c1) = sk_c8) | (multiply(sk_c4, sk_c7) = sk_c8)) <=> ((inverse(sk_c1) = sk_c8) | (multiply(sk_c4, sk_c7) = sk_c8))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(272,axiom,((inverse(sk_c1) = sk_c8) | (multiply(sk_c4, sk_c7) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_3')).
% 0.42/0.58 tff(273,plain,
% 0.42/0.58 ((inverse(sk_c1) = sk_c8) | (multiply(sk_c4, sk_c7) = sk_c8)),
% 0.42/0.58 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.42/0.58 tff(274,plain,
% 0.42/0.58 (multiply(sk_c4, sk_c7) = sk_c8),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[273, 235])).
% 0.42/0.58 tff(275,plain,
% 0.42/0.58 (sk_c8 = multiply(sk_c4, sk_c7)),
% 0.42/0.58 inference(symmetry,[status(thm)],[274])).
% 0.42/0.58 tff(276,plain,
% 0.42/0.58 (multiply(sk_c8, sk_c8) = multiply(sk_c8, multiply(sk_c4, sk_c7))),
% 0.42/0.58 inference(monotonicity,[status(thm)],[275])).
% 0.42/0.58 tff(277,plain,
% 0.42/0.58 (multiply(sk_c8, sk_c7) = multiply(sk_c8, sk_c8)),
% 0.42/0.58 inference(monotonicity,[status(thm)],[262])).
% 0.42/0.58 tff(278,plain,
% 0.42/0.58 (multiply(sk_c8, sk_c7) = sk_c8),
% 0.42/0.58 inference(transitivity,[status(thm)],[277, 276, 270, 267, 9, 261, 241, 105, 260, 61])).
% 0.42/0.58 tff(279,plain,
% 0.42/0.58 (multiply(sk_c8, inverse(sk_c8)) = sk_c7),
% 0.42/0.58 inference(modus_ponens,[status(thm)],[278, 265])).
% 0.42/0.58 tff(280,plain,
% 0.42/0.58 (multiply(multiply(identity, sk_c8), sk_c8) = multiply(sk_c8, sk_c8)),
% 0.42/0.58 inference(monotonicity,[status(thm)],[61])).
% 0.42/0.58 tff(281,plain,
% 0.42/0.58 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, sk_c8), sk_c8) = multiply(identity, multiply(sk_c8, sk_c8)))),
% 0.42/0.58 inference(quant_inst,[status(thm)],[])).
% 0.42/0.58 tff(282,plain,
% 0.42/0.58 (multiply(multiply(identity, sk_c8), sk_c8) = multiply(identity, multiply(sk_c8, sk_c8))),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[281, 47])).
% 0.42/0.58 tff(283,plain,
% 0.42/0.58 (multiply(identity, multiply(sk_c8, sk_c8)) = multiply(multiply(identity, sk_c8), sk_c8)),
% 0.42/0.58 inference(symmetry,[status(thm)],[282])).
% 0.42/0.58 tff(284,plain,
% 0.42/0.58 (multiply(multiply(sk_c8, sk_c5), multiply(sk_c8, sk_c8)) = multiply(identity, multiply(sk_c8, sk_c8))),
% 0.42/0.58 inference(monotonicity,[status(thm)],[259])).
% 0.42/0.58 tff(285,plain,
% 0.42/0.58 ((~![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))))),
% 0.42/0.58 inference(quant_inst,[status(thm)],[])).
% 0.42/0.58 tff(286,plain,
% 0.42/0.58 (multiply(multiply(sk_c8, sk_c5), multiply(sk_c8, sk_c8)) = multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c8)))),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[285, 47])).
% 0.42/0.58 tff(287,plain,
% 0.42/0.58 (multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c8))) = multiply(multiply(sk_c8, sk_c5), multiply(sk_c8, sk_c8))),
% 0.42/0.58 inference(symmetry,[status(thm)],[286])).
% 0.42/0.58 tff(288,plain,
% 0.42/0.58 ((~![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)))),
% 0.42/0.58 inference(quant_inst,[status(thm)],[])).
% 0.42/0.58 tff(289,plain,
% 0.42/0.58 (multiply(multiply(sk_c5, sk_c8), sk_c8) = multiply(sk_c5, multiply(sk_c8, sk_c8))),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[288, 47])).
% 0.42/0.58 tff(290,plain,
% 0.42/0.58 (multiply(sk_c6, sk_c8) = multiply(multiply(sk_c5, sk_c8), sk_c8)),
% 0.42/0.58 inference(monotonicity,[status(thm)],[240])).
% 0.42/0.58 tff(291,plain,
% 0.42/0.58 (multiply(sk_c6, sk_c8) = multiply(sk_c5, multiply(sk_c8, sk_c8))),
% 0.42/0.58 inference(transitivity,[status(thm)],[290, 289])).
% 0.42/0.58 tff(292,plain,
% 0.42/0.58 (multiply(sk_c8, multiply(sk_c6, sk_c8)) = multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c8)))),
% 0.42/0.58 inference(monotonicity,[status(thm)],[291])).
% 0.42/0.58 tff(293,plain,
% 0.42/0.58 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c6), sk_c8) = multiply(sk_c8, multiply(sk_c6, sk_c8)))),
% 0.42/0.58 inference(quant_inst,[status(thm)],[])).
% 0.42/0.58 tff(294,plain,
% 0.42/0.58 (multiply(multiply(sk_c8, sk_c6), sk_c8) = multiply(sk_c8, multiply(sk_c6, sk_c8))),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[293, 47])).
% 0.42/0.58 tff(295,plain,
% 0.42/0.58 (inverse(sk_c8) = multiply(sk_c8, sk_c6)),
% 0.42/0.58 inference(transitivity,[status(thm)],[38, 261])).
% 0.42/0.58 tff(296,plain,
% 0.42/0.58 (multiply(inverse(sk_c8), sk_c8) = multiply(multiply(sk_c8, sk_c6), sk_c8)),
% 0.42/0.58 inference(monotonicity,[status(thm)],[295])).
% 0.42/0.58 tff(297,plain,
% 0.42/0.58 (multiply(inverse(sk_c8), sk_c8) = sk_c7),
% 0.42/0.58 inference(transitivity,[status(thm)],[296, 294, 292, 287, 284, 283, 280, 276, 270, 267, 9])).
% 0.42/0.58 tff(298,plain,
% 0.42/0.58 (inverse(sk_c8) = sk_c8),
% 0.42/0.58 inference(transitivity,[status(thm)],[38, 261, 241, 105, 260, 61])).
% 0.42/0.58 tff(299,plain,
% 0.42/0.58 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(multiply(inverse(sk_c8), sk_c8) = sk_c7)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(multiply(inverse(sk_c8), sk_c8) = sk_c7)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(300,plain,
% 0.42/0.58 (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(inverse(sk_c8), sk_c8) = sk_c7)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(multiply(inverse(sk_c8), sk_c8) = sk_c7)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(301,plain,
% 0.42/0.58 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(inverse(sk_c8), sk_c8) = sk_c7)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(multiply(inverse(sk_c8), sk_c8) = sk_c7)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7))))),
% 0.42/0.58 inference(monotonicity,[status(thm)],[300])).
% 0.42/0.58 tff(302,plain,
% 0.42/0.58 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(inverse(sk_c8), sk_c8) = sk_c7)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(multiply(inverse(sk_c8), sk_c8) = sk_c7)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)))),
% 0.42/0.58 inference(transitivity,[status(thm)],[301, 299])).
% 0.42/0.58 tff(303,plain,
% 0.42/0.58 ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(inverse(sk_c8), sk_c8) = sk_c7)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c8)))),
% 0.42/0.58 inference(quant_inst,[status(thm)],[])).
% 0.42/0.58 tff(304,plain,
% 0.42/0.58 ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(multiply(inverse(sk_c8), sk_c8) = sk_c7)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7))),
% 0.42/0.58 inference(modus_ponens,[status(thm)],[303, 302])).
% 0.42/0.58 tff(305,plain,
% 0.42/0.58 ((~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(multiply(inverse(sk_c8), sk_c8) = sk_c7)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7))),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[304, 38, 253, 143])).
% 0.42/0.58 tff(306,plain,
% 0.42/0.58 ($false),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[305, 278, 298, 297, 279, 258])).
% 0.42/0.58 tff(307,plain,(inverse(sk_c1) = sk_c8), inference(lemma,lemma(discharge,[]))).
% 0.42/0.58 tff(308,plain,
% 0.42/0.58 (sk_c8 = inverse(sk_c1)),
% 0.42/0.58 inference(symmetry,[status(thm)],[307])).
% 0.42/0.58 tff(309,plain,
% 0.42/0.58 (multiply(sk_c8, sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.42/0.58 inference(monotonicity,[status(thm)],[308])).
% 0.42/0.58 tff(310,plain,
% 0.42/0.58 (multiply(inverse(sk_c1), sk_c1) = multiply(sk_c8, sk_c1)),
% 0.42/0.58 inference(symmetry,[status(thm)],[309])).
% 0.42/0.58 tff(311,plain,
% 0.42/0.58 (identity = multiply(sk_c8, sk_c1)),
% 0.42/0.58 inference(transitivity,[status(thm)],[29, 310])).
% 0.42/0.58 tff(312,plain,
% 0.42/0.58 (multiply(identity, sk_c7) = multiply(multiply(sk_c8, sk_c1), sk_c7)),
% 0.42/0.58 inference(monotonicity,[status(thm)],[311])).
% 0.42/0.58 tff(313,plain,
% 0.42/0.58 (multiply(multiply(sk_c8, sk_c1), sk_c7) = multiply(identity, sk_c7)),
% 0.42/0.58 inference(symmetry,[status(thm)],[312])).
% 0.42/0.58 tff(314,assumption,(~(multiply(sk_c1, sk_c7) = sk_c8)), introduced(assumption)).
% 0.42/0.58 tff(315,plain,
% 0.42/0.58 (((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6)) <=> ((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(316,axiom,((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_10')).
% 0.42/0.58 tff(317,plain,
% 0.42/0.58 ((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c5, sk_c8) = sk_c6)),
% 0.42/0.58 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.42/0.58 tff(318,plain,
% 0.42/0.58 (multiply(sk_c5, sk_c8) = sk_c6),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[317, 314])).
% 0.42/0.58 tff(319,plain,
% 0.42/0.58 (sk_c6 = multiply(sk_c5, sk_c8)),
% 0.42/0.58 inference(symmetry,[status(thm)],[318])).
% 0.42/0.58 tff(320,plain,
% 0.42/0.58 (multiply(sk_c8, sk_c6) = multiply(sk_c8, multiply(sk_c5, sk_c8))),
% 0.42/0.58 inference(monotonicity,[status(thm)],[319])).
% 0.42/0.58 tff(321,plain,
% 0.42/0.58 (multiply(sk_c8, multiply(sk_c5, sk_c8)) = multiply(sk_c8, sk_c6)),
% 0.42/0.58 inference(symmetry,[status(thm)],[320])).
% 0.42/0.58 tff(322,assumption,(~(inverse(sk_c5) = sk_c8)), introduced(assumption)).
% 0.42/0.58 tff(323,plain,
% 0.42/0.58 (((inverse(sk_c5) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8)) <=> ((inverse(sk_c5) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(324,plain,
% 0.42/0.58 (((multiply(sk_c1, sk_c7) = sk_c8) | (inverse(sk_c5) = sk_c8)) <=> ((inverse(sk_c5) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(325,axiom,((multiply(sk_c1, sk_c7) = sk_c8) | (inverse(sk_c5) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_11')).
% 0.42/0.58 tff(326,plain,
% 0.42/0.58 ((inverse(sk_c5) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8)),
% 0.42/0.58 inference(modus_ponens,[status(thm)],[325, 324])).
% 0.42/0.58 tff(327,plain,
% 0.42/0.58 ((inverse(sk_c5) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8)),
% 0.42/0.58 inference(modus_ponens,[status(thm)],[326, 323])).
% 0.42/0.58 tff(328,plain,
% 0.42/0.58 (multiply(sk_c1, sk_c7) = sk_c8),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[327, 322])).
% 0.42/0.58 tff(329,plain,
% 0.42/0.58 (multiply(sk_c8, multiply(sk_c1, sk_c7)) = multiply(sk_c8, sk_c8)),
% 0.42/0.58 inference(monotonicity,[status(thm)],[328])).
% 0.42/0.58 tff(330,plain,
% 0.42/0.58 (multiply(sk_c8, sk_c8) = multiply(sk_c8, multiply(sk_c1, sk_c7))),
% 0.42/0.58 inference(symmetry,[status(thm)],[329])).
% 0.42/0.58 tff(331,plain,
% 0.42/0.58 (multiply(multiply(sk_c1, sk_c7), sk_c8) = multiply(sk_c8, sk_c8)),
% 0.42/0.58 inference(monotonicity,[status(thm)],[328])).
% 0.42/0.58 tff(332,plain,
% 0.42/0.58 (multiply(sk_c1, sk_c7) = inverse(sk_c1)),
% 0.42/0.58 inference(transitivity,[status(thm)],[328, 308])).
% 0.42/0.58 tff(333,plain,
% 0.42/0.58 (multiply(multiply(sk_c1, sk_c7), sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.42/0.58 inference(monotonicity,[status(thm)],[332])).
% 0.42/0.58 tff(334,plain,
% 0.42/0.58 (multiply(sk_c1, multiply(sk_c7, sk_c1)) = multiply(sk_c7, sk_c8)),
% 0.42/0.58 inference(transitivity,[status(thm)],[199, 333, 18, 171, 214])).
% 0.42/0.58 tff(335,plain,
% 0.42/0.58 (multiply(sk_c1, multiply(sk_c1, multiply(sk_c7, sk_c1))) = multiply(sk_c1, multiply(sk_c7, sk_c8))),
% 0.42/0.58 inference(monotonicity,[status(thm)],[334])).
% 0.42/0.58 tff(336,plain,
% 0.42/0.58 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c1), multiply(sk_c7, sk_c1)) = multiply(sk_c1, multiply(sk_c1, multiply(sk_c7, sk_c1))))),
% 0.42/0.58 inference(quant_inst,[status(thm)],[])).
% 0.42/0.58 tff(337,plain,
% 0.42/0.58 (multiply(multiply(sk_c1, sk_c1), multiply(sk_c7, sk_c1)) = multiply(sk_c1, multiply(sk_c1, multiply(sk_c7, sk_c1)))),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[336, 47])).
% 0.42/0.58 tff(338,plain,
% 0.42/0.58 (((inverse(sk_c5) = sk_c8) | (multiply(sk_c2, sk_c3) = sk_c7)) <=> ((inverse(sk_c5) = sk_c8) | (multiply(sk_c2, sk_c3) = sk_c7))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(339,plain,
% 0.42/0.58 (((multiply(sk_c2, sk_c3) = sk_c7) | (inverse(sk_c5) = sk_c8)) <=> ((inverse(sk_c5) = sk_c8) | (multiply(sk_c2, sk_c3) = sk_c7))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(340,axiom,((multiply(sk_c2, sk_c3) = sk_c7) | (inverse(sk_c5) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_16')).
% 0.42/0.58 tff(341,plain,
% 0.42/0.58 ((inverse(sk_c5) = sk_c8) | (multiply(sk_c2, sk_c3) = sk_c7)),
% 0.42/0.58 inference(modus_ponens,[status(thm)],[340, 339])).
% 0.42/0.58 tff(342,plain,
% 0.42/0.58 ((inverse(sk_c5) = sk_c8) | (multiply(sk_c2, sk_c3) = sk_c7)),
% 0.42/0.58 inference(modus_ponens,[status(thm)],[341, 338])).
% 0.42/0.58 tff(343,plain,
% 0.42/0.58 (multiply(sk_c2, sk_c3) = sk_c7),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[342, 322])).
% 0.42/0.58 tff(344,plain,
% 0.42/0.58 (multiply(sk_c2, sk_c3) = inverse(sk_c8)),
% 0.42/0.58 inference(transitivity,[status(thm)],[343, 39])).
% 0.42/0.58 tff(345,plain,
% 0.42/0.58 (multiply(multiply(sk_c2, sk_c3), sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.42/0.58 inference(monotonicity,[status(thm)],[344])).
% 0.42/0.58 tff(346,plain,
% 0.42/0.58 (multiply(inverse(sk_c8), sk_c8) = multiply(multiply(sk_c2, sk_c3), sk_c8)),
% 0.42/0.58 inference(symmetry,[status(thm)],[345])).
% 0.42/0.58 tff(347,plain,
% 0.42/0.58 (multiply(sk_c8, sk_c1) = multiply(sk_c2, sk_c7)),
% 0.42/0.58 inference(transitivity,[status(thm)],[309, 18, 171, 346, 163, 161])).
% 0.42/0.58 tff(348,plain,
% 0.42/0.58 (multiply(sk_c3, multiply(sk_c8, sk_c1)) = multiply(sk_c3, multiply(sk_c2, sk_c7))),
% 0.42/0.58 inference(monotonicity,[status(thm)],[347])).
% 0.42/0.58 tff(349,plain,
% 0.42/0.58 (multiply(sk_c3, multiply(sk_c2, sk_c7)) = multiply(sk_c3, multiply(sk_c8, sk_c1))),
% 0.42/0.58 inference(symmetry,[status(thm)],[348])).
% 0.42/0.58 tff(350,plain,
% 0.42/0.58 (((inverse(sk_c2) = sk_c3) | (inverse(sk_c5) = sk_c8)) <=> ((inverse(sk_c2) = sk_c3) | (inverse(sk_c5) = sk_c8))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(351,axiom,((inverse(sk_c2) = sk_c3) | (inverse(sk_c5) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_21')).
% 0.42/0.58 tff(352,plain,
% 0.42/0.58 ((inverse(sk_c2) = sk_c3) | (inverse(sk_c5) = sk_c8)),
% 0.42/0.58 inference(modus_ponens,[status(thm)],[351, 350])).
% 0.42/0.58 tff(353,plain,
% 0.42/0.58 (inverse(sk_c2) = sk_c3),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[352, 322])).
% 0.42/0.58 tff(354,plain,
% 0.42/0.58 (sk_c3 = inverse(sk_c2)),
% 0.42/0.58 inference(symmetry,[status(thm)],[353])).
% 0.42/0.58 tff(355,plain,
% 0.42/0.58 (multiply(sk_c3, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.42/0.58 inference(monotonicity,[status(thm)],[354])).
% 0.42/0.58 tff(356,plain,
% 0.42/0.58 (multiply(sk_c3, sk_c2) = multiply(sk_c8, sk_c1)),
% 0.42/0.58 inference(transitivity,[status(thm)],[355, 178, 29, 310])).
% 0.42/0.58 tff(357,plain,
% 0.42/0.58 (multiply(multiply(sk_c3, sk_c2), sk_c7) = multiply(multiply(sk_c8, sk_c1), sk_c7)),
% 0.42/0.58 inference(monotonicity,[status(thm)],[356])).
% 0.42/0.58 tff(358,plain,
% 0.42/0.58 (multiply(multiply(sk_c8, sk_c1), sk_c7) = multiply(multiply(sk_c3, sk_c2), sk_c7)),
% 0.42/0.58 inference(symmetry,[status(thm)],[357])).
% 0.42/0.58 tff(359,plain,
% 0.42/0.58 (sk_c7 = multiply(sk_c7, sk_c1)),
% 0.42/0.58 inference(transitivity,[status(thm)],[189, 312, 358, 176, 349, 159, 156])).
% 0.42/0.58 tff(360,plain,
% 0.42/0.58 (multiply(multiply(sk_c1, sk_c1), sk_c7) = multiply(multiply(sk_c1, sk_c1), multiply(sk_c7, sk_c1))),
% 0.42/0.58 inference(monotonicity,[status(thm)],[359])).
% 0.42/0.58 tff(361,plain,
% 0.42/0.58 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c1), sk_c7) = multiply(sk_c1, multiply(sk_c1, sk_c7)))),
% 0.42/0.58 inference(quant_inst,[status(thm)],[])).
% 0.42/0.58 tff(362,plain,
% 0.42/0.58 (multiply(multiply(sk_c1, sk_c1), sk_c7) = multiply(sk_c1, multiply(sk_c1, sk_c7))),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[361, 47])).
% 0.42/0.58 tff(363,plain,
% 0.42/0.58 (multiply(sk_c1, multiply(sk_c1, sk_c7)) = multiply(multiply(sk_c1, sk_c1), sk_c7)),
% 0.42/0.58 inference(symmetry,[status(thm)],[362])).
% 0.42/0.58 tff(364,plain,
% 0.42/0.58 (sk_c8 = multiply(sk_c1, sk_c7)),
% 0.42/0.59 inference(symmetry,[status(thm)],[328])).
% 0.42/0.59 tff(365,plain,
% 0.42/0.59 (multiply(sk_c1, sk_c8) = multiply(sk_c1, multiply(sk_c1, sk_c7))),
% 0.42/0.59 inference(monotonicity,[status(thm)],[364])).
% 0.42/0.59 tff(366,plain,
% 0.42/0.59 (multiply(sk_c1, sk_c8) = sk_c7),
% 0.42/0.59 inference(transitivity,[status(thm)],[365, 363, 360, 337, 335, 212, 331, 330, 207, 313, 9])).
% 0.42/0.59 tff(367,plain,
% 0.42/0.59 (multiply(sk_c1, sk_c7) = multiply(sk_c1, multiply(sk_c7, sk_c1))),
% 0.42/0.59 inference(monotonicity,[status(thm)],[359])).
% 0.42/0.59 tff(368,plain,
% 0.42/0.59 (sk_c8 = multiply(sk_c8, sk_c1)),
% 0.42/0.59 inference(transitivity,[status(thm)],[364, 367, 199, 333, 310])).
% 0.42/0.59 tff(369,plain,
% 0.42/0.59 (multiply(sk_c8, multiply(sk_c1, sk_c8)) = multiply(multiply(sk_c8, sk_c1), sk_c7)),
% 0.42/0.59 inference(monotonicity,[status(thm)],[368, 366])).
% 0.42/0.59 tff(370,plain,
% 0.42/0.59 (multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7),
% 0.42/0.59 inference(transitivity,[status(thm)],[369, 313, 9])).
% 0.42/0.59 tff(371,plain,
% 0.42/0.59 (multiply(sk_c2, inverse(sk_c2)) = multiply(sk_c2, sk_c3)),
% 0.42/0.59 inference(monotonicity,[status(thm)],[353])).
% 0.42/0.59 tff(372,plain,
% 0.42/0.59 (multiply(sk_c2, inverse(sk_c2)) = sk_c7),
% 0.42/0.59 inference(transitivity,[status(thm)],[371, 343])).
% 0.42/0.59 tff(373,plain,
% 0.42/0.59 (multiply(inverse(sk_c2), sk_c8) = multiply(sk_c3, sk_c8)),
% 0.42/0.59 inference(monotonicity,[status(thm)],[353])).
% 0.42/0.59 tff(374,plain,
% 0.42/0.59 (multiply(inverse(sk_c2), sk_c8) = sk_c7),
% 0.42/0.59 inference(transitivity,[status(thm)],[373, 153])).
% 0.42/0.59 tff(375,plain,
% 0.42/0.59 ((~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(inverse(sk_c2), sk_c8) = sk_c7)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c7))),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[230, 38, 307, 328, 143])).
% 0.42/0.59 tff(376,plain,
% 0.42/0.59 (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[375, 374, 372])).
% 0.42/0.59 tff(377,plain,
% 0.42/0.59 ($false),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[376, 370])).
% 0.42/0.59 tff(378,plain,(inverse(sk_c5) = sk_c8), inference(lemma,lemma(discharge,[]))).
% 0.42/0.59 tff(379,plain,
% 0.42/0.59 (sk_c8 = inverse(sk_c5)),
% 0.42/0.59 inference(symmetry,[status(thm)],[378])).
% 0.42/0.59 tff(380,plain,
% 0.42/0.59 (multiply(sk_c8, sk_c5) = multiply(inverse(sk_c5), sk_c5)),
% 0.42/0.59 inference(monotonicity,[status(thm)],[379])).
% 0.42/0.59 tff(381,plain,
% 0.42/0.59 (multiply(inverse(sk_c5), sk_c5) = multiply(sk_c8, sk_c5)),
% 0.42/0.59 inference(symmetry,[status(thm)],[380])).
% 0.42/0.59 tff(382,plain,
% 0.42/0.59 (multiply(sk_c8, sk_c1) = multiply(sk_c8, sk_c5)),
% 0.42/0.59 inference(transitivity,[status(thm)],[309, 18, 84, 381])).
% 0.42/0.59 tff(383,plain,
% 0.42/0.59 (multiply(multiply(sk_c8, sk_c1), sk_c8) = multiply(multiply(sk_c8, sk_c5), sk_c8)),
% 0.42/0.59 inference(monotonicity,[status(thm)],[382])).
% 0.42/0.59 tff(384,plain,
% 0.42/0.59 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c1), sk_c8) = multiply(sk_c8, multiply(sk_c1, sk_c8)))),
% 0.42/0.59 inference(quant_inst,[status(thm)],[])).
% 0.42/0.59 tff(385,plain,
% 0.42/0.59 (multiply(multiply(sk_c8, sk_c1), sk_c8) = multiply(sk_c8, multiply(sk_c1, sk_c8))),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[384, 47])).
% 0.42/0.59 tff(386,plain,
% 0.42/0.59 (multiply(sk_c8, multiply(sk_c1, sk_c8)) = multiply(multiply(sk_c8, sk_c1), sk_c8)),
% 0.42/0.59 inference(symmetry,[status(thm)],[385])).
% 0.42/0.59 tff(387,plain,
% 0.42/0.59 (multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7),
% 0.42/0.59 inference(transitivity,[status(thm)],[386, 383, 72, 321, 234])).
% 0.42/0.59 tff(388,plain,
% 0.42/0.59 (multiply(sk_c8, sk_c5) = identity),
% 0.42/0.59 inference(transitivity,[status(thm)],[380, 83])).
% 0.42/0.59 tff(389,plain,
% 0.42/0.59 (multiply(multiply(sk_c8, sk_c5), sk_c8) = multiply(identity, sk_c8)),
% 0.42/0.59 inference(monotonicity,[status(thm)],[388])).
% 0.42/0.59 tff(390,plain,
% 0.42/0.59 (sk_c7 = sk_c8),
% 0.42/0.59 inference(transitivity,[status(thm)],[261, 320, 105, 389, 61])).
% 0.42/0.59 tff(391,plain,
% 0.42/0.59 ((multiply(sk_c8, inverse(sk_c8)) = sk_c7) <=> (multiply(sk_c8, sk_c7) = sk_c8)),
% 0.42/0.59 inference(monotonicity,[status(thm)],[263, 390])).
% 0.42/0.59 tff(392,plain,
% 0.42/0.59 ((multiply(sk_c8, sk_c7) = sk_c8) <=> (multiply(sk_c8, inverse(sk_c8)) = sk_c7)),
% 0.42/0.59 inference(symmetry,[status(thm)],[391])).
% 0.42/0.59 tff(393,plain,
% 0.42/0.59 (((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(394,plain,
% 0.42/0.59 (((multiply(sk_c1, sk_c7) = sk_c8) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(395,axiom,((multiply(sk_c1, sk_c7) = sk_c8) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_7')).
% 0.42/0.59 tff(396,plain,
% 0.42/0.59 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8)),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[395, 394])).
% 0.42/0.59 tff(397,plain,
% 0.42/0.59 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c1, sk_c7) = sk_c8)),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[396, 393])).
% 0.42/0.59 tff(398,plain,
% 0.42/0.59 (inverse(sk_c4) = sk_c8),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[397, 314])).
% 0.42/0.59 tff(399,plain,
% 0.42/0.59 (sk_c8 = inverse(sk_c4)),
% 0.42/0.59 inference(symmetry,[status(thm)],[398])).
% 0.42/0.59 tff(400,plain,
% 0.42/0.59 (multiply(sk_c8, sk_c4) = multiply(inverse(sk_c4), sk_c4)),
% 0.42/0.59 inference(monotonicity,[status(thm)],[399])).
% 0.42/0.59 tff(401,plain,
% 0.42/0.59 (multiply(sk_c8, sk_c4) = identity),
% 0.42/0.59 inference(transitivity,[status(thm)],[400, 90])).
% 0.42/0.59 tff(402,plain,
% 0.42/0.59 (multiply(multiply(sk_c8, sk_c4), sk_c7) = multiply(identity, sk_c7)),
% 0.42/0.59 inference(monotonicity,[status(thm)],[401])).
% 0.42/0.59 tff(403,plain,
% 0.42/0.59 (((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c4, sk_c7) = sk_c8)) <=> ((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c4, sk_c7) = sk_c8))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(404,axiom,((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c4, sk_c7) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_8')).
% 0.42/0.59 tff(405,plain,
% 0.42/0.59 ((multiply(sk_c1, sk_c7) = sk_c8) | (multiply(sk_c4, sk_c7) = sk_c8)),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[404, 403])).
% 0.42/0.59 tff(406,plain,
% 0.42/0.59 (multiply(sk_c4, sk_c7) = sk_c8),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[405, 314])).
% 0.42/0.59 tff(407,plain,
% 0.42/0.59 (sk_c8 = multiply(sk_c4, sk_c7)),
% 0.42/0.59 inference(symmetry,[status(thm)],[406])).
% 0.42/0.59 tff(408,plain,
% 0.42/0.59 (multiply(sk_c8, sk_c8) = multiply(sk_c8, multiply(sk_c4, sk_c7))),
% 0.42/0.59 inference(monotonicity,[status(thm)],[407])).
% 0.42/0.59 tff(409,plain,
% 0.42/0.59 (multiply(sk_c8, sk_c7) = multiply(sk_c8, sk_c8)),
% 0.42/0.59 inference(monotonicity,[status(thm)],[390])).
% 0.42/0.59 tff(410,plain,
% 0.42/0.59 (multiply(sk_c8, sk_c7) = sk_c8),
% 0.42/0.59 inference(transitivity,[status(thm)],[409, 408, 270, 402, 9, 261, 320, 105, 389, 61])).
% 0.42/0.59 tff(411,plain,
% 0.42/0.59 (multiply(sk_c8, inverse(sk_c8)) = sk_c7),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[410, 392])).
% 0.42/0.59 tff(412,plain,
% 0.42/0.59 (multiply(multiply(sk_c8, sk_c5), multiply(sk_c8, sk_c8)) = multiply(identity, multiply(sk_c8, sk_c8))),
% 0.42/0.59 inference(monotonicity,[status(thm)],[388])).
% 0.42/0.59 tff(413,plain,
% 0.42/0.59 (multiply(sk_c6, sk_c8) = multiply(multiply(sk_c5, sk_c8), sk_c8)),
% 0.42/0.59 inference(monotonicity,[status(thm)],[319])).
% 0.42/0.59 tff(414,plain,
% 0.42/0.59 (multiply(sk_c6, sk_c8) = multiply(sk_c5, multiply(sk_c8, sk_c8))),
% 0.42/0.59 inference(transitivity,[status(thm)],[413, 289])).
% 0.42/0.59 tff(415,plain,
% 0.42/0.59 (multiply(sk_c8, multiply(sk_c6, sk_c8)) = multiply(sk_c8, multiply(sk_c5, multiply(sk_c8, sk_c8)))),
% 0.42/0.59 inference(monotonicity,[status(thm)],[414])).
% 0.42/0.59 tff(416,plain,
% 0.42/0.59 (multiply(inverse(sk_c8), sk_c8) = sk_c7),
% 0.42/0.59 inference(transitivity,[status(thm)],[296, 294, 415, 287, 412, 283, 280, 408, 270, 402, 9])).
% 0.42/0.59 tff(417,plain,
% 0.42/0.59 (inverse(sk_c8) = sk_c8),
% 0.42/0.59 inference(transitivity,[status(thm)],[38, 261, 320, 105, 389, 61])).
% 0.42/0.59 tff(418,plain,
% 0.42/0.59 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(multiply(inverse(sk_c8), sk_c8) = sk_c7)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(multiply(inverse(sk_c8), sk_c8) = sk_c7)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(419,plain,
% 0.42/0.59 (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(inverse(sk_c8), sk_c8) = sk_c7)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(multiply(inverse(sk_c8), sk_c8) = sk_c7)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(420,plain,
% 0.42/0.59 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(inverse(sk_c8), sk_c8) = sk_c7)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(multiply(inverse(sk_c8), sk_c8) = sk_c7)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7))))),
% 0.42/0.59 inference(monotonicity,[status(thm)],[419])).
% 0.42/0.59 tff(421,plain,
% 0.42/0.59 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(inverse(sk_c8), sk_c8) = sk_c7)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(multiply(inverse(sk_c8), sk_c8) = sk_c7)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)))),
% 0.42/0.59 inference(transitivity,[status(thm)],[420, 418])).
% 0.42/0.59 tff(422,plain,
% 0.42/0.59 ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(inverse(sk_c8), sk_c8) = sk_c7)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7)) | (~(multiply(sk_c8, sk_c7) = sk_c8)))),
% 0.42/0.59 inference(quant_inst,[status(thm)],[])).
% 0.42/0.59 tff(423,plain,
% 0.42/0.59 ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(multiply(inverse(sk_c8), sk_c8) = sk_c7)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c7)) | (~(inverse(sk_c1) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[422, 421])).
% 0.42/0.59 tff(424,plain,
% 0.42/0.59 ((~(inverse(sk_c8) = sk_c8)) | (~(multiply(sk_c8, sk_c7) = sk_c8)) | (~(multiply(inverse(sk_c8), sk_c8) = sk_c7)) | (~(multiply(sk_c8, inverse(sk_c8)) = sk_c7)) | (~(multiply(sk_c8, multiply(sk_c1, sk_c8)) = sk_c7))),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[423, 38, 307, 143])).
% 0.42/0.59 tff(425,plain,
% 0.42/0.59 ($false),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[424, 410, 417, 416, 411, 387])).
% 0.42/0.59 tff(426,plain,(multiply(sk_c1, sk_c7) = sk_c8), inference(lemma,lemma(discharge,[]))).
% 0.42/0.59 tff(427,plain,
% 0.42/0.59 (sk_c8 = multiply(sk_c1, sk_c7)),
% 0.42/0.59 inference(symmetry,[status(thm)],[426])).
% 0.42/0.59 tff(428,plain,
% 0.42/0.59 (multiply(sk_c8, sk_c8) = multiply(sk_c8, multiply(sk_c1, sk_c7))),
% 0.42/0.59 inference(monotonicity,[status(thm)],[427])).
% 0.42/0.59 tff(429,plain,
% 0.42/0.59 (multiply(sk_c7, sk_c6) = multiply(multiply(sk_c3, sk_c8), sk_c6)),
% 0.42/0.59 inference(monotonicity,[status(thm)],[154])).
% 0.42/0.59 tff(430,plain,
% 0.42/0.59 (multiply(multiply(sk_c3, sk_c8), sk_c6) = multiply(sk_c7, sk_c6)),
% 0.42/0.59 inference(symmetry,[status(thm)],[429])).
% 0.42/0.59 tff(431,plain,
% 0.42/0.59 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c3, sk_c8), sk_c6) = multiply(sk_c3, multiply(sk_c8, sk_c6)))),
% 0.42/0.59 inference(quant_inst,[status(thm)],[])).
% 0.42/0.59 tff(432,plain,
% 0.42/0.59 (multiply(multiply(sk_c3, sk_c8), sk_c6) = multiply(sk_c3, multiply(sk_c8, sk_c6))),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[431, 47])).
% 0.42/0.59 tff(433,plain,
% 0.42/0.59 (multiply(sk_c3, multiply(sk_c8, sk_c6)) = multiply(multiply(sk_c3, sk_c8), sk_c6)),
% 0.42/0.59 inference(symmetry,[status(thm)],[432])).
% 0.42/0.59 tff(434,plain,
% 0.42/0.59 (multiply(sk_c8, multiply(sk_c1, sk_c7)) = multiply(sk_c8, sk_c8)),
% 0.42/0.59 inference(symmetry,[status(thm)],[428])).
% 0.42/0.59 tff(435,plain,
% 0.42/0.59 (multiply(sk_c8, sk_c6) = multiply(sk_c8, sk_c8)),
% 0.42/0.59 inference(transitivity,[status(thm)],[234, 189, 312, 206, 434])).
% 0.42/0.59 tff(436,plain,
% 0.42/0.59 (multiply(sk_c3, multiply(sk_c8, sk_c6)) = multiply(sk_c3, multiply(sk_c8, sk_c8))),
% 0.42/0.59 inference(monotonicity,[status(thm)],[435])).
% 0.42/0.59 tff(437,plain,
% 0.42/0.59 (multiply(sk_c3, multiply(sk_c8, sk_c8)) = multiply(sk_c3, multiply(sk_c8, sk_c6))),
% 0.42/0.59 inference(symmetry,[status(thm)],[436])).
% 0.42/0.59 tff(438,plain,
% 0.42/0.59 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c3, sk_c8), sk_c8) = multiply(sk_c3, multiply(sk_c8, sk_c8)))),
% 0.42/0.59 inference(quant_inst,[status(thm)],[])).
% 0.42/0.59 tff(439,plain,
% 0.42/0.59 (multiply(multiply(sk_c3, sk_c8), sk_c8) = multiply(sk_c3, multiply(sk_c8, sk_c8))),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[438, 47])).
% 0.42/0.59 tff(440,plain,
% 0.42/0.59 (multiply(sk_c3, sk_c8) = inverse(sk_c8)),
% 0.42/0.59 inference(transitivity,[status(thm)],[153, 39])).
% 0.42/0.59 tff(441,plain,
% 0.42/0.59 (multiply(multiply(sk_c3, sk_c8), sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.42/0.59 inference(monotonicity,[status(thm)],[440])).
% 0.42/0.59 tff(442,plain,
% 0.42/0.59 (multiply(inverse(sk_c8), sk_c8) = multiply(multiply(sk_c3, sk_c8), sk_c8)),
% 0.42/0.59 inference(symmetry,[status(thm)],[441])).
% 0.42/0.59 tff(443,plain,
% 0.42/0.59 (identity = multiply(sk_c7, sk_c6)),
% 0.42/0.59 inference(transitivity,[status(thm)],[171, 442, 439, 437, 433, 430])).
% 0.42/0.59 tff(444,plain,
% 0.42/0.59 (multiply(identity, sk_c8) = multiply(multiply(sk_c7, sk_c6), sk_c8)),
% 0.42/0.59 inference(monotonicity,[status(thm)],[443])).
% 0.42/0.59 tff(445,plain,
% 0.42/0.59 (multiply(multiply(sk_c7, sk_c6), sk_c8) = multiply(identity, sk_c8)),
% 0.42/0.59 inference(symmetry,[status(thm)],[444])).
% 0.42/0.59 tff(446,plain,
% 0.42/0.59 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c6), sk_c8) = multiply(sk_c7, multiply(sk_c6, sk_c8)))),
% 0.42/0.59 inference(quant_inst,[status(thm)],[])).
% 0.42/0.59 tff(447,plain,
% 0.42/0.59 (multiply(multiply(sk_c7, sk_c6), sk_c8) = multiply(sk_c7, multiply(sk_c6, sk_c8))),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[446, 47])).
% 0.42/0.59 tff(448,plain,
% 0.42/0.59 (multiply(sk_c7, multiply(sk_c6, sk_c8)) = multiply(multiply(sk_c7, sk_c6), sk_c8)),
% 0.42/0.59 inference(symmetry,[status(thm)],[447])).
% 0.42/0.59 tff(449,plain,
% 0.42/0.59 (multiply(sk_c6, sk_c8) = multiply(sk_c6, multiply(sk_c1, sk_c7))),
% 0.42/0.59 inference(monotonicity,[status(thm)],[427])).
% 0.42/0.59 tff(450,plain,
% 0.42/0.59 (multiply(sk_c7, multiply(sk_c6, sk_c8)) = multiply(multiply(sk_c3, sk_c8), multiply(sk_c6, multiply(sk_c1, sk_c7)))),
% 0.42/0.59 inference(monotonicity,[status(thm)],[154, 449])).
% 0.42/0.59 tff(451,plain,
% 0.42/0.59 (multiply(multiply(sk_c3, sk_c8), multiply(sk_c6, multiply(sk_c1, sk_c7))) = multiply(sk_c7, multiply(sk_c6, sk_c8))),
% 0.42/0.59 inference(symmetry,[status(thm)],[450])).
% 0.42/0.59 tff(452,plain,
% 0.42/0.59 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c3, sk_c8), multiply(sk_c6, multiply(sk_c1, sk_c7))) = multiply(sk_c3, multiply(sk_c8, multiply(sk_c6, multiply(sk_c1, sk_c7)))))),
% 0.42/0.59 inference(quant_inst,[status(thm)],[])).
% 0.42/0.59 tff(453,plain,
% 0.42/0.59 (multiply(multiply(sk_c3, sk_c8), multiply(sk_c6, multiply(sk_c1, sk_c7))) = multiply(sk_c3, multiply(sk_c8, multiply(sk_c6, multiply(sk_c1, sk_c7))))),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[452, 47])).
% 0.42/0.59 tff(454,plain,
% 0.42/0.59 (multiply(sk_c3, multiply(sk_c8, multiply(sk_c6, multiply(sk_c1, sk_c7)))) = multiply(multiply(sk_c3, sk_c8), multiply(sk_c6, multiply(sk_c1, sk_c7)))),
% 0.42/0.59 inference(symmetry,[status(thm)],[453])).
% 0.42/0.59 tff(455,plain,
% 0.42/0.59 (multiply(sk_c8, sk_c6) = inverse(sk_c8)),
% 0.42/0.59 inference(transitivity,[status(thm)],[234, 39])).
% 0.42/0.59 tff(456,plain,
% 0.42/0.59 (multiply(multiply(sk_c8, sk_c6), sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.42/0.59 inference(monotonicity,[status(thm)],[455])).
% 0.42/0.59 tff(457,plain,
% 0.42/0.59 (multiply(sk_c8, multiply(sk_c6, sk_c8)) = multiply(multiply(sk_c8, sk_c6), sk_c8)),
% 0.42/0.59 inference(symmetry,[status(thm)],[294])).
% 0.42/0.59 tff(458,plain,
% 0.42/0.59 (multiply(sk_c6, multiply(sk_c1, sk_c7)) = multiply(sk_c6, sk_c8)),
% 0.42/0.59 inference(symmetry,[status(thm)],[449])).
% 0.42/0.59 tff(459,plain,
% 0.42/0.59 (multiply(sk_c8, multiply(sk_c6, multiply(sk_c1, sk_c7))) = multiply(sk_c8, multiply(sk_c6, sk_c8))),
% 0.42/0.59 inference(monotonicity,[status(thm)],[458])).
% 0.42/0.59 tff(460,plain,
% 0.42/0.59 (multiply(sk_c8, multiply(sk_c6, multiply(sk_c1, sk_c7))) = multiply(sk_c8, sk_c1)),
% 0.42/0.59 inference(transitivity,[status(thm)],[459, 457, 456, 31, 29, 310])).
% 0.42/0.59 tff(461,plain,
% 0.42/0.59 (multiply(sk_c3, multiply(sk_c8, multiply(sk_c6, multiply(sk_c1, sk_c7)))) = multiply(sk_c3, multiply(sk_c8, sk_c1))),
% 0.42/0.59 inference(monotonicity,[status(thm)],[460])).
% 0.42/0.59 tff(462,plain,
% 0.42/0.59 (multiply(sk_c3, multiply(sk_c8, sk_c1)) = multiply(sk_c3, multiply(sk_c8, multiply(sk_c6, multiply(sk_c1, sk_c7))))),
% 0.42/0.59 inference(symmetry,[status(thm)],[461])).
% 0.42/0.59 tff(463,plain,
% 0.42/0.59 (multiply(multiply(sk_c3, sk_c8), sk_c1) = multiply(sk_c7, sk_c1)),
% 0.42/0.59 inference(monotonicity,[status(thm)],[153])).
% 0.42/0.59 tff(464,plain,
% 0.42/0.59 (multiply(sk_c7, sk_c1) = multiply(multiply(sk_c3, sk_c8), sk_c1)),
% 0.42/0.59 inference(symmetry,[status(thm)],[463])).
% 0.42/0.60 tff(465,plain,
% 0.42/0.60 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c3, sk_c1), sk_c7) = multiply(sk_c3, multiply(sk_c1, sk_c7)))),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(466,plain,
% 0.42/0.60 (multiply(multiply(sk_c3, sk_c1), sk_c7) = multiply(sk_c3, multiply(sk_c1, sk_c7))),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[465, 47])).
% 0.42/0.60 tff(467,plain,
% 0.42/0.60 (multiply(sk_c3, multiply(sk_c1, sk_c7)) = multiply(multiply(sk_c3, sk_c1), sk_c7)),
% 0.42/0.60 inference(symmetry,[status(thm)],[466])).
% 0.42/0.60 tff(468,plain,
% 0.42/0.60 (multiply(sk_c3, multiply(sk_c1, sk_c7)) = multiply(sk_c3, sk_c8)),
% 0.42/0.60 inference(monotonicity,[status(thm)],[426])).
% 0.42/0.60 tff(469,plain,
% 0.42/0.60 (multiply(sk_c3, sk_c8) = multiply(sk_c3, multiply(sk_c1, sk_c7))),
% 0.42/0.60 inference(symmetry,[status(thm)],[468])).
% 0.42/0.60 tff(470,plain,
% 0.42/0.60 (sk_c7 = multiply(multiply(sk_c3, sk_c1), sk_c7)),
% 0.42/0.60 inference(transitivity,[status(thm)],[154, 469, 467])).
% 0.42/0.60 tff(471,plain,
% 0.42/0.60 (multiply(sk_c7, sk_c1) = multiply(multiply(multiply(sk_c3, sk_c1), sk_c7), sk_c1)),
% 0.42/0.60 inference(monotonicity,[status(thm)],[470])).
% 0.42/0.60 tff(472,plain,
% 0.42/0.60 (multiply(multiply(multiply(sk_c3, sk_c1), sk_c7), sk_c1) = multiply(sk_c7, sk_c1)),
% 0.42/0.60 inference(symmetry,[status(thm)],[471])).
% 0.42/0.60 tff(473,plain,
% 0.42/0.60 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c3, sk_c1), sk_c7), sk_c1) = multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(474,plain,
% 0.42/0.60 (multiply(multiply(multiply(sk_c3, sk_c1), sk_c7), sk_c1) = multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[473, 47])).
% 0.42/0.60 tff(475,plain,
% 0.42/0.60 (multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)) = multiply(multiply(multiply(sk_c3, sk_c1), sk_c7), sk_c1)),
% 0.42/0.60 inference(symmetry,[status(thm)],[474])).
% 0.42/0.60 tff(476,plain,
% 0.42/0.60 (multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)) = sk_c8),
% 0.42/0.60 inference(transitivity,[status(thm)],[475, 472, 464, 158, 462, 454, 451, 448, 445, 61])).
% 0.42/0.60 tff(477,plain,
% 0.42/0.60 (multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = multiply(sk_c8, sk_c8)),
% 0.42/0.60 inference(monotonicity,[status(thm)],[476, 476])).
% 0.42/0.60 tff(478,plain,
% 0.42/0.60 (multiply(sk_c1, multiply(sk_c3, sk_c8)) = multiply(sk_c1, sk_c7)),
% 0.42/0.60 inference(monotonicity,[status(thm)],[153])).
% 0.42/0.60 tff(479,plain,
% 0.42/0.60 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c3), sk_c8) = multiply(sk_c1, multiply(sk_c3, sk_c8)))),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(480,plain,
% 0.42/0.60 (multiply(multiply(sk_c1, sk_c3), sk_c8) = multiply(sk_c1, multiply(sk_c3, sk_c8))),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[479, 47])).
% 0.42/0.60 tff(481,plain,
% 0.42/0.60 (multiply(multiply(sk_c1, sk_c3), sk_c8) = sk_c8),
% 0.42/0.60 inference(transitivity,[status(thm)],[480, 478, 426])).
% 0.42/0.60 tff(482,plain,
% 0.42/0.60 (multiply(sk_c7, multiply(multiply(sk_c1, sk_c3), sk_c8)) = multiply(inverse(sk_c8), sk_c8)),
% 0.42/0.60 inference(monotonicity,[status(thm)],[39, 481])).
% 0.42/0.60 tff(483,plain,
% 0.42/0.60 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8) = multiply(sk_c7, multiply(multiply(sk_c1, sk_c3), sk_c8)))),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(484,plain,
% 0.42/0.60 (multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8) = multiply(sk_c7, multiply(multiply(sk_c1, sk_c3), sk_c8))),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[483, 47])).
% 0.42/0.60 tff(485,plain,
% 0.42/0.60 (multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8) = identity),
% 0.42/0.60 inference(transitivity,[status(thm)],[484, 482, 31])).
% 0.42/0.60 tff(486,plain,
% 0.42/0.60 (multiply(multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8), sk_c8) = multiply(identity, sk_c8)),
% 0.42/0.60 inference(monotonicity,[status(thm)],[485])).
% 0.42/0.60 tff(487,plain,
% 0.42/0.60 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8), sk_c8) = multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), multiply(sk_c8, sk_c8)))),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(488,plain,
% 0.42/0.60 (multiply(multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8), sk_c8) = multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), multiply(sk_c8, sk_c8))),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[487, 47])).
% 0.42/0.60 tff(489,plain,
% 0.42/0.60 (multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), multiply(sk_c8, sk_c8)) = multiply(multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8), sk_c8)),
% 0.42/0.60 inference(symmetry,[status(thm)],[488])).
% 0.42/0.60 tff(490,plain,
% 0.42/0.60 (multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), multiply(sk_c8, sk_c6)) = multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), multiply(sk_c8, sk_c8))),
% 0.42/0.60 inference(monotonicity,[status(thm)],[435])).
% 0.42/0.60 tff(491,plain,
% 0.42/0.60 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8), sk_c6) = multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), multiply(sk_c8, sk_c6)))),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(492,plain,
% 0.42/0.60 (multiply(multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8), sk_c6) = multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), multiply(sk_c8, sk_c6))),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[491, 47])).
% 0.42/0.60 tff(493,plain,
% 0.42/0.60 (multiply(sk_c7, multiply(multiply(sk_c1, sk_c3), sk_c8)) = multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8)),
% 0.42/0.60 inference(symmetry,[status(thm)],[484])).
% 0.42/0.60 tff(494,plain,
% 0.42/0.60 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c7, multiply(multiply(sk_c1, sk_c3), sk_c8))),
% 0.42/0.60 inference(symmetry,[status(thm)],[482])).
% 0.42/0.60 tff(495,plain,
% 0.42/0.60 (multiply(sk_c3, multiply(sk_c8, sk_c8)) = multiply(multiply(sk_c3, sk_c8), sk_c8)),
% 0.42/0.60 inference(symmetry,[status(thm)],[439])).
% 0.42/0.60 tff(496,plain,
% 0.42/0.60 (multiply(sk_c7, sk_c6) = multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8)),
% 0.42/0.60 inference(transitivity,[status(thm)],[429, 432, 436, 495, 441, 494, 493])).
% 0.42/0.60 tff(497,plain,
% 0.42/0.60 (multiply(multiply(sk_c7, sk_c6), sk_c6) = multiply(multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8), sk_c6)),
% 0.42/0.60 inference(monotonicity,[status(thm)],[496])).
% 0.42/0.60 tff(498,plain,
% 0.42/0.60 (multiply(identity, sk_c6) = multiply(multiply(sk_c7, sk_c6), sk_c6)),
% 0.42/0.60 inference(monotonicity,[status(thm)],[443])).
% 0.42/0.60 tff(499,plain,
% 0.42/0.60 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c6) = sk_c6)),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(500,plain,
% 0.42/0.60 (multiply(identity, sk_c6) = sk_c6),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[499, 7])).
% 0.42/0.60 tff(501,plain,
% 0.42/0.60 (sk_c6 = multiply(identity, sk_c6)),
% 0.42/0.60 inference(symmetry,[status(thm)],[500])).
% 0.42/0.60 tff(502,plain,
% 0.42/0.60 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c5) = sk_c5)),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(503,plain,
% 0.42/0.60 (multiply(identity, sk_c5) = sk_c5),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[502, 7])).
% 0.42/0.60 tff(504,plain,
% 0.42/0.60 (inverse(sk_c8) = multiply(sk_c3, sk_c8)),
% 0.42/0.60 inference(transitivity,[status(thm)],[38, 154])).
% 0.42/0.60 tff(505,plain,
% 0.42/0.60 (multiply(inverse(sk_c8), sk_c8) = multiply(multiply(sk_c3, sk_c8), sk_c8)),
% 0.42/0.60 inference(monotonicity,[status(thm)],[504])).
% 0.42/0.60 tff(506,plain,
% 0.42/0.60 (identity = multiply(sk_c7, sk_c6)),
% 0.42/0.60 inference(transitivity,[status(thm)],[171, 505, 439, 437, 433, 430])).
% 0.42/0.60 tff(507,plain,
% 0.42/0.60 (multiply(identity, sk_c5) = multiply(multiply(sk_c7, sk_c6), sk_c5)),
% 0.42/0.60 inference(monotonicity,[status(thm)],[506])).
% 0.42/0.60 tff(508,plain,
% 0.42/0.60 (multiply(multiply(sk_c7, sk_c6), sk_c5) = multiply(identity, sk_c5)),
% 0.42/0.60 inference(symmetry,[status(thm)],[507])).
% 0.42/0.60 tff(509,plain,
% 0.42/0.60 (multiply(multiply(sk_c3, sk_c8), sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.42/0.60 inference(symmetry,[status(thm)],[505])).
% 0.42/0.60 tff(510,plain,
% 0.42/0.60 (multiply(sk_c7, sk_c6) = multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8)),
% 0.42/0.60 inference(transitivity,[status(thm)],[429, 432, 436, 495, 509, 494, 493])).
% 0.42/0.60 tff(511,plain,
% 0.42/0.60 (multiply(multiply(sk_c7, sk_c6), sk_c5) = multiply(multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8), sk_c5)),
% 0.42/0.60 inference(monotonicity,[status(thm)],[510])).
% 0.42/0.60 tff(512,plain,
% 0.42/0.60 (multiply(multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8), sk_c5) = multiply(multiply(sk_c7, sk_c6), sk_c5)),
% 0.42/0.60 inference(symmetry,[status(thm)],[511])).
% 0.42/0.60 tff(513,plain,
% 0.42/0.60 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8), sk_c5) = multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), multiply(sk_c8, sk_c5)))),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(514,plain,
% 0.42/0.60 (multiply(multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8), sk_c5) = multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), multiply(sk_c8, sk_c5))),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[513, 47])).
% 0.42/0.60 tff(515,plain,
% 0.42/0.60 (multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), multiply(sk_c8, sk_c5)) = multiply(multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8), sk_c5)),
% 0.42/0.60 inference(symmetry,[status(thm)],[514])).
% 0.42/0.60 tff(516,plain,
% 0.42/0.60 (multiply(sk_c8, multiply(sk_c6, sk_c8)) = multiply(sk_c8, multiply(sk_c6, multiply(sk_c1, sk_c7)))),
% 0.42/0.60 inference(symmetry,[status(thm)],[459])).
% 0.42/0.60 tff(517,plain,
% 0.42/0.60 (multiply(inverse(sk_c8), sk_c8) = multiply(multiply(sk_c8, sk_c6), sk_c8)),
% 0.42/0.60 inference(symmetry,[status(thm)],[456])).
% 0.42/0.60 tff(518,plain,
% 0.42/0.60 (multiply(sk_c8, sk_c5) = multiply(sk_c8, multiply(sk_c6, multiply(sk_c1, sk_c7)))),
% 0.42/0.60 inference(transitivity,[status(thm)],[380, 83, 171, 517, 294, 516])).
% 0.42/0.60 tff(519,plain,
% 0.42/0.60 (multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), multiply(sk_c8, sk_c5)) = multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), multiply(sk_c8, multiply(sk_c6, multiply(sk_c1, sk_c7))))),
% 0.42/0.60 inference(monotonicity,[status(thm)],[518])).
% 0.42/0.60 tff(520,plain,
% 0.42/0.60 (multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), multiply(sk_c8, multiply(sk_c6, multiply(sk_c1, sk_c7)))) = multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), multiply(sk_c8, sk_c5))),
% 0.42/0.60 inference(symmetry,[status(thm)],[519])).
% 0.42/0.60 tff(521,plain,
% 0.42/0.60 (multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), multiply(sk_c8, multiply(sk_c6, multiply(sk_c1, sk_c7)))) = multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), multiply(sk_c8, sk_c1))),
% 0.42/0.60 inference(monotonicity,[status(thm)],[460])).
% 0.42/0.60 tff(522,plain,
% 0.42/0.60 (multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), multiply(sk_c8, sk_c1)) = multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), multiply(sk_c8, multiply(sk_c6, multiply(sk_c1, sk_c7))))),
% 0.42/0.60 inference(symmetry,[status(thm)],[521])).
% 0.42/0.60 tff(523,plain,
% 0.42/0.60 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8), sk_c1) = multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), multiply(sk_c8, sk_c1)))),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(524,plain,
% 0.42/0.60 (multiply(multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8), sk_c1) = multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), multiply(sk_c8, sk_c1))),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[523, 47])).
% 0.42/0.60 tff(525,plain,
% 0.42/0.60 (multiply(multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8), sk_c1) = multiply(identity, sk_c1)),
% 0.42/0.60 inference(monotonicity,[status(thm)],[485])).
% 0.42/0.60 tff(526,plain,
% 0.42/0.60 (multiply(identity, sk_c1) = multiply(multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8), sk_c1)),
% 0.42/0.60 inference(symmetry,[status(thm)],[525])).
% 0.42/0.60 tff(527,plain,
% 0.42/0.60 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c1) = sk_c1)),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(528,plain,
% 0.42/0.60 (multiply(identity, sk_c1) = sk_c1),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[527, 7])).
% 0.42/0.60 tff(529,plain,
% 0.42/0.60 (sk_c1 = multiply(identity, sk_c1)),
% 0.42/0.60 inference(symmetry,[status(thm)],[528])).
% 0.42/0.60 tff(530,plain,
% 0.42/0.60 (multiply(identity, sk_c1) = multiply(identity, multiply(identity, sk_c1))),
% 0.42/0.60 inference(monotonicity,[status(thm)],[529])).
% 0.42/0.60 tff(531,plain,
% 0.42/0.60 (multiply(identity, multiply(identity, sk_c1)) = multiply(identity, sk_c1)),
% 0.42/0.60 inference(symmetry,[status(thm)],[530])).
% 0.42/0.60 tff(532,plain,
% 0.42/0.60 (multiply(sk_c8, sk_c8) = sk_c7),
% 0.42/0.60 inference(transitivity,[status(thm)],[428, 207, 313, 9])).
% 0.42/0.60 tff(533,plain,
% 0.42/0.60 (multiply(multiply(sk_c8, sk_c8), sk_c6) = multiply(sk_c7, sk_c6)),
% 0.42/0.60 inference(monotonicity,[status(thm)],[532])).
% 0.42/0.60 tff(534,plain,
% 0.42/0.60 (multiply(sk_c7, sk_c6) = multiply(multiply(sk_c8, sk_c8), sk_c6)),
% 0.42/0.60 inference(symmetry,[status(thm)],[533])).
% 0.42/0.60 tff(535,plain,
% 0.42/0.60 (identity = multiply(multiply(sk_c8, sk_c8), sk_c6)),
% 0.42/0.60 inference(transitivity,[status(thm)],[171, 505, 439, 437, 433, 430, 534])).
% 0.42/0.60 tff(536,plain,
% 0.42/0.60 (multiply(identity, multiply(identity, sk_c1)) = multiply(multiply(multiply(sk_c8, sk_c8), sk_c6), sk_c1)),
% 0.42/0.60 inference(monotonicity,[status(thm)],[535, 528])).
% 0.42/0.60 tff(537,plain,
% 0.42/0.60 (multiply(multiply(multiply(sk_c8, sk_c8), sk_c6), sk_c1) = multiply(identity, multiply(identity, sk_c1))),
% 0.42/0.60 inference(symmetry,[status(thm)],[536])).
% 0.42/0.60 tff(538,plain,
% 0.42/0.60 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c8, sk_c8), sk_c6), sk_c1) = multiply(multiply(sk_c8, sk_c8), multiply(sk_c6, sk_c1)))),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(539,plain,
% 0.42/0.60 (multiply(multiply(multiply(sk_c8, sk_c8), sk_c6), sk_c1) = multiply(multiply(sk_c8, sk_c8), multiply(sk_c6, sk_c1))),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[538, 47])).
% 0.42/0.60 tff(540,plain,
% 0.42/0.60 (multiply(multiply(sk_c8, sk_c8), multiply(sk_c6, sk_c1)) = multiply(multiply(multiply(sk_c8, sk_c8), sk_c6), sk_c1)),
% 0.42/0.60 inference(symmetry,[status(thm)],[539])).
% 0.42/0.60 tff(541,plain,
% 0.42/0.60 (multiply(multiply(sk_c8, sk_c8), multiply(sk_c6, sk_c1)) = multiply(sk_c7, multiply(sk_c6, sk_c1))),
% 0.42/0.60 inference(monotonicity,[status(thm)],[532])).
% 0.42/0.60 tff(542,plain,
% 0.42/0.60 (multiply(sk_c7, multiply(sk_c6, sk_c1)) = multiply(multiply(sk_c8, sk_c8), multiply(sk_c6, sk_c1))),
% 0.42/0.60 inference(symmetry,[status(thm)],[541])).
% 0.42/0.60 tff(543,plain,
% 0.42/0.60 (multiply(sk_c7, multiply(sk_c6, sk_c1)) = multiply(multiply(sk_c3, sk_c8), multiply(sk_c6, sk_c1))),
% 0.42/0.60 inference(monotonicity,[status(thm)],[154])).
% 0.42/0.60 tff(544,plain,
% 0.42/0.60 (multiply(multiply(sk_c3, sk_c8), multiply(sk_c6, sk_c1)) = multiply(sk_c7, multiply(sk_c6, sk_c1))),
% 0.42/0.60 inference(symmetry,[status(thm)],[543])).
% 0.42/0.60 tff(545,plain,
% 0.42/0.60 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c3, sk_c8), multiply(sk_c6, sk_c1)) = multiply(sk_c3, multiply(sk_c8, multiply(sk_c6, sk_c1))))),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(546,plain,
% 0.42/0.60 (multiply(multiply(sk_c3, sk_c8), multiply(sk_c6, sk_c1)) = multiply(sk_c3, multiply(sk_c8, multiply(sk_c6, sk_c1)))),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[545, 47])).
% 0.42/0.60 tff(547,plain,
% 0.42/0.60 (multiply(sk_c3, multiply(sk_c8, multiply(sk_c6, sk_c1))) = multiply(multiply(sk_c3, sk_c8), multiply(sk_c6, sk_c1))),
% 0.42/0.60 inference(symmetry,[status(thm)],[546])).
% 0.42/0.60 tff(548,plain,
% 0.42/0.60 (multiply(identity, sk_c8) = multiply(multiply(sk_c7, sk_c6), sk_c8)),
% 0.42/0.60 inference(monotonicity,[status(thm)],[506])).
% 0.42/0.60 tff(549,plain,
% 0.42/0.60 (multiply(multiply(sk_c7, sk_c6), sk_c8) = multiply(identity, sk_c8)),
% 0.42/0.60 inference(symmetry,[status(thm)],[548])).
% 0.42/0.60 tff(550,plain,
% 0.42/0.60 (multiply(multiply(sk_c8, sk_c6), sk_c1) = multiply(sk_c7, sk_c1)),
% 0.42/0.60 inference(monotonicity,[status(thm)],[234])).
% 0.42/0.60 tff(551,plain,
% 0.42/0.60 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c6), sk_c1) = multiply(sk_c8, multiply(sk_c6, sk_c1)))),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(552,plain,
% 0.42/0.60 (multiply(multiply(sk_c8, sk_c6), sk_c1) = multiply(sk_c8, multiply(sk_c6, sk_c1))),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[551, 47])).
% 0.42/0.60 tff(553,plain,
% 0.42/0.60 (multiply(sk_c8, multiply(sk_c6, sk_c1)) = multiply(multiply(sk_c8, sk_c6), sk_c1)),
% 0.42/0.60 inference(symmetry,[status(thm)],[552])).
% 0.42/0.60 tff(554,plain,
% 0.42/0.60 (multiply(sk_c8, multiply(sk_c6, sk_c1)) = multiply(identity, sk_c8)),
% 0.42/0.60 inference(transitivity,[status(thm)],[553, 550, 464, 158, 462, 454, 451, 448, 549])).
% 0.42/0.60 tff(555,plain,
% 0.42/0.60 (multiply(sk_c3, multiply(sk_c8, multiply(sk_c6, sk_c1))) = multiply(sk_c3, multiply(identity, sk_c8))),
% 0.42/0.60 inference(monotonicity,[status(thm)],[554])).
% 0.42/0.60 tff(556,plain,
% 0.42/0.60 (multiply(sk_c3, multiply(identity, sk_c8)) = multiply(sk_c3, multiply(sk_c8, multiply(sk_c6, sk_c1)))),
% 0.42/0.60 inference(symmetry,[status(thm)],[555])).
% 0.42/0.60 tff(557,plain,
% 0.42/0.60 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c3, identity), sk_c8) = multiply(sk_c3, multiply(identity, sk_c8)))),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(558,plain,
% 0.42/0.60 (multiply(multiply(sk_c3, identity), sk_c8) = multiply(sk_c3, multiply(identity, sk_c8))),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[557, 47])).
% 0.42/0.60 tff(559,plain,
% 0.42/0.60 (multiply(sk_c3, identity) = multiply(sk_c3, multiply(sk_c8, sk_c1))),
% 0.42/0.60 inference(monotonicity,[status(thm)],[311])).
% 0.42/0.60 tff(560,plain,
% 0.42/0.60 (multiply(sk_c3, identity) = multiply(sk_c7, sk_c1)),
% 0.42/0.60 inference(transitivity,[status(thm)],[559, 159, 463])).
% 0.42/0.60 tff(561,plain,
% 0.42/0.60 (multiply(multiply(sk_c3, identity), sk_c8) = multiply(multiply(sk_c7, sk_c1), sk_c8)),
% 0.42/0.60 inference(monotonicity,[status(thm)],[560])).
% 0.42/0.60 tff(562,plain,
% 0.42/0.60 (multiply(multiply(sk_c7, sk_c1), sk_c8) = multiply(multiply(sk_c3, identity), sk_c8)),
% 0.42/0.60 inference(symmetry,[status(thm)],[561])).
% 0.42/0.60 tff(563,plain,
% 0.42/0.60 (multiply(sk_c7, sk_c1) = multiply(identity, sk_c8)),
% 0.42/0.60 inference(transitivity,[status(thm)],[464, 158, 462, 454, 451, 448, 549])).
% 0.42/0.60 tff(564,plain,
% 0.42/0.60 (multiply(multiply(sk_c7, sk_c1), sk_c8) = multiply(multiply(identity, sk_c8), sk_c8)),
% 0.42/0.60 inference(monotonicity,[status(thm)],[563])).
% 0.42/0.60 tff(565,plain,
% 0.42/0.60 (multiply(multiply(identity, sk_c8), sk_c8) = multiply(multiply(sk_c7, sk_c1), sk_c8)),
% 0.42/0.60 inference(symmetry,[status(thm)],[564])).
% 0.42/0.60 tff(566,plain,
% 0.42/0.60 (multiply(identity, multiply(sk_c8, sk_c8)) = multiply(multiply(sk_c8, sk_c1), sk_c7)),
% 0.42/0.60 inference(monotonicity,[status(thm)],[311, 532])).
% 0.42/0.60 tff(567,plain,
% 0.42/0.60 (multiply(multiply(sk_c8, sk_c1), sk_c7) = multiply(identity, multiply(sk_c8, sk_c8))),
% 0.42/0.60 inference(symmetry,[status(thm)],[566])).
% 0.42/0.60 tff(568,plain,
% 0.42/0.60 (multiply(sk_c8, sk_c8) = sk_c5),
% 0.42/0.60 inference(transitivity,[status(thm)],[428, 207, 567, 283, 565, 562, 558, 556, 547, 544, 542, 540, 537, 531, 526, 524, 522, 520, 515, 512, 508, 503])).
% 0.42/0.60 tff(569,plain,
% 0.42/0.60 (inverse(multiply(sk_c8, sk_c8)) = inverse(sk_c5)),
% 0.42/0.60 inference(monotonicity,[status(thm)],[568])).
% 0.42/0.60 tff(570,plain,
% 0.42/0.60 (inverse(multiply(sk_c8, sk_c8)) = sk_c8),
% 0.42/0.60 inference(transitivity,[status(thm)],[569, 378])).
% 0.42/0.60 tff(571,assumption,(~(multiply(sk_c5, sk_c8) = sk_c6)), introduced(assumption)).
% 0.42/0.60 tff(572,plain,
% 0.42/0.60 (((multiply(sk_c2, sk_c3) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6)) <=> ((multiply(sk_c2, sk_c3) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6))),
% 0.42/0.60 inference(rewrite,[status(thm)],[])).
% 0.42/0.60 tff(573,axiom,((multiply(sk_c2, sk_c3) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_15')).
% 0.42/0.60 tff(574,plain,
% 0.42/0.60 ((multiply(sk_c2, sk_c3) = sk_c7) | (multiply(sk_c5, sk_c8) = sk_c6)),
% 0.42/0.60 inference(modus_ponens,[status(thm)],[573, 572])).
% 0.42/0.60 tff(575,plain,
% 0.42/0.60 (multiply(sk_c2, sk_c3) = sk_c7),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[574, 571])).
% 0.42/0.60 tff(576,plain,
% 0.42/0.60 (((inverse(sk_c2) = sk_c3) | (multiply(sk_c5, sk_c8) = sk_c6)) <=> ((inverse(sk_c2) = sk_c3) | (multiply(sk_c5, sk_c8) = sk_c6))),
% 0.42/0.60 inference(rewrite,[status(thm)],[])).
% 0.42/0.60 tff(577,axiom,((inverse(sk_c2) = sk_c3) | (multiply(sk_c5, sk_c8) = sk_c6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_20')).
% 0.42/0.60 tff(578,plain,
% 0.42/0.60 ((inverse(sk_c2) = sk_c3) | (multiply(sk_c5, sk_c8) = sk_c6)),
% 0.42/0.60 inference(modus_ponens,[status(thm)],[577, 576])).
% 0.42/0.60 tff(579,plain,
% 0.42/0.60 (inverse(sk_c2) = sk_c3),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[578, 571])).
% 0.42/0.60 tff(580,plain,
% 0.42/0.60 (multiply(sk_c2, inverse(sk_c2)) = multiply(sk_c2, sk_c3)),
% 0.42/0.60 inference(monotonicity,[status(thm)],[579])).
% 0.42/0.60 tff(581,plain,
% 0.42/0.60 (multiply(sk_c2, inverse(sk_c2)) = sk_c7),
% 0.42/0.60 inference(transitivity,[status(thm)],[580, 575])).
% 0.42/0.60 tff(582,plain,
% 0.42/0.60 (multiply(sk_c3, multiply(identity, sk_c8)) = multiply(multiply(sk_c3, identity), sk_c8)),
% 0.42/0.60 inference(symmetry,[status(thm)],[558])).
% 0.42/0.60 tff(583,plain,
% 0.42/0.60 (multiply(sk_c7, sk_c1) = multiply(multiply(sk_c8, sk_c6), sk_c1)),
% 0.42/0.60 inference(symmetry,[status(thm)],[550])).
% 0.42/0.60 tff(584,plain,
% 0.42/0.60 (sk_c8 = multiply(sk_c8, multiply(sk_c6, sk_c1))),
% 0.42/0.60 inference(transitivity,[status(thm)],[87, 548, 447, 450, 453, 461, 159, 463, 583, 552])).
% 0.42/0.60 tff(585,plain,
% 0.42/0.60 (multiply(inverse(sk_c2), sk_c8) = multiply(sk_c3, multiply(sk_c8, multiply(sk_c6, sk_c1)))),
% 0.42/0.60 inference(monotonicity,[status(thm)],[579, 584])).
% 0.42/0.60 tff(586,plain,
% 0.42/0.60 (multiply(inverse(sk_c2), sk_c8) = sk_c7),
% 0.42/0.60 inference(transitivity,[status(thm)],[585, 555, 582, 561, 564, 282, 566, 313, 9])).
% 0.42/0.60 tff(587,plain,
% 0.42/0.60 (multiply(sk_c1, multiply(sk_c8, sk_c8)) = multiply(sk_c1, sk_c7)),
% 0.42/0.60 inference(monotonicity,[status(thm)],[532])).
% 0.42/0.60 tff(588,plain,
% 0.42/0.60 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c8), sk_c8) = multiply(sk_c1, multiply(sk_c8, sk_c8)))),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(589,plain,
% 0.42/0.60 (multiply(multiply(sk_c1, sk_c8), sk_c8) = multiply(sk_c1, multiply(sk_c8, sk_c8))),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[588, 47])).
% 0.42/0.60 tff(590,plain,
% 0.42/0.60 (multiply(sk_c1, multiply(sk_c8, sk_c8)) = sk_c8),
% 0.42/0.60 inference(transitivity,[status(thm)],[587, 426])).
% 0.42/0.60 tff(591,plain,
% 0.42/0.60 (multiply(multiply(sk_c1, sk_c8), multiply(sk_c1, multiply(sk_c8, sk_c8))) = multiply(multiply(sk_c1, sk_c8), sk_c8)),
% 0.42/0.60 inference(monotonicity,[status(thm)],[590])).
% 0.42/0.60 tff(592,plain,
% 0.42/0.60 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c1, sk_c8), sk_c1), multiply(sk_c8, sk_c8)) = multiply(multiply(sk_c1, sk_c8), multiply(sk_c1, multiply(sk_c8, sk_c8))))),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(593,plain,
% 0.42/0.60 (multiply(multiply(multiply(sk_c1, sk_c8), sk_c1), multiply(sk_c8, sk_c8)) = multiply(multiply(sk_c1, sk_c8), multiply(sk_c1, multiply(sk_c8, sk_c8)))),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[592, 47])).
% 0.42/0.60 tff(594,plain,
% 0.42/0.60 (sk_c7 = multiply(sk_c8, sk_c8)),
% 0.42/0.60 inference(transitivity,[status(thm)],[189, 312, 206, 434])).
% 0.42/0.60 tff(595,plain,
% 0.42/0.60 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c8), sk_c1) = multiply(sk_c1, multiply(sk_c8, sk_c1)))),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(596,plain,
% 0.42/0.60 (multiply(multiply(sk_c1, sk_c8), sk_c1) = multiply(sk_c1, multiply(sk_c8, sk_c1))),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[595, 47])).
% 0.42/0.60 tff(597,plain,
% 0.42/0.60 (multiply(sk_c1, multiply(sk_c8, sk_c1)) = multiply(multiply(sk_c1, sk_c8), sk_c1)),
% 0.42/0.60 inference(symmetry,[status(thm)],[596])).
% 0.42/0.60 tff(598,plain,
% 0.42/0.60 (multiply(sk_c8, sk_c1) = multiply(sk_c7, sk_c8)),
% 0.42/0.60 inference(transitivity,[status(thm)],[309, 18, 171, 214])).
% 0.42/0.60 tff(599,plain,
% 0.42/0.60 (multiply(sk_c1, multiply(sk_c8, sk_c1)) = multiply(sk_c1, multiply(sk_c7, sk_c8))),
% 0.42/0.60 inference(monotonicity,[status(thm)],[598])).
% 0.42/0.60 tff(600,plain,
% 0.42/0.60 (multiply(sk_c1, multiply(sk_c7, sk_c8)) = multiply(sk_c1, multiply(sk_c8, sk_c1))),
% 0.42/0.60 inference(symmetry,[status(thm)],[599])).
% 0.42/0.60 tff(601,plain,
% 0.42/0.60 (multiply(multiply(sk_c1, sk_c7), sk_c8) = multiply(sk_c8, sk_c8)),
% 0.42/0.60 inference(monotonicity,[status(thm)],[426])).
% 0.42/0.60 tff(602,plain,
% 0.42/0.60 (multiply(sk_c8, sk_c8) = multiply(multiply(sk_c1, sk_c7), sk_c8)),
% 0.42/0.60 inference(symmetry,[status(thm)],[601])).
% 0.42/0.60 tff(603,plain,
% 0.42/0.60 (sk_c7 = multiply(multiply(sk_c1, sk_c8), sk_c1)),
% 0.42/0.60 inference(transitivity,[status(thm)],[189, 312, 206, 434, 602, 211, 600, 597])).
% 0.42/0.60 tff(604,plain,
% 0.42/0.60 (multiply(sk_c7, sk_c7) = multiply(multiply(multiply(sk_c1, sk_c8), sk_c1), multiply(sk_c8, sk_c8))),
% 0.42/0.60 inference(monotonicity,[status(thm)],[603, 594])).
% 0.42/0.60 tff(605,plain,
% 0.42/0.60 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c3) = sk_c3)),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(606,plain,
% 0.42/0.60 (multiply(identity, sk_c3) = sk_c3),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[605, 7])).
% 0.42/0.60 tff(607,plain,
% 0.42/0.60 (multiply(multiply(sk_c3, sk_c1), sk_c7) = inverse(sk_c8)),
% 0.42/0.61 inference(transitivity,[status(thm)],[466, 468, 153, 39])).
% 0.42/0.61 tff(608,plain,
% 0.42/0.61 (multiply(multiply(multiply(sk_c3, sk_c1), sk_c7), sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.42/0.61 inference(monotonicity,[status(thm)],[607])).
% 0.42/0.61 tff(609,plain,
% 0.42/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c3, sk_c1), sk_c7), sk_c8) = multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c8)))),
% 0.42/0.61 inference(quant_inst,[status(thm)],[])).
% 0.42/0.61 tff(610,plain,
% 0.42/0.61 (multiply(multiply(multiply(sk_c3, sk_c1), sk_c7), sk_c8) = multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c8))),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[609, 47])).
% 0.42/0.61 tff(611,plain,
% 0.42/0.61 (multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c8)) = multiply(multiply(multiply(sk_c3, sk_c1), sk_c7), sk_c8)),
% 0.42/0.61 inference(symmetry,[status(thm)],[610])).
% 0.42/0.61 tff(612,plain,
% 0.42/0.61 (identity = multiply(sk_c7, sk_c8)),
% 0.42/0.61 inference(transitivity,[status(thm)],[171, 214])).
% 0.42/0.61 tff(613,plain,
% 0.42/0.61 (multiply(multiply(sk_c3, sk_c1), identity) = multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c8))),
% 0.42/0.61 inference(monotonicity,[status(thm)],[612])).
% 0.42/0.61 tff(614,plain,
% 0.42/0.61 (multiply(multiply(sk_c3, sk_c1), identity) = identity),
% 0.42/0.61 inference(transitivity,[status(thm)],[613, 611, 608, 31])).
% 0.42/0.61 tff(615,plain,
% 0.42/0.61 (multiply(multiply(multiply(sk_c3, sk_c1), identity), sk_c3) = multiply(identity, sk_c3)),
% 0.42/0.61 inference(monotonicity,[status(thm)],[614])).
% 0.42/0.61 tff(616,plain,
% 0.42/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c3, sk_c1), identity), sk_c3) = multiply(multiply(sk_c3, sk_c1), multiply(identity, sk_c3)))),
% 0.42/0.61 inference(quant_inst,[status(thm)],[])).
% 0.42/0.61 tff(617,plain,
% 0.42/0.61 (multiply(multiply(multiply(sk_c3, sk_c1), identity), sk_c3) = multiply(multiply(sk_c3, sk_c1), multiply(identity, sk_c3))),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[616, 47])).
% 0.42/0.61 tff(618,plain,
% 0.42/0.61 (multiply(multiply(sk_c3, sk_c1), multiply(identity, sk_c3)) = multiply(multiply(multiply(sk_c3, sk_c1), identity), sk_c3)),
% 0.42/0.61 inference(symmetry,[status(thm)],[617])).
% 0.42/0.61 tff(619,plain,
% 0.42/0.61 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, multiply(sk_c3, sk_c1)) = multiply(sk_c3, sk_c1))),
% 0.42/0.61 inference(quant_inst,[status(thm)],[])).
% 0.42/0.61 tff(620,plain,
% 0.42/0.61 (multiply(identity, multiply(sk_c3, sk_c1)) = multiply(sk_c3, sk_c1)),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[619, 7])).
% 0.42/0.61 tff(621,plain,
% 0.42/0.61 (multiply(multiply(identity, multiply(sk_c3, sk_c1)), multiply(identity, sk_c3)) = multiply(multiply(sk_c3, sk_c1), multiply(identity, sk_c3))),
% 0.42/0.61 inference(monotonicity,[status(thm)],[620])).
% 0.42/0.61 tff(622,plain,
% 0.42/0.61 (sk_c3 = multiply(identity, sk_c3)),
% 0.42/0.61 inference(symmetry,[status(thm)],[606])).
% 0.42/0.61 tff(623,plain,
% 0.42/0.61 (multiply(multiply(identity, multiply(sk_c3, sk_c1)), sk_c3) = multiply(multiply(identity, multiply(sk_c3, sk_c1)), multiply(identity, sk_c3))),
% 0.42/0.61 inference(monotonicity,[status(thm)],[622])).
% 0.42/0.61 tff(624,plain,
% 0.42/0.61 (multiply(sk_c3, sk_c1) = multiply(identity, multiply(sk_c3, sk_c1))),
% 0.42/0.61 inference(symmetry,[status(thm)],[620])).
% 0.42/0.61 tff(625,plain,
% 0.42/0.61 (multiply(multiply(sk_c3, sk_c1), sk_c3) = multiply(multiply(identity, multiply(sk_c3, sk_c1)), sk_c3)),
% 0.42/0.61 inference(monotonicity,[status(thm)],[624])).
% 0.42/0.61 tff(626,plain,
% 0.42/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c3, sk_c1), sk_c3) = multiply(sk_c3, multiply(sk_c1, sk_c3)))),
% 0.42/0.61 inference(quant_inst,[status(thm)],[])).
% 0.42/0.61 tff(627,plain,
% 0.42/0.61 (multiply(multiply(sk_c3, sk_c1), sk_c3) = multiply(sk_c3, multiply(sk_c1, sk_c3))),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[626, 47])).
% 0.42/0.61 tff(628,plain,
% 0.42/0.61 (multiply(sk_c3, multiply(sk_c1, sk_c3)) = multiply(multiply(sk_c3, sk_c1), sk_c3)),
% 0.42/0.61 inference(symmetry,[status(thm)],[627])).
% 0.42/0.61 tff(629,plain,
% 0.42/0.61 (multiply(sk_c1, sk_c3) = multiply(multiply(identity, sk_c1), sk_c3)),
% 0.42/0.61 inference(monotonicity,[status(thm)],[529])).
% 0.42/0.61 tff(630,plain,
% 0.42/0.61 (multiply(multiply(identity, sk_c1), sk_c3) = multiply(sk_c1, sk_c3)),
% 0.42/0.61 inference(symmetry,[status(thm)],[629])).
% 0.42/0.61 tff(631,plain,
% 0.42/0.61 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, multiply(sk_c6, multiply(sk_c1, sk_c7))) = multiply(sk_c6, multiply(sk_c1, sk_c7)))),
% 0.42/0.61 inference(quant_inst,[status(thm)],[])).
% 0.42/0.61 tff(632,plain,
% 0.42/0.61 (multiply(identity, multiply(sk_c6, multiply(sk_c1, sk_c7))) = multiply(sk_c6, multiply(sk_c1, sk_c7))),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[631, 7])).
% 0.42/0.61 tff(633,plain,
% 0.42/0.61 (multiply(identity, multiply(sk_c6, multiply(sk_c1, sk_c7))) = multiply(multiply(sk_c7, sk_c6), multiply(sk_c6, multiply(sk_c1, sk_c7)))),
% 0.42/0.61 inference(monotonicity,[status(thm)],[506])).
% 0.42/0.61 tff(634,plain,
% 0.42/0.61 (multiply(multiply(sk_c7, sk_c6), multiply(sk_c6, multiply(sk_c1, sk_c7))) = multiply(identity, multiply(sk_c6, multiply(sk_c1, sk_c7)))),
% 0.42/0.61 inference(symmetry,[status(thm)],[633])).
% 0.42/0.61 tff(635,plain,
% 0.42/0.61 (multiply(multiply(sk_c7, sk_c6), multiply(sk_c6, multiply(sk_c1, sk_c7))) = multiply(multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8), multiply(sk_c6, multiply(sk_c1, sk_c7)))),
% 0.42/0.61 inference(monotonicity,[status(thm)],[510])).
% 0.42/0.61 tff(636,plain,
% 0.42/0.61 (multiply(multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8), multiply(sk_c6, multiply(sk_c1, sk_c7))) = multiply(multiply(sk_c7, sk_c6), multiply(sk_c6, multiply(sk_c1, sk_c7)))),
% 0.42/0.61 inference(symmetry,[status(thm)],[635])).
% 0.42/0.61 tff(637,plain,
% 0.42/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8), multiply(sk_c6, multiply(sk_c1, sk_c7))) = multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), multiply(sk_c8, multiply(sk_c6, multiply(sk_c1, sk_c7)))))),
% 0.42/0.61 inference(quant_inst,[status(thm)],[])).
% 0.42/0.61 tff(638,plain,
% 0.42/0.61 (multiply(multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8), multiply(sk_c6, multiply(sk_c1, sk_c7))) = multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), multiply(sk_c8, multiply(sk_c6, multiply(sk_c1, sk_c7))))),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[637, 47])).
% 0.42/0.61 tff(639,plain,
% 0.42/0.61 (multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), multiply(sk_c8, multiply(sk_c6, multiply(sk_c1, sk_c7)))) = multiply(multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8), multiply(sk_c6, multiply(sk_c1, sk_c7)))),
% 0.42/0.61 inference(symmetry,[status(thm)],[638])).
% 0.42/0.61 tff(640,plain,
% 0.42/0.61 (multiply(identity, sk_c1) = multiply(sk_c6, multiply(sk_c1, sk_c7))),
% 0.42/0.61 inference(transitivity,[status(thm)],[526, 524, 522, 639, 636, 634, 632])).
% 0.42/0.61 tff(641,plain,
% 0.42/0.61 (multiply(multiply(identity, sk_c1), sk_c3) = multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3)),
% 0.42/0.61 inference(monotonicity,[status(thm)],[640])).
% 0.42/0.61 tff(642,plain,
% 0.42/0.61 (multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3) = multiply(multiply(identity, sk_c1), sk_c3)),
% 0.42/0.61 inference(symmetry,[status(thm)],[641])).
% 0.42/0.61 tff(643,plain,
% 0.42/0.61 (multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3) = multiply(sk_c1, sk_c3)),
% 0.42/0.61 inference(transitivity,[status(thm)],[642, 630])).
% 0.42/0.61 tff(644,plain,
% 0.42/0.61 (multiply(sk_c3, multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3)) = multiply(sk_c3, multiply(sk_c1, sk_c3))),
% 0.42/0.61 inference(monotonicity,[status(thm)],[643])).
% 0.42/0.61 tff(645,plain,
% 0.42/0.61 (multiply(sk_c3, multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3)) = sk_c3),
% 0.42/0.61 inference(transitivity,[status(thm)],[644, 628, 625, 623, 621, 618, 615, 606])).
% 0.42/0.61 tff(646,plain,
% 0.42/0.61 (multiply(sk_c2, multiply(sk_c3, multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3))) = multiply(sk_c2, sk_c3)),
% 0.42/0.61 inference(monotonicity,[status(thm)],[645])).
% 0.42/0.61 tff(647,plain,
% 0.42/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, sk_c3), multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3)) = multiply(sk_c2, multiply(sk_c3, multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3))))),
% 0.42/0.61 inference(quant_inst,[status(thm)],[])).
% 0.42/0.61 tff(648,plain,
% 0.42/0.61 (multiply(multiply(sk_c2, sk_c3), multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3)) = multiply(sk_c2, multiply(sk_c3, multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3)))),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[647, 47])).
% 0.42/0.61 tff(649,plain,
% 0.42/0.61 (sk_c7 = multiply(sk_c2, sk_c3)),
% 0.42/0.61 inference(symmetry,[status(thm)],[575])).
% 0.42/0.61 tff(650,plain,
% 0.42/0.61 (multiply(sk_c8, sk_c8) = multiply(sk_c2, sk_c3)),
% 0.42/0.61 inference(transitivity,[status(thm)],[428, 207, 313, 9, 649])).
% 0.42/0.61 tff(651,plain,
% 0.42/0.61 (multiply(multiply(sk_c8, sk_c8), multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3)) = multiply(multiply(sk_c2, sk_c3), multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3))),
% 0.42/0.61 inference(monotonicity,[status(thm)],[650])).
% 0.42/0.61 tff(652,plain,
% 0.42/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c8, sk_c8), multiply(sk_c6, multiply(sk_c1, sk_c7))), sk_c3) = multiply(multiply(sk_c8, sk_c8), multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3)))),
% 0.42/0.61 inference(quant_inst,[status(thm)],[])).
% 0.42/0.61 tff(653,plain,
% 0.42/0.61 (multiply(multiply(multiply(sk_c8, sk_c8), multiply(sk_c6, multiply(sk_c1, sk_c7))), sk_c3) = multiply(multiply(sk_c8, sk_c8), multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3))),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[652, 47])).
% 0.42/0.61 tff(654,plain,
% 0.42/0.61 (multiply(multiply(sk_c8, sk_c8), multiply(sk_c6, multiply(sk_c1, sk_c7))) = multiply(sk_c7, multiply(sk_c6, sk_c8))),
% 0.42/0.61 inference(monotonicity,[status(thm)],[532, 458])).
% 0.42/0.61 tff(655,plain,
% 0.42/0.61 (multiply(sk_c7, multiply(sk_c6, sk_c8)) = multiply(multiply(sk_c8, sk_c8), multiply(sk_c6, multiply(sk_c1, sk_c7)))),
% 0.42/0.61 inference(symmetry,[status(thm)],[654])).
% 0.42/0.61 tff(656,plain,
% 0.42/0.61 (multiply(sk_c7, sk_c1) = multiply(multiply(sk_c8, sk_c8), multiply(sk_c6, multiply(sk_c1, sk_c7)))),
% 0.42/0.61 inference(transitivity,[status(thm)],[464, 158, 462, 454, 451, 655])).
% 0.42/0.61 tff(657,plain,
% 0.42/0.61 (multiply(multiply(sk_c7, sk_c1), sk_c3) = multiply(multiply(multiply(sk_c8, sk_c8), multiply(sk_c6, multiply(sk_c1, sk_c7))), sk_c3)),
% 0.42/0.61 inference(monotonicity,[status(thm)],[656])).
% 0.42/0.61 tff(658,plain,
% 0.42/0.61 (sk_c8 = multiply(sk_c7, sk_c1)),
% 0.42/0.61 inference(transitivity,[status(thm)],[87, 548, 447, 450, 453, 461, 159, 463])).
% 0.42/0.61 tff(659,plain,
% 0.42/0.61 (multiply(sk_c8, sk_c3) = multiply(multiply(sk_c7, sk_c1), sk_c3)),
% 0.42/0.61 inference(monotonicity,[status(thm)],[658])).
% 0.42/0.61 tff(660,plain,
% 0.42/0.61 (multiply(sk_c8, sk_c3) = sk_c7),
% 0.42/0.61 inference(transitivity,[status(thm)],[659, 657, 653, 651, 648, 646, 575])).
% 0.42/0.61 tff(661,plain,
% 0.42/0.61 (multiply(multiply(sk_c7, sk_c1), sk_c3) = sk_c7),
% 0.42/0.61 inference(transitivity,[status(thm)],[657, 653, 651, 648, 646, 575])).
% 0.42/0.61 tff(662,plain,
% 0.42/0.61 (multiply(multiply(multiply(sk_c7, sk_c1), sk_c3), multiply(sk_c8, sk_c3)) = multiply(sk_c7, sk_c7)),
% 0.42/0.61 inference(monotonicity,[status(thm)],[661, 660])).
% 0.42/0.61 tff(663,plain,
% 0.42/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(multiply(sk_c7, sk_c1), sk_c3), sk_c8), sk_c3) = multiply(multiply(multiply(sk_c7, sk_c1), sk_c3), multiply(sk_c8, sk_c3)))),
% 0.42/0.61 inference(quant_inst,[status(thm)],[])).
% 0.42/0.61 tff(664,plain,
% 0.42/0.61 (multiply(multiply(multiply(multiply(sk_c7, sk_c1), sk_c3), sk_c8), sk_c3) = multiply(multiply(multiply(sk_c7, sk_c1), sk_c3), multiply(sk_c8, sk_c3))),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[663, 47])).
% 0.42/0.61 tff(665,plain,
% 0.42/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(sk_c7, sk_c1), sk_c3), sk_c8) = multiply(multiply(sk_c7, sk_c1), multiply(sk_c3, sk_c8)))),
% 0.42/0.61 inference(quant_inst,[status(thm)],[])).
% 0.42/0.61 tff(666,plain,
% 0.42/0.61 (multiply(multiply(multiply(sk_c7, sk_c1), sk_c3), sk_c8) = multiply(multiply(sk_c7, sk_c1), multiply(sk_c3, sk_c8))),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[665, 47])).
% 0.42/0.61 tff(667,plain,
% 0.42/0.61 (multiply(multiply(sk_c7, sk_c1), multiply(sk_c3, sk_c8)) = multiply(multiply(multiply(sk_c7, sk_c1), sk_c3), sk_c8)),
% 0.42/0.61 inference(symmetry,[status(thm)],[666])).
% 0.42/0.61 tff(668,plain,
% 0.42/0.61 (multiply(multiply(sk_c7, sk_c1), multiply(sk_c3, sk_c8)) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.42/0.61 inference(monotonicity,[status(thm)],[153])).
% 0.42/0.61 tff(669,plain,
% 0.42/0.61 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(multiply(sk_c7, sk_c1), multiply(sk_c3, sk_c8))),
% 0.42/0.61 inference(symmetry,[status(thm)],[668])).
% 0.42/0.61 tff(670,plain,
% 0.42/0.61 (multiply(sk_c7, multiply(sk_c1, sk_c7)) = multiply(inverse(sk_c8), sk_c8)),
% 0.42/0.61 inference(monotonicity,[status(thm)],[39, 426])).
% 0.42/0.61 tff(671,plain,
% 0.42/0.61 (multiply(inverse(sk_c8), sk_c8) = multiply(sk_c7, multiply(sk_c1, sk_c7))),
% 0.42/0.61 inference(symmetry,[status(thm)],[670])).
% 0.42/0.61 tff(672,plain,
% 0.42/0.61 (identity = multiply(multiply(multiply(sk_c7, sk_c1), sk_c3), sk_c8)),
% 0.42/0.61 inference(transitivity,[status(thm)],[171, 671, 193, 669, 667])).
% 0.42/0.61 tff(673,plain,
% 0.42/0.61 (multiply(identity, sk_c3) = multiply(multiply(multiply(multiply(sk_c7, sk_c1), sk_c3), sk_c8), sk_c3)),
% 0.42/0.61 inference(monotonicity,[status(thm)],[672])).
% 0.42/0.61 tff(674,plain,
% 0.42/0.61 (inverse(sk_c2) = sk_c8),
% 0.42/0.61 inference(transitivity,[status(thm)],[579, 622, 673, 664, 662, 604, 593, 591, 589, 587, 426])).
% 0.42/0.61 tff(675,plain,
% 0.42/0.61 ((sk_c8 = inverse(sk_c8)) <=> (inverse(sk_c8) = sk_c8)),
% 0.42/0.61 inference(commutativity,[status(thm)],[])).
% 0.42/0.61 tff(676,plain,
% 0.42/0.61 (sk_c3 = inverse(sk_c2)),
% 0.42/0.61 inference(symmetry,[status(thm)],[579])).
% 0.42/0.61 tff(677,plain,
% 0.42/0.61 (multiply(sk_c3, sk_c2) = multiply(inverse(sk_c2), sk_c2)),
% 0.42/0.61 inference(monotonicity,[status(thm)],[676])).
% 0.42/0.61 tff(678,plain,
% 0.42/0.61 (multiply(sk_c3, sk_c2) = identity),
% 0.42/0.61 inference(transitivity,[status(thm)],[677, 178])).
% 0.42/0.61 tff(679,plain,
% 0.42/0.61 (multiply(multiply(sk_c3, sk_c2), sk_c3) = multiply(identity, sk_c3)),
% 0.42/0.61 inference(monotonicity,[status(thm)],[678])).
% 0.42/0.61 tff(680,plain,
% 0.42/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c3, sk_c2), sk_c3) = multiply(sk_c3, multiply(sk_c2, sk_c3)))),
% 0.42/0.61 inference(quant_inst,[status(thm)],[])).
% 0.42/0.61 tff(681,plain,
% 0.42/0.61 (multiply(multiply(sk_c3, sk_c2), sk_c3) = multiply(sk_c3, multiply(sk_c2, sk_c3))),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[680, 47])).
% 0.42/0.61 tff(682,plain,
% 0.42/0.61 (multiply(sk_c3, multiply(sk_c2, sk_c3)) = multiply(multiply(sk_c3, sk_c2), sk_c3)),
% 0.42/0.61 inference(symmetry,[status(thm)],[681])).
% 0.42/0.61 tff(683,plain,
% 0.42/0.61 (multiply(sk_c3, multiply(sk_c8, sk_c8)) = multiply(sk_c3, multiply(sk_c2, sk_c3))),
% 0.42/0.61 inference(monotonicity,[status(thm)],[650])).
% 0.42/0.61 tff(684,plain,
% 0.42/0.61 (multiply(sk_c7, sk_c8) = multiply(sk_c8, sk_c1)),
% 0.42/0.61 inference(transitivity,[status(thm)],[213, 31, 29, 310])).
% 0.42/0.61 tff(685,plain,
% 0.42/0.61 (multiply(multiply(sk_c7, sk_c8), sk_c7) = multiply(multiply(sk_c8, sk_c1), sk_c7)),
% 0.42/0.61 inference(monotonicity,[status(thm)],[684])).
% 0.42/0.61 tff(686,plain,
% 0.42/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c7, sk_c8), sk_c7) = multiply(sk_c7, multiply(sk_c8, sk_c7)))),
% 0.42/0.61 inference(quant_inst,[status(thm)],[])).
% 0.42/0.61 tff(687,plain,
% 0.42/0.61 (multiply(multiply(sk_c7, sk_c8), sk_c7) = multiply(sk_c7, multiply(sk_c8, sk_c7))),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[686, 47])).
% 0.42/0.61 tff(688,plain,
% 0.42/0.61 (multiply(sk_c7, multiply(sk_c8, sk_c7)) = multiply(multiply(sk_c7, sk_c8), sk_c7)),
% 0.42/0.61 inference(symmetry,[status(thm)],[687])).
% 0.42/0.61 tff(689,plain,
% 0.42/0.61 (multiply(sk_c8, sk_c7) = multiply(sk_c8, multiply(sk_c8, sk_c8))),
% 0.42/0.61 inference(monotonicity,[status(thm)],[594])).
% 0.42/0.61 tff(690,plain,
% 0.42/0.61 (multiply(sk_c8, multiply(sk_c8, sk_c8)) = multiply(sk_c8, sk_c7)),
% 0.42/0.61 inference(symmetry,[status(thm)],[689])).
% 0.42/0.61 tff(691,plain,
% 0.42/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c8), sk_c8) = multiply(sk_c8, multiply(sk_c8, sk_c8)))),
% 0.42/0.61 inference(quant_inst,[status(thm)],[])).
% 0.42/0.61 tff(692,plain,
% 0.42/0.61 (multiply(multiply(sk_c8, sk_c8), sk_c8) = multiply(sk_c8, multiply(sk_c8, sk_c8))),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[691, 47])).
% 0.42/0.61 tff(693,plain,
% 0.42/0.61 (multiply(sk_c8, sk_c8) = inverse(sk_c8)),
% 0.42/0.61 inference(transitivity,[status(thm)],[428, 207, 313, 9, 39])).
% 0.42/0.61 tff(694,plain,
% 0.42/0.61 (multiply(multiply(sk_c8, sk_c8), sk_c8) = multiply(inverse(sk_c8), sk_c8)),
% 0.42/0.61 inference(monotonicity,[status(thm)],[693])).
% 0.42/0.61 tff(695,plain,
% 0.42/0.61 (multiply(inverse(sk_c8), sk_c8) = multiply(multiply(sk_c8, sk_c8), sk_c8)),
% 0.42/0.61 inference(symmetry,[status(thm)],[694])).
% 0.42/0.61 tff(696,plain,
% 0.42/0.61 (multiply(sk_c8, multiply(sk_c6, multiply(sk_c1, sk_c7))) = multiply(sk_c8, sk_c7)),
% 0.42/0.61 inference(transitivity,[status(thm)],[459, 457, 456, 695, 692, 690])).
% 0.42/0.61 tff(697,plain,
% 0.42/0.61 (multiply(multiply(sk_c8, sk_c8), multiply(sk_c8, multiply(sk_c6, multiply(sk_c1, sk_c7)))) = multiply(sk_c7, multiply(sk_c8, sk_c7))),
% 0.42/0.61 inference(monotonicity,[status(thm)],[532, 696])).
% 0.42/0.61 tff(698,plain,
% 0.42/0.61 (identity = multiply(sk_c8, multiply(sk_c6, multiply(sk_c1, sk_c7)))),
% 0.42/0.61 inference(transitivity,[status(thm)],[171, 517, 294, 516])).
% 0.42/0.61 tff(699,plain,
% 0.42/0.61 (multiply(sk_c2, sk_c3) = multiply(sk_c8, sk_c8)),
% 0.42/0.61 inference(transitivity,[status(thm)],[575, 189, 312, 206, 434])).
% 0.42/0.61 tff(700,plain,
% 0.42/0.61 (multiply(multiply(sk_c2, sk_c3), identity) = multiply(multiply(sk_c8, sk_c8), multiply(sk_c8, multiply(sk_c6, multiply(sk_c1, sk_c7))))),
% 0.42/0.61 inference(monotonicity,[status(thm)],[699, 698])).
% 0.42/0.61 tff(701,plain,
% 0.42/0.61 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, sk_c3), identity) = multiply(sk_c2, multiply(sk_c3, identity)))),
% 0.42/0.61 inference(quant_inst,[status(thm)],[])).
% 0.42/0.61 tff(702,plain,
% 0.42/0.61 (multiply(multiply(sk_c2, sk_c3), identity) = multiply(sk_c2, multiply(sk_c3, identity))),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[701, 47])).
% 0.42/0.61 tff(703,plain,
% 0.42/0.61 (multiply(sk_c2, multiply(sk_c3, identity)) = multiply(multiply(sk_c2, sk_c3), identity)),
% 0.42/0.61 inference(symmetry,[status(thm)],[702])).
% 0.42/0.61 tff(704,plain,
% 0.42/0.61 (multiply(sk_c3, multiply(sk_c8, sk_c1)) = multiply(sk_c3, identity)),
% 0.42/0.61 inference(symmetry,[status(thm)],[559])).
% 0.42/0.61 tff(705,plain,
% 0.42/0.61 (multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)) = multiply(sk_c3, identity)),
% 0.42/0.61 inference(transitivity,[status(thm)],[475, 472, 464, 158, 704])).
% 0.42/0.61 tff(706,plain,
% 0.42/0.61 (multiply(sk_c2, multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = multiply(sk_c2, multiply(sk_c3, identity))),
% 0.42/0.61 inference(monotonicity,[status(thm)],[705])).
% 0.42/0.61 tff(707,plain,
% 0.42/0.61 (sk_c8 = multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))),
% 0.42/0.61 inference(transitivity,[status(thm)],[87, 548, 447, 450, 453, 461, 159, 463, 471, 474])).
% 0.42/0.61 tff(708,plain,
% 0.42/0.61 (multiply(sk_c2, sk_c8) = multiply(sk_c2, multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))),
% 0.42/0.61 inference(monotonicity,[status(thm)],[707])).
% 0.42/0.61 tff(709,plain,
% 0.42/0.61 (multiply(sk_c2, sk_c8) = sk_c7),
% 0.42/0.61 inference(transitivity,[status(thm)],[708, 706, 703, 700, 697, 688, 685, 313, 9])).
% 0.42/0.61 tff(710,plain,
% 0.42/0.61 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.42/0.61 inference(monotonicity,[status(thm)],[658, 709])).
% 0.42/0.61 tff(711,plain,
% 0.42/0.61 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c8),
% 0.42/0.61 inference(transitivity,[status(thm)],[710, 49, 670, 505, 439, 683, 682, 679, 673, 664, 662, 604, 593, 591, 589, 587, 426])).
% 0.42/0.61 tff(712,plain,
% 0.42/0.61 ((multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7) <=> (sk_c8 = inverse(sk_c8))),
% 0.42/0.61 inference(monotonicity,[status(thm)],[711, 39])).
% 0.42/0.61 tff(713,plain,
% 0.42/0.61 ((multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7) <=> (inverse(sk_c8) = sk_c8)),
% 0.42/0.61 inference(transitivity,[status(thm)],[712, 675])).
% 0.42/0.61 tff(714,plain,
% 0.42/0.61 ((inverse(sk_c8) = sk_c8) <=> (multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)),
% 0.42/0.61 inference(symmetry,[status(thm)],[713])).
% 0.42/0.61 tff(715,plain,
% 0.42/0.61 (multiply(sk_c8, sk_c1) = multiply(sk_c7, sk_c1)),
% 0.42/0.61 inference(transitivity,[status(thm)],[309, 18, 171, 505, 439, 683, 682, 679, 673, 664, 662, 604, 593, 591, 589, 587, 426, 87, 548, 447, 450, 453, 461, 159, 463])).
% 0.42/0.61 tff(716,plain,
% 0.42/0.61 (multiply(multiply(sk_c8, sk_c1), sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.42/0.61 inference(monotonicity,[status(thm)],[715])).
% 0.42/0.61 tff(717,plain,
% 0.42/0.61 (inverse(sk_c8) = sk_c8),
% 0.42/0.61 inference(transitivity,[status(thm)],[38, 189, 312, 716, 49, 670, 505, 439, 683, 682, 679, 673, 664, 662, 604, 593, 591, 589, 587, 426])).
% 0.42/0.61 tff(718,plain,
% 0.42/0.61 (multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7),
% 0.42/0.61 inference(modus_ponens,[status(thm)],[717, 714])).
% 0.42/0.61 tff(719,plain,
% 0.42/0.61 (multiply(multiply(sk_c8, sk_c8), sk_c7) = multiply(sk_c7, sk_c7)),
% 0.42/0.61 inference(monotonicity,[status(thm)],[532])).
% 0.42/0.61 tff(720,plain,
% 0.42/0.61 (multiply(multiply(sk_c8, sk_c8), sk_c7) = sk_c8),
% 0.42/0.61 inference(transitivity,[status(thm)],[719, 604, 593, 591, 589, 587, 426])).
% 0.42/0.61 tff(721,plain,
% 0.42/0.61 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(inverse(sk_c2), sk_c8) = sk_c7)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c7)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(multiply(sk_c8, sk_c8), sk_c7) = sk_c8)) | (~(inverse(multiply(sk_c8, sk_c8)) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(inverse(sk_c2), sk_c8) = sk_c7)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c7)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(multiply(sk_c8, sk_c8), sk_c7) = sk_c8)) | (~(inverse(multiply(sk_c8, sk_c8)) = sk_c8)))),
% 0.42/0.61 inference(rewrite,[status(thm)],[])).
% 0.42/0.61 tff(722,plain,
% 0.42/0.61 (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(multiply(sk_c8, sk_c8)) = sk_c8)) | (~(multiply(multiply(sk_c8, sk_c8), sk_c7) = sk_c8)) | (~(inverse(multiply(sk_c8, sk_c8)) = sk_c8)) | (~(multiply(inverse(sk_c2), sk_c8) = sk_c7)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c7)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(multiply(sk_c8, sk_c8), sk_c7) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(inverse(sk_c2), sk_c8) = sk_c7)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c7)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(multiply(sk_c8, sk_c8), sk_c7) = sk_c8)) | (~(inverse(multiply(sk_c8, sk_c8)) = sk_c8)))),
% 0.42/0.62 inference(rewrite,[status(thm)],[])).
% 0.42/0.62 tff(723,plain,
% 0.42/0.62 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(multiply(sk_c8, sk_c8)) = sk_c8)) | (~(multiply(multiply(sk_c8, sk_c8), sk_c7) = sk_c8)) | (~(inverse(multiply(sk_c8, sk_c8)) = sk_c8)) | (~(multiply(inverse(sk_c2), sk_c8) = sk_c7)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c7)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(multiply(sk_c8, sk_c8), sk_c7) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(multiply(inverse(sk_c2), sk_c8) = sk_c7)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c7)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(multiply(sk_c8, sk_c8), sk_c7) = sk_c8)) | (~(inverse(multiply(sk_c8, sk_c8)) = sk_c8))))),
% 0.42/0.62 inference(monotonicity,[status(thm)],[722])).
% 0.42/0.62 tff(724,plain,
% 0.42/0.62 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(multiply(sk_c8, sk_c8)) = sk_c8)) | (~(multiply(multiply(sk_c8, sk_c8), sk_c7) = sk_c8)) | (~(inverse(multiply(sk_c8, sk_c8)) = sk_c8)) | (~(multiply(inverse(sk_c2), sk_c8) = sk_c7)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c7)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(multiply(sk_c8, sk_c8), sk_c7) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(inverse(sk_c2), sk_c8) = sk_c7)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c7)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(multiply(sk_c8, sk_c8), sk_c7) = sk_c8)) | (~(inverse(multiply(sk_c8, sk_c8)) = sk_c8)))),
% 0.42/0.62 inference(transitivity,[status(thm)],[723, 721])).
% 0.42/0.62 tff(725,plain,
% 0.42/0.62 ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(multiply(sk_c8, sk_c8)) = sk_c8)) | (~(multiply(multiply(sk_c8, sk_c8), sk_c7) = sk_c8)) | (~(inverse(multiply(sk_c8, sk_c8)) = sk_c8)) | (~(multiply(inverse(sk_c2), sk_c8) = sk_c7)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c7)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(multiply(sk_c8, sk_c8), sk_c7) = sk_c8)))),
% 0.42/0.62 inference(quant_inst,[status(thm)],[])).
% 0.42/0.62 tff(726,plain,
% 0.42/0.62 ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(multiply(inverse(sk_c2), sk_c8) = sk_c7)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c7)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(multiply(multiply(sk_c8, sk_c8), sk_c7) = sk_c8)) | (~(inverse(multiply(sk_c8, sk_c8)) = sk_c8))),
% 0.42/0.62 inference(modus_ponens,[status(thm)],[725, 724])).
% 0.42/0.62 tff(727,plain,
% 0.42/0.62 ((~(multiply(inverse(sk_c2), sk_c8) = sk_c7)) | (~(multiply(sk_c2, inverse(sk_c2)) = sk_c7)) | (~(inverse(sk_c2) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c2, sk_c8)) = sk_c7)) | (~(inverse(multiply(sk_c8, sk_c8)) = sk_c8))),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[726, 38, 143, 720])).
% 0.42/0.62 tff(728,plain,
% 0.42/0.62 ($false),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[727, 718, 674, 586, 581, 570])).
% 0.42/0.62 tff(729,plain,(multiply(sk_c5, sk_c8) = sk_c6), inference(lemma,lemma(discharge,[]))).
% 0.42/0.62 tff(730,plain,
% 0.42/0.62 (multiply(sk_c5, multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = multiply(sk_c5, sk_c8)),
% 0.42/0.62 inference(monotonicity,[status(thm)],[476])).
% 0.42/0.62 tff(731,plain,
% 0.42/0.62 (multiply(identity, sk_c5) = multiply(multiply(sk_c7, sk_c6), sk_c5)),
% 0.42/0.62 inference(monotonicity,[status(thm)],[443])).
% 0.42/0.62 tff(732,plain,
% 0.42/0.62 (multiply(multiply(sk_c7, sk_c6), sk_c5) = multiply(identity, sk_c5)),
% 0.42/0.62 inference(symmetry,[status(thm)],[731])).
% 0.42/0.62 tff(733,plain,
% 0.42/0.62 (multiply(multiply(sk_c7, sk_c6), sk_c5) = multiply(multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8), sk_c5)),
% 0.42/0.62 inference(monotonicity,[status(thm)],[496])).
% 0.42/0.62 tff(734,plain,
% 0.42/0.62 (multiply(multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8), sk_c5) = multiply(multiply(sk_c7, sk_c6), sk_c5)),
% 0.42/0.62 inference(symmetry,[status(thm)],[733])).
% 0.42/0.62 tff(735,plain,
% 0.42/0.62 (multiply(multiply(sk_c7, sk_c6), multiply(sk_c6, multiply(sk_c1, sk_c7))) = multiply(multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8), multiply(sk_c6, multiply(sk_c1, sk_c7)))),
% 0.42/0.62 inference(monotonicity,[status(thm)],[496])).
% 0.42/0.62 tff(736,plain,
% 0.42/0.62 (multiply(identity, multiply(sk_c6, multiply(sk_c1, sk_c7))) = multiply(multiply(sk_c7, sk_c6), multiply(sk_c6, multiply(sk_c1, sk_c7)))),
% 0.42/0.62 inference(monotonicity,[status(thm)],[443])).
% 0.42/0.62 tff(737,plain,
% 0.42/0.62 (multiply(sk_c6, multiply(sk_c1, sk_c7)) = multiply(identity, multiply(sk_c6, multiply(sk_c1, sk_c7)))),
% 0.42/0.62 inference(symmetry,[status(thm)],[632])).
% 0.42/0.62 tff(738,plain,
% 0.42/0.62 (multiply(sk_c6, multiply(sk_c1, sk_c7)) = sk_c5),
% 0.42/0.62 inference(transitivity,[status(thm)],[737, 736, 735, 638, 520, 515, 734, 732, 503])).
% 0.42/0.62 tff(739,plain,
% 0.42/0.62 (multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = multiply(sk_c5, multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))),
% 0.42/0.62 inference(monotonicity,[status(thm)],[738])).
% 0.42/0.62 tff(740,plain,
% 0.42/0.62 (multiply(multiply(sk_c7, sk_c6), multiply(sk_c6, multiply(sk_c1, sk_c7))) = multiply(identity, multiply(sk_c6, multiply(sk_c1, sk_c7)))),
% 0.42/0.62 inference(symmetry,[status(thm)],[736])).
% 0.42/0.62 tff(741,plain,
% 0.42/0.62 (multiply(multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8), multiply(sk_c6, multiply(sk_c1, sk_c7))) = multiply(multiply(sk_c7, sk_c6), multiply(sk_c6, multiply(sk_c1, sk_c7)))),
% 0.42/0.62 inference(symmetry,[status(thm)],[735])).
% 0.42/0.62 tff(742,plain,
% 0.42/0.62 (multiply(identity, sk_c1) = multiply(sk_c6, multiply(sk_c1, sk_c7))),
% 0.42/0.62 inference(transitivity,[status(thm)],[526, 524, 522, 639, 741, 740, 632])).
% 0.42/0.62 tff(743,plain,
% 0.42/0.62 (multiply(multiply(identity, sk_c1), multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))),
% 0.42/0.62 inference(monotonicity,[status(thm)],[742])).
% 0.42/0.62 tff(744,plain,
% 0.42/0.62 (multiply(sk_c7, sk_c1) = multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))),
% 0.42/0.62 inference(transitivity,[status(thm)],[471, 474])).
% 0.42/0.62 tff(745,plain,
% 0.42/0.62 (multiply(sk_c1, multiply(sk_c7, sk_c1)) = multiply(multiply(identity, sk_c1), multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))),
% 0.42/0.62 inference(monotonicity,[status(thm)],[529, 744])).
% 0.42/0.62 tff(746,plain,
% 0.42/0.62 (inverse(sk_c1) = multiply(sk_c1, sk_c7)),
% 0.42/0.62 inference(transitivity,[status(thm)],[307, 427])).
% 0.42/0.62 tff(747,plain,
% 0.42/0.62 (multiply(inverse(sk_c1), sk_c1) = multiply(multiply(sk_c1, sk_c7), sk_c1)),
% 0.42/0.62 inference(monotonicity,[status(thm)],[746])).
% 0.42/0.62 tff(748,plain,
% 0.42/0.62 (multiply(sk_c8, sk_c1) = multiply(sk_c7, sk_c1)),
% 0.42/0.62 inference(transitivity,[status(thm)],[309, 747, 198, 745, 743, 739, 730, 729, 501, 498, 497, 492, 490, 489, 486, 444, 447, 450, 453, 461, 159, 463])).
% 0.42/0.62 tff(749,plain,
% 0.42/0.62 (multiply(multiply(sk_c8, sk_c1), sk_c7) = multiply(multiply(sk_c7, sk_c1), sk_c7)),
% 0.42/0.62 inference(monotonicity,[status(thm)],[748])).
% 0.42/0.62 tff(750,plain,
% 0.42/0.62 (inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = inverse(sk_c8)),
% 0.42/0.62 inference(monotonicity,[status(thm)],[476])).
% 0.42/0.62 tff(751,plain,
% 0.42/0.62 (inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))),
% 0.42/0.62 inference(transitivity,[status(thm)],[750, 38, 189, 312, 749, 49, 670, 31, 29, 747, 198, 745, 743, 739, 730, 729, 501, 498, 497, 492, 490, 489, 486, 444, 447, 450, 453, 461, 159, 463, 471, 474])).
% 0.42/0.62 tff(752,plain,
% 0.42/0.62 (multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))) = multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))),
% 0.42/0.62 inference(monotonicity,[status(thm)],[751])).
% 0.42/0.62 tff(753,plain,
% 0.42/0.62 (multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))) = sk_c7),
% 0.42/0.62 inference(transitivity,[status(thm)],[752, 477, 428, 207, 313, 9])).
% 0.42/0.62 tff(754,plain,
% 0.42/0.62 (sk_c8 = multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))),
% 0.42/0.62 inference(transitivity,[status(thm)],[87, 444, 447, 450, 453, 461, 159, 463, 471, 474])).
% 0.42/0.62 tff(755,plain,
% 0.42/0.62 (multiply(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))), sk_c8) = multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))),
% 0.42/0.62 inference(monotonicity,[status(thm)],[751, 754])).
% 0.42/0.62 tff(756,plain,
% 0.42/0.62 (multiply(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))), sk_c8) = sk_c7),
% 0.42/0.62 inference(transitivity,[status(thm)],[755, 477, 428, 207, 313, 9])).
% 0.42/0.62 tff(757,plain,
% 0.42/0.62 (sk_c7 = multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))),
% 0.42/0.62 inference(transitivity,[status(thm)],[189, 312, 749, 49, 670, 31, 29, 747, 198, 745, 743, 739, 730, 729, 501, 498, 497, 492, 490, 489, 486, 444, 447, 450, 453, 461, 159, 463, 471, 474])).
% 0.42/0.62 tff(758,plain,
% 0.42/0.62 (multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))),
% 0.42/0.62 inference(monotonicity,[status(thm)],[757])).
% 0.42/0.62 tff(759,plain,
% 0.42/0.62 (multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8),
% 0.42/0.62 inference(transitivity,[status(thm)],[758, 477, 428, 207, 749, 49, 670, 31, 29, 747, 198, 745, 743, 739, 730, 729, 501, 498, 497, 492, 490, 489, 486, 61])).
% 0.42/0.62 tff(760,plain,
% 0.42/0.62 (inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8),
% 0.42/0.62 inference(transitivity,[status(thm)],[750, 38, 189, 312, 749, 49, 670, 31, 29, 747, 198, 745, 743, 739, 730, 729, 501, 498, 497, 492, 490, 489, 486, 61])).
% 0.42/0.62 tff(761,assumption,(~(multiply(sk_c2, sk_c3) = sk_c7)), introduced(assumption)).
% 0.42/0.62 tff(762,plain,
% 0.42/0.62 (((multiply(sk_c2, sk_c3) = sk_c7) | (multiply(sk_c4, sk_c7) = sk_c8)) <=> ((multiply(sk_c2, sk_c3) = sk_c7) | (multiply(sk_c4, sk_c7) = sk_c8))),
% 0.42/0.62 inference(rewrite,[status(thm)],[])).
% 0.42/0.62 tff(763,axiom,((multiply(sk_c2, sk_c3) = sk_c7) | (multiply(sk_c4, sk_c7) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_13')).
% 0.42/0.62 tff(764,plain,
% 0.42/0.62 ((multiply(sk_c2, sk_c3) = sk_c7) | (multiply(sk_c4, sk_c7) = sk_c8)),
% 0.42/0.62 inference(modus_ponens,[status(thm)],[763, 762])).
% 0.42/0.62 tff(765,plain,
% 0.42/0.62 (multiply(sk_c4, sk_c7) = sk_c8),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[764, 761])).
% 0.42/0.62 tff(766,plain,
% 0.42/0.62 (multiply(multiply(sk_c7, sk_c1), sk_c7) = multiply(multiply(sk_c8, sk_c1), sk_c7)),
% 0.42/0.62 inference(symmetry,[status(thm)],[749])).
% 0.42/0.62 tff(767,plain,
% 0.42/0.62 (multiply(multiply(sk_c1, sk_c7), sk_c1) = multiply(inverse(sk_c1), sk_c1)),
% 0.42/0.62 inference(symmetry,[status(thm)],[747])).
% 0.42/0.62 tff(768,plain,
% 0.42/0.62 (multiply(multiply(identity, sk_c1), multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = multiply(sk_c1, multiply(sk_c7, sk_c1))),
% 0.42/0.62 inference(symmetry,[status(thm)],[745])).
% 0.42/0.62 tff(769,plain,
% 0.42/0.62 (multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = multiply(multiply(identity, sk_c1), multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))),
% 0.42/0.62 inference(symmetry,[status(thm)],[743])).
% 0.42/0.62 tff(770,plain,
% 0.42/0.62 (multiply(sk_c5, multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))),
% 0.42/0.62 inference(symmetry,[status(thm)],[739])).
% 0.42/0.62 tff(771,plain,
% 0.42/0.62 (multiply(sk_c5, sk_c8) = multiply(sk_c5, multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))),
% 0.42/0.62 inference(symmetry,[status(thm)],[730])).
% 0.42/0.62 tff(772,plain,
% 0.42/0.62 (sk_c6 = multiply(sk_c5, sk_c8)),
% 0.42/0.62 inference(symmetry,[status(thm)],[729])).
% 0.42/0.62 tff(773,plain,
% 0.42/0.62 (multiply(multiply(sk_c7, sk_c6), sk_c6) = multiply(identity, sk_c6)),
% 0.42/0.62 inference(symmetry,[status(thm)],[498])).
% 0.42/0.62 tff(774,plain,
% 0.42/0.62 (multiply(multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8), sk_c6) = multiply(multiply(sk_c7, sk_c6), sk_c6)),
% 0.42/0.62 inference(symmetry,[status(thm)],[497])).
% 0.42/0.62 tff(775,plain,
% 0.42/0.62 (multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), multiply(sk_c8, sk_c6)) = multiply(multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8), sk_c6)),
% 0.42/0.62 inference(symmetry,[status(thm)],[492])).
% 0.42/0.62 tff(776,plain,
% 0.42/0.62 (multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), multiply(sk_c8, sk_c8)) = multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), multiply(sk_c8, sk_c6))),
% 0.42/0.62 inference(symmetry,[status(thm)],[490])).
% 0.42/0.62 tff(777,plain,
% 0.42/0.62 (multiply(identity, sk_c8) = multiply(multiply(multiply(sk_c7, multiply(sk_c1, sk_c3)), sk_c8), sk_c8)),
% 0.42/0.62 inference(symmetry,[status(thm)],[486])).
% 0.42/0.62 tff(778,plain,
% 0.42/0.62 (sk_c8 = sk_c7),
% 0.42/0.62 inference(transitivity,[status(thm)],[87, 777, 488, 776, 775, 774, 773, 500, 772, 771, 770, 769, 768, 199, 767, 18, 171, 671, 193, 766, 313, 9])).
% 0.42/0.62 tff(779,plain,
% 0.42/0.62 (multiply(sk_c4, sk_c8) = multiply(sk_c4, sk_c7)),
% 0.42/0.62 inference(monotonicity,[status(thm)],[778])).
% 0.42/0.62 tff(780,plain,
% 0.42/0.62 (multiply(sk_c4, sk_c8) = multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))),
% 0.42/0.62 inference(transitivity,[status(thm)],[779, 765, 87, 444, 447, 450, 453, 461, 159, 463, 471, 474])).
% 0.42/0.62 tff(781,plain,
% 0.42/0.62 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))),
% 0.42/0.62 inference(monotonicity,[status(thm)],[754, 780])).
% 0.42/0.62 tff(782,plain,
% 0.42/0.62 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7),
% 0.42/0.62 inference(transitivity,[status(thm)],[781, 477, 428, 207, 313, 9])).
% 0.42/0.62 tff(783,plain,
% 0.42/0.62 (((inverse(sk_c4) = sk_c8) | (multiply(sk_c2, sk_c3) = sk_c7)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c2, sk_c3) = sk_c7))),
% 0.42/0.62 inference(rewrite,[status(thm)],[])).
% 0.42/0.62 tff(784,plain,
% 0.42/0.62 (((multiply(sk_c2, sk_c3) = sk_c7) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c4) = sk_c8) | (multiply(sk_c2, sk_c3) = sk_c7))),
% 0.42/0.62 inference(rewrite,[status(thm)],[])).
% 0.42/0.62 tff(785,axiom,((multiply(sk_c2, sk_c3) = sk_c7) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_12')).
% 0.42/0.62 tff(786,plain,
% 0.42/0.62 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c2, sk_c3) = sk_c7)),
% 0.42/0.62 inference(modus_ponens,[status(thm)],[785, 784])).
% 0.42/0.62 tff(787,plain,
% 0.42/0.62 ((inverse(sk_c4) = sk_c8) | (multiply(sk_c2, sk_c3) = sk_c7)),
% 0.42/0.62 inference(modus_ponens,[status(thm)],[786, 783])).
% 0.42/0.62 tff(788,plain,
% 0.42/0.62 (inverse(sk_c4) = sk_c8),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[787, 761])).
% 0.42/0.62 tff(789,plain,
% 0.42/0.62 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8)) | (~(multiply(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))), sk_c8) = sk_c7)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))) = sk_c7)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8)) | (~(multiply(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))), sk_c8) = sk_c7)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))) = sk_c7)))),
% 0.42/0.63 inference(rewrite,[status(thm)],[])).
% 0.42/0.63 tff(790,plain,
% 0.42/0.63 (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8)) | (~(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8)) | (~(multiply(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))), sk_c8) = sk_c7)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8)) | (~(multiply(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))), sk_c8) = sk_c7)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))) = sk_c7)))),
% 0.42/0.63 inference(rewrite,[status(thm)],[])).
% 0.42/0.63 tff(791,plain,
% 0.42/0.63 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8)) | (~(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8)) | (~(multiply(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))), sk_c8) = sk_c7)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8)) | (~(multiply(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))), sk_c8) = sk_c7)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))) = sk_c7))))),
% 0.42/0.63 inference(monotonicity,[status(thm)],[790])).
% 0.42/0.63 tff(792,plain,
% 0.42/0.63 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8)) | (~(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8)) | (~(multiply(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))), sk_c8) = sk_c7)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8)) | (~(multiply(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))), sk_c8) = sk_c7)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))) = sk_c7)))),
% 0.42/0.63 inference(transitivity,[status(thm)],[791, 789])).
% 0.42/0.63 tff(793,plain,
% 0.42/0.63 ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8)) | (~(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8)) | (~(multiply(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))), sk_c8) = sk_c7)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8)))),
% 0.42/0.63 inference(quant_inst,[status(thm)],[])).
% 0.42/0.63 tff(794,plain,
% 0.42/0.63 ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(sk_c4) = sk_c8)) | (~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8)) | (~(multiply(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))), sk_c8) = sk_c7)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))) = sk_c7))),
% 0.42/0.63 inference(modus_ponens,[status(thm)],[793, 792])).
% 0.42/0.63 tff(795,plain,
% 0.42/0.63 ((~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8)) | (~(multiply(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))), sk_c8) = sk_c7)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))) = sk_c7))),
% 0.42/0.63 inference(unit_resolution,[status(thm)],[794, 38, 788, 143])).
% 0.48/0.63 tff(796,plain,
% 0.48/0.63 ($false),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[795, 782, 760, 759, 756, 753])).
% 0.48/0.63 tff(797,plain,(multiply(sk_c2, sk_c3) = sk_c7), inference(lemma,lemma(discharge,[]))).
% 0.48/0.63 tff(798,plain,
% 0.48/0.63 (multiply(sk_c7, sk_c1) = identity),
% 0.48/0.63 inference(transitivity,[status(thm)],[464, 158, 462, 454, 451, 448, 445, 777, 488, 776, 775, 774, 773, 500, 772, 771, 770, 769, 768, 199, 767, 18])).
% 0.48/0.63 tff(799,plain,
% 0.48/0.63 (multiply(multiply(sk_c7, sk_c1), sk_c3) = multiply(identity, sk_c3)),
% 0.48/0.63 inference(monotonicity,[status(thm)],[798])).
% 0.48/0.63 tff(800,plain,
% 0.48/0.63 (multiply(sk_c8, multiply(sk_c6, sk_c1)) = multiply(sk_c7, sk_c1)),
% 0.48/0.63 inference(transitivity,[status(thm)],[553, 550])).
% 0.48/0.63 tff(801,plain,
% 0.48/0.63 (multiply(multiply(sk_c8, multiply(sk_c6, sk_c1)), sk_c3) = multiply(multiply(sk_c7, sk_c1), sk_c3)),
% 0.48/0.63 inference(monotonicity,[status(thm)],[800])).
% 0.48/0.63 tff(802,plain,
% 0.48/0.63 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, multiply(sk_c6, sk_c1)), sk_c3) = multiply(sk_c8, multiply(multiply(sk_c6, sk_c1), sk_c3)))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(803,plain,
% 0.48/0.63 (multiply(multiply(sk_c8, multiply(sk_c6, sk_c1)), sk_c3) = multiply(sk_c8, multiply(multiply(sk_c6, sk_c1), sk_c3))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[802, 47])).
% 0.48/0.63 tff(804,plain,
% 0.48/0.63 (multiply(sk_c8, multiply(multiply(sk_c6, sk_c1), sk_c3)) = multiply(multiply(sk_c8, multiply(sk_c6, sk_c1)), sk_c3)),
% 0.48/0.63 inference(symmetry,[status(thm)],[803])).
% 0.48/0.63 tff(805,plain,
% 0.48/0.63 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c6, sk_c1), sk_c3) = multiply(sk_c6, multiply(sk_c1, sk_c3)))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(806,plain,
% 0.48/0.63 (multiply(multiply(sk_c6, sk_c1), sk_c3) = multiply(sk_c6, multiply(sk_c1, sk_c3))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[805, 47])).
% 0.48/0.63 tff(807,plain,
% 0.48/0.63 (multiply(sk_c6, multiply(sk_c1, sk_c3)) = multiply(multiply(sk_c6, sk_c1), sk_c3)),
% 0.48/0.63 inference(symmetry,[status(thm)],[806])).
% 0.48/0.63 tff(808,plain,
% 0.48/0.63 (multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), multiply(sk_c6, multiply(sk_c1, sk_c3))) = multiply(sk_c8, multiply(multiply(sk_c6, sk_c1), sk_c3))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[476, 807])).
% 0.48/0.63 tff(809,plain,
% 0.48/0.63 (multiply(sk_c8, multiply(sk_c6, multiply(sk_c1, sk_c3))) = multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), multiply(sk_c6, multiply(sk_c1, sk_c3)))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[754])).
% 0.48/0.63 tff(810,plain,
% 0.48/0.63 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, sk_c6), multiply(sk_c1, sk_c3)) = multiply(sk_c8, multiply(sk_c6, multiply(sk_c1, sk_c3))))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(811,plain,
% 0.48/0.63 (multiply(multiply(sk_c8, sk_c6), multiply(sk_c1, sk_c3)) = multiply(sk_c8, multiply(sk_c6, multiply(sk_c1, sk_c3)))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[810, 47])).
% 0.48/0.63 tff(812,plain,
% 0.48/0.63 (multiply(sk_c7, multiply(sk_c1, sk_c3)) = multiply(multiply(sk_c8, sk_c6), multiply(sk_c1, sk_c3))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[261])).
% 0.48/0.63 tff(813,plain,
% 0.48/0.63 (multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3)) = multiply(sk_c7, multiply(sk_c1, sk_c3))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[532])).
% 0.48/0.63 tff(814,plain,
% 0.48/0.63 (multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3)) = sk_c3),
% 0.48/0.63 inference(transitivity,[status(thm)],[813, 812, 811, 809, 808, 804, 801, 799, 606])).
% 0.48/0.63 tff(815,plain,
% 0.48/0.63 (multiply(sk_c2, multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3))) = multiply(sk_c2, sk_c3)),
% 0.48/0.63 inference(monotonicity,[status(thm)],[814])).
% 0.48/0.63 tff(816,plain,
% 0.48/0.63 (multiply(sk_c2, multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3))) = multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))),
% 0.48/0.63 inference(transitivity,[status(thm)],[815, 797, 189, 312, 749, 49, 670, 31, 29, 747, 198, 745, 743, 739, 730, 729, 501, 498, 497, 492, 490, 489, 486, 444, 447, 450, 453, 461, 159, 463, 471, 474])).
% 0.48/0.63 tff(817,plain,
% 0.48/0.63 (multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), multiply(sk_c2, multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3)))) = multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[816])).
% 0.48/0.63 tff(818,plain,
% 0.48/0.63 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2), multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3))) = multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), multiply(sk_c2, multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3)))))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(819,plain,
% 0.48/0.63 (multiply(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2), multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3))) = multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), multiply(sk_c2, multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3))))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[818, 47])).
% 0.48/0.63 tff(820,plain,
% 0.48/0.63 (multiply(sk_c7, multiply(sk_c1, sk_c3)) = multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3))),
% 0.48/0.63 inference(symmetry,[status(thm)],[813])).
% 0.48/0.63 tff(821,plain,
% 0.48/0.63 (multiply(multiply(sk_c8, sk_c6), multiply(sk_c1, sk_c3)) = multiply(sk_c7, multiply(sk_c1, sk_c3))),
% 0.48/0.63 inference(symmetry,[status(thm)],[812])).
% 0.48/0.63 tff(822,plain,
% 0.48/0.63 (multiply(sk_c8, multiply(sk_c6, multiply(sk_c1, sk_c3))) = multiply(multiply(sk_c8, sk_c6), multiply(sk_c1, sk_c3))),
% 0.48/0.63 inference(symmetry,[status(thm)],[811])).
% 0.48/0.63 tff(823,plain,
% 0.48/0.63 (multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), multiply(sk_c6, multiply(sk_c1, sk_c3))) = multiply(sk_c8, multiply(sk_c6, multiply(sk_c1, sk_c3)))),
% 0.48/0.63 inference(symmetry,[status(thm)],[809])).
% 0.48/0.63 tff(824,plain,
% 0.48/0.63 (multiply(sk_c8, multiply(multiply(sk_c6, sk_c1), sk_c3)) = multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), multiply(sk_c6, multiply(sk_c1, sk_c3)))),
% 0.48/0.63 inference(symmetry,[status(thm)],[808])).
% 0.48/0.63 tff(825,plain,
% 0.48/0.63 (multiply(multiply(sk_c7, sk_c1), sk_c3) = multiply(multiply(sk_c8, multiply(sk_c6, sk_c1)), sk_c3)),
% 0.48/0.63 inference(symmetry,[status(thm)],[801])).
% 0.48/0.63 tff(826,plain,
% 0.48/0.63 (multiply(identity, sk_c3) = multiply(multiply(sk_c7, sk_c1), sk_c3)),
% 0.48/0.63 inference(symmetry,[status(thm)],[799])).
% 0.48/0.63 tff(827,plain,
% 0.48/0.63 (multiply(identity, sk_c3) = multiply(multiply(sk_c8, multiply(sk_c6, multiply(sk_c1, sk_c7))), sk_c3)),
% 0.48/0.63 inference(monotonicity,[status(thm)],[698])).
% 0.48/0.63 tff(828,plain,
% 0.48/0.63 (multiply(multiply(sk_c8, multiply(sk_c6, multiply(sk_c1, sk_c7))), sk_c3) = multiply(identity, sk_c3)),
% 0.48/0.63 inference(symmetry,[status(thm)],[827])).
% 0.48/0.63 tff(829,plain,
% 0.48/0.63 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c8, multiply(sk_c6, multiply(sk_c1, sk_c7))), sk_c3) = multiply(sk_c8, multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3)))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(830,plain,
% 0.48/0.63 (multiply(multiply(sk_c8, multiply(sk_c6, multiply(sk_c1, sk_c7))), sk_c3) = multiply(sk_c8, multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[829, 47])).
% 0.48/0.63 tff(831,plain,
% 0.48/0.63 (multiply(sk_c8, multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3)) = multiply(multiply(sk_c8, multiply(sk_c6, multiply(sk_c1, sk_c7))), sk_c3)),
% 0.48/0.63 inference(symmetry,[status(thm)],[830])).
% 0.48/0.63 tff(832,plain,
% 0.48/0.63 (multiply(multiply(identity, sk_c1), sk_c3) = multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3)),
% 0.48/0.63 inference(monotonicity,[status(thm)],[742])).
% 0.48/0.63 tff(833,plain,
% 0.48/0.63 (multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3) = multiply(multiply(identity, sk_c1), sk_c3)),
% 0.48/0.63 inference(symmetry,[status(thm)],[832])).
% 0.48/0.63 tff(834,plain,
% 0.48/0.63 (multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3) = multiply(sk_c1, sk_c3)),
% 0.48/0.63 inference(transitivity,[status(thm)],[833, 630])).
% 0.48/0.63 tff(835,plain,
% 0.48/0.63 (sk_c8 = identity),
% 0.48/0.63 inference(transitivity,[status(thm)],[87, 777, 488, 776, 775, 774, 773, 500, 772, 771, 770, 769, 768, 199, 767, 18])).
% 0.48/0.63 tff(836,plain,
% 0.48/0.63 (multiply(sk_c8, multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3)) = multiply(identity, multiply(sk_c1, sk_c3))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[835, 834])).
% 0.48/0.63 tff(837,plain,
% 0.48/0.63 (multiply(identity, multiply(sk_c1, sk_c3)) = multiply(sk_c8, multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3))),
% 0.48/0.63 inference(symmetry,[status(thm)],[836])).
% 0.48/0.63 tff(838,plain,
% 0.48/0.63 (multiply(sk_c1, sk_c3) = multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3)),
% 0.48/0.63 inference(transitivity,[status(thm)],[629, 832])).
% 0.48/0.63 tff(839,plain,
% 0.48/0.63 (identity = multiply(sk_c3, multiply(sk_c8, sk_c8))),
% 0.48/0.63 inference(transitivity,[status(thm)],[171, 442, 439])).
% 0.48/0.63 tff(840,plain,
% 0.48/0.63 (multiply(identity, multiply(sk_c1, sk_c3)) = multiply(multiply(sk_c3, multiply(sk_c8, sk_c8)), multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[839, 838])).
% 0.48/0.63 tff(841,plain,
% 0.48/0.63 (multiply(multiply(sk_c3, multiply(sk_c8, sk_c8)), multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3)) = multiply(identity, multiply(sk_c1, sk_c3))),
% 0.48/0.63 inference(symmetry,[status(thm)],[840])).
% 0.48/0.63 tff(842,plain,
% 0.48/0.63 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c3, multiply(sk_c8, sk_c8)), multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3)) = multiply(sk_c3, multiply(multiply(sk_c8, sk_c8), multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3))))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(843,plain,
% 0.48/0.63 (multiply(multiply(sk_c3, multiply(sk_c8, sk_c8)), multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3)) = multiply(sk_c3, multiply(multiply(sk_c8, sk_c8), multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3)))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[842, 47])).
% 0.48/0.63 tff(844,plain,
% 0.48/0.63 (multiply(sk_c3, multiply(multiply(sk_c8, sk_c8), multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3))) = multiply(multiply(sk_c3, multiply(sk_c8, sk_c8)), multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3))),
% 0.48/0.63 inference(symmetry,[status(thm)],[843])).
% 0.48/0.63 tff(845,plain,
% 0.48/0.63 (multiply(multiply(sk_c8, sk_c8), multiply(sk_c6, multiply(sk_c1, sk_c7))) = multiply(sk_c7, sk_c1)),
% 0.48/0.63 inference(transitivity,[status(thm)],[654, 450, 453, 461, 159, 463])).
% 0.48/0.63 tff(846,plain,
% 0.48/0.63 (multiply(multiply(multiply(sk_c8, sk_c8), multiply(sk_c6, multiply(sk_c1, sk_c7))), sk_c3) = multiply(multiply(sk_c7, sk_c1), sk_c3)),
% 0.48/0.63 inference(monotonicity,[status(thm)],[845])).
% 0.48/0.63 tff(847,plain,
% 0.48/0.63 (multiply(multiply(sk_c8, sk_c8), multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3)) = multiply(multiply(multiply(sk_c8, sk_c8), multiply(sk_c6, multiply(sk_c1, sk_c7))), sk_c3)),
% 0.48/0.63 inference(symmetry,[status(thm)],[653])).
% 0.48/0.63 tff(848,plain,
% 0.48/0.63 (multiply(multiply(sk_c8, sk_c8), multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3)) = multiply(sk_c7, multiply(sk_c1, sk_c3))),
% 0.48/0.63 inference(transitivity,[status(thm)],[847, 846, 825, 803, 824, 823, 822, 821])).
% 0.48/0.63 tff(849,plain,
% 0.48/0.63 (multiply(sk_c3, multiply(multiply(sk_c8, sk_c8), multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3))) = multiply(sk_c3, multiply(sk_c7, multiply(sk_c1, sk_c3)))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[848])).
% 0.48/0.63 tff(850,plain,
% 0.48/0.63 (multiply(sk_c3, multiply(sk_c7, multiply(sk_c1, sk_c3))) = multiply(sk_c3, multiply(multiply(sk_c8, sk_c8), multiply(multiply(sk_c6, multiply(sk_c1, sk_c7)), sk_c3)))),
% 0.48/0.63 inference(symmetry,[status(thm)],[849])).
% 0.48/0.63 tff(851,plain,
% 0.48/0.63 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(identity, multiply(sk_c8, sk_c8)), multiply(sk_c1, sk_c3)) = multiply(identity, multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3))))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(852,plain,
% 0.48/0.63 (multiply(multiply(identity, multiply(sk_c8, sk_c8)), multiply(sk_c1, sk_c3)) = multiply(identity, multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3)))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[851, 47])).
% 0.48/0.63 tff(853,plain,
% 0.48/0.63 (multiply(identity, multiply(sk_c8, sk_c8)) = sk_c7),
% 0.48/0.63 inference(transitivity,[status(thm)],[566, 313, 9])).
% 0.48/0.63 tff(854,plain,
% 0.48/0.63 (multiply(multiply(identity, multiply(sk_c8, sk_c8)), multiply(sk_c1, sk_c3)) = multiply(sk_c7, multiply(sk_c1, sk_c3))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[853])).
% 0.48/0.63 tff(855,plain,
% 0.48/0.63 (multiply(sk_c7, multiply(sk_c1, sk_c3)) = multiply(multiply(identity, multiply(sk_c8, sk_c8)), multiply(sk_c1, sk_c3))),
% 0.48/0.63 inference(symmetry,[status(thm)],[854])).
% 0.48/0.63 tff(856,plain,
% 0.48/0.63 (multiply(sk_c7, multiply(sk_c1, sk_c3)) = multiply(identity, multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3)))),
% 0.48/0.63 inference(transitivity,[status(thm)],[855, 852])).
% 0.48/0.63 tff(857,plain,
% 0.48/0.63 (multiply(sk_c3, multiply(sk_c7, multiply(sk_c1, sk_c3))) = multiply(sk_c3, multiply(identity, multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3))))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[856])).
% 0.48/0.63 tff(858,plain,
% 0.48/0.63 (multiply(sk_c3, multiply(identity, multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3)))) = multiply(sk_c3, multiply(sk_c7, multiply(sk_c1, sk_c3)))),
% 0.48/0.64 inference(symmetry,[status(thm)],[857])).
% 0.48/0.64 tff(859,plain,
% 0.48/0.64 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c3, identity), multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3))) = multiply(sk_c3, multiply(identity, multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3)))))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(860,plain,
% 0.48/0.64 (multiply(multiply(sk_c3, identity), multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3))) = multiply(sk_c3, multiply(identity, multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3))))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[859, 47])).
% 0.48/0.64 tff(861,plain,
% 0.48/0.64 (multiply(sk_c1, sk_c1) = multiply(multiply(identity, sk_c1), multiply(identity, sk_c1))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[529, 529])).
% 0.48/0.64 tff(862,plain,
% 0.48/0.64 (multiply(multiply(identity, sk_c1), multiply(identity, sk_c1)) = multiply(sk_c1, sk_c1)),
% 0.48/0.64 inference(symmetry,[status(thm)],[861])).
% 0.48/0.64 tff(863,plain,
% 0.48/0.64 (multiply(sk_c7, sk_c6) = identity),
% 0.48/0.64 inference(transitivity,[status(thm)],[429, 432, 436, 495, 441, 31])).
% 0.48/0.64 tff(864,plain,
% 0.48/0.64 (multiply(multiply(sk_c7, sk_c6), sk_c1) = multiply(identity, sk_c1)),
% 0.48/0.64 inference(monotonicity,[status(thm)],[863])).
% 0.48/0.64 tff(865,plain,
% 0.48/0.64 (multiply(identity, sk_c1) = multiply(multiply(sk_c7, sk_c6), sk_c1)),
% 0.48/0.64 inference(symmetry,[status(thm)],[864])).
% 0.48/0.64 tff(866,plain,
% 0.48/0.64 (multiply(multiply(identity, sk_c1), multiply(identity, sk_c1)) = multiply(sk_c1, multiply(multiply(sk_c7, sk_c6), sk_c1))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[528, 865])).
% 0.48/0.64 tff(867,plain,
% 0.48/0.64 (multiply(sk_c1, multiply(multiply(sk_c7, sk_c6), sk_c1)) = multiply(multiply(identity, sk_c1), multiply(identity, sk_c1))),
% 0.48/0.64 inference(symmetry,[status(thm)],[866])).
% 0.48/0.64 tff(868,plain,
% 0.48/0.64 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, multiply(sk_c7, sk_c6)), sk_c1) = multiply(sk_c1, multiply(multiply(sk_c7, sk_c6), sk_c1)))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(869,plain,
% 0.48/0.64 (multiply(multiply(sk_c1, multiply(sk_c7, sk_c6)), sk_c1) = multiply(sk_c1, multiply(multiply(sk_c7, sk_c6), sk_c1))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[868, 47])).
% 0.48/0.64 tff(870,plain,
% 0.48/0.64 (multiply(multiply(sk_c1, sk_c7), sk_c6) = multiply(sk_c8, sk_c6)),
% 0.48/0.64 inference(monotonicity,[status(thm)],[426])).
% 0.48/0.64 tff(871,plain,
% 0.48/0.64 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c1, sk_c7), sk_c6) = multiply(sk_c1, multiply(sk_c7, sk_c6)))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(872,plain,
% 0.48/0.64 (multiply(multiply(sk_c1, sk_c7), sk_c6) = multiply(sk_c1, multiply(sk_c7, sk_c6))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[871, 47])).
% 0.48/0.64 tff(873,plain,
% 0.48/0.64 (multiply(sk_c1, multiply(sk_c7, sk_c6)) = multiply(multiply(sk_c1, sk_c7), sk_c6)),
% 0.48/0.64 inference(symmetry,[status(thm)],[872])).
% 0.48/0.64 tff(874,plain,
% 0.48/0.64 (multiply(sk_c1, multiply(sk_c7, sk_c6)) = sk_c7),
% 0.48/0.64 inference(transitivity,[status(thm)],[873, 870, 234])).
% 0.48/0.64 tff(875,plain,
% 0.48/0.64 (multiply(multiply(sk_c1, multiply(sk_c7, sk_c6)), sk_c1) = multiply(sk_c7, sk_c1)),
% 0.48/0.64 inference(monotonicity,[status(thm)],[874])).
% 0.48/0.64 tff(876,plain,
% 0.48/0.64 (multiply(sk_c7, sk_c1) = multiply(multiply(sk_c1, multiply(sk_c7, sk_c6)), sk_c1)),
% 0.48/0.64 inference(symmetry,[status(thm)],[875])).
% 0.48/0.64 tff(877,plain,
% 0.48/0.64 (multiply(sk_c3, identity) = multiply(sk_c1, sk_c1)),
% 0.48/0.64 inference(transitivity,[status(thm)],[559, 159, 463, 876, 869, 867, 862])).
% 0.48/0.64 tff(878,plain,
% 0.48/0.64 (multiply(multiply(sk_c3, identity), multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3))) = multiply(multiply(sk_c1, sk_c1), multiply(sk_c7, multiply(sk_c1, sk_c3)))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[877, 813])).
% 0.48/0.64 tff(879,plain,
% 0.48/0.64 (multiply(multiply(sk_c1, sk_c1), multiply(sk_c7, multiply(sk_c1, sk_c3))) = multiply(multiply(sk_c3, identity), multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3)))),
% 0.48/0.64 inference(symmetry,[status(thm)],[878])).
% 0.48/0.64 tff(880,plain,
% 0.48/0.64 (multiply(sk_c2, sk_c3) = multiply(sk_c2, multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3)))),
% 0.48/0.64 inference(symmetry,[status(thm)],[815])).
% 0.48/0.64 tff(881,plain,
% 0.48/0.64 (sk_c7 = multiply(sk_c2, sk_c3)),
% 0.48/0.64 inference(symmetry,[status(thm)],[797])).
% 0.48/0.64 tff(882,plain,
% 0.48/0.64 (multiply(sk_c1, multiply(multiply(sk_c7, sk_c6), sk_c1)) = multiply(multiply(sk_c1, multiply(sk_c7, sk_c6)), sk_c1)),
% 0.48/0.64 inference(symmetry,[status(thm)],[869])).
% 0.48/0.64 tff(883,plain,
% 0.48/0.64 (multiply(sk_c1, sk_c1) = multiply(sk_c2, multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3)))),
% 0.48/0.64 inference(transitivity,[status(thm)],[861, 866, 882, 875, 464, 158, 462, 454, 451, 448, 445, 777, 488, 776, 775, 774, 773, 500, 772, 771, 770, 769, 768, 199, 767, 18, 171, 671, 193, 766, 313, 9, 881, 880])).
% 0.48/0.64 tff(884,plain,
% 0.48/0.64 (multiply(multiply(sk_c1, sk_c1), multiply(sk_c7, multiply(sk_c1, sk_c3))) = multiply(multiply(sk_c2, multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3))), multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3)))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[883, 820])).
% 0.48/0.64 tff(885,plain,
% 0.48/0.64 (multiply(multiply(sk_c2, multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3))), multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3))) = multiply(multiply(sk_c1, sk_c1), multiply(sk_c7, multiply(sk_c1, sk_c3)))),
% 0.48/0.64 inference(symmetry,[status(thm)],[884])).
% 0.48/0.64 tff(886,plain,
% 0.48/0.64 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(sk_c2, multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3))), multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3))) = multiply(sk_c2, multiply(multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3)), multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3)))))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(887,plain,
% 0.48/0.64 (multiply(multiply(sk_c2, multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3))), multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3))) = multiply(sk_c2, multiply(multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3)), multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3))))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[886, 47])).
% 0.48/0.64 tff(888,plain,
% 0.48/0.64 (multiply(sk_c2, multiply(multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3)), multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3)))) = multiply(multiply(sk_c2, multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3))), multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3)))),
% 0.48/0.64 inference(symmetry,[status(thm)],[887])).
% 0.48/0.64 tff(889,plain,
% 0.48/0.64 (multiply(multiply(multiply(sk_c7, sk_c1), sk_c3), sk_c8) = identity),
% 0.48/0.64 inference(transitivity,[status(thm)],[666, 668, 49, 670, 31])).
% 0.48/0.64 tff(890,plain,
% 0.48/0.64 (multiply(multiply(multiply(multiply(sk_c7, sk_c1), sk_c3), sk_c8), sk_c3) = multiply(identity, sk_c3)),
% 0.48/0.64 inference(monotonicity,[status(thm)],[889])).
% 0.48/0.64 tff(891,plain,
% 0.48/0.64 (multiply(multiply(multiply(sk_c7, sk_c1), sk_c3), multiply(sk_c8, sk_c3)) = multiply(multiply(multiply(multiply(sk_c7, sk_c1), sk_c3), sk_c8), sk_c3)),
% 0.48/0.64 inference(symmetry,[status(thm)],[664])).
% 0.48/0.64 tff(892,plain,
% 0.48/0.64 (sk_c8 = multiply(sk_c7, sk_c1)),
% 0.48/0.64 inference(transitivity,[status(thm)],[87, 444, 447, 450, 453, 461, 159, 463])).
% 0.48/0.64 tff(893,plain,
% 0.48/0.64 (multiply(sk_c8, sk_c3) = multiply(multiply(sk_c7, sk_c1), sk_c3)),
% 0.48/0.64 inference(monotonicity,[status(thm)],[892])).
% 0.48/0.64 tff(894,plain,
% 0.48/0.64 (multiply(multiply(sk_c7, sk_c1), sk_c3) = multiply(sk_c8, sk_c3)),
% 0.48/0.64 inference(symmetry,[status(thm)],[893])).
% 0.48/0.64 tff(895,plain,
% 0.48/0.64 (multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3)) = multiply(sk_c8, sk_c3)),
% 0.48/0.64 inference(transitivity,[status(thm)],[813, 812, 811, 809, 808, 804, 801, 894])).
% 0.48/0.64 tff(896,plain,
% 0.48/0.64 (multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3)) = multiply(multiply(sk_c7, sk_c1), sk_c3)),
% 0.48/0.64 inference(transitivity,[status(thm)],[813, 812, 811, 809, 808, 804, 801])).
% 0.48/0.64 tff(897,plain,
% 0.48/0.64 (multiply(multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3)), multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3))) = multiply(multiply(multiply(sk_c7, sk_c1), sk_c3), multiply(sk_c8, sk_c3))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[896, 895])).
% 0.48/0.64 tff(898,plain,
% 0.48/0.64 (multiply(multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3)), multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3))) = sk_c3),
% 0.48/0.64 inference(transitivity,[status(thm)],[897, 891, 890, 606])).
% 0.48/0.64 tff(899,plain,
% 0.48/0.64 (multiply(sk_c2, multiply(multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3)), multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3)))) = multiply(sk_c2, sk_c3)),
% 0.48/0.64 inference(monotonicity,[status(thm)],[898])).
% 0.48/0.64 tff(900,plain,
% 0.48/0.64 (multiply(sk_c2, sk_c3) = multiply(sk_c2, multiply(multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3)), multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3))))),
% 0.48/0.64 inference(symmetry,[status(thm)],[899])).
% 0.48/0.64 tff(901,plain,
% 0.48/0.64 (sk_c8 = multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3))),
% 0.48/0.64 inference(transitivity,[status(thm)],[87, 777, 488, 776, 775, 774, 773, 500, 772, 771, 770, 769, 768, 199, 767, 18, 171, 671, 193, 766, 313, 9, 881, 900, 888, 885, 879, 860, 858, 850, 844, 841, 837, 831, 828, 826, 825, 803, 824, 823, 822, 821, 820])).
% 0.48/0.64 tff(902,plain,
% 0.48/0.64 (multiply(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2), sk_c8) = multiply(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2), multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3)))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[901])).
% 0.48/0.64 tff(903,plain,
% 0.48/0.64 (multiply(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2), sk_c8) = multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))),
% 0.48/0.64 inference(transitivity,[status(thm)],[902, 819, 817, 477, 428, 207, 749, 49, 670, 31, 29, 747, 198, 745, 743, 739, 730, 729, 501, 498, 497, 492, 490, 489, 486, 444, 447, 450, 453, 461, 159, 463, 471, 474])).
% 0.48/0.64 tff(904,plain,
% 0.48/0.64 (multiply(sk_c8, multiply(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2), sk_c8)) = multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[754, 903])).
% 0.48/0.64 tff(905,plain,
% 0.48/0.64 (multiply(sk_c8, multiply(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2), sk_c8)) = sk_c7),
% 0.48/0.64 inference(transitivity,[status(thm)],[904, 477, 428, 207, 313, 9])).
% 0.48/0.64 tff(906,plain,
% 0.48/0.64 (multiply(sk_c3, multiply(identity, multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3)))) = multiply(multiply(sk_c3, identity), multiply(multiply(sk_c8, sk_c8), multiply(sk_c1, sk_c3)))),
% 0.48/0.64 inference(symmetry,[status(thm)],[860])).
% 0.48/0.64 tff(907,assumption,(inverse(sk_c2) = sk_c3), introduced(assumption)).
% 0.48/0.64 tff(908,plain,
% 0.48/0.64 ((~![X: $i] : (multiply(identity, X) = X)) | (multiply(identity, sk_c2) = sk_c2)),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(909,plain,
% 0.48/0.64 (multiply(identity, sk_c2) = sk_c2),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[908, 7])).
% 0.48/0.64 tff(910,plain,
% 0.48/0.64 (identity = multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))),
% 0.48/0.64 inference(transitivity,[status(thm)],[29, 747, 198, 745, 743, 739, 730, 729, 501, 498, 497, 492, 490, 489, 486, 444, 447, 450, 453, 461, 159, 463, 471, 474])).
% 0.48/0.64 tff(911,plain,
% 0.48/0.64 (multiply(identity, sk_c2) = multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2)),
% 0.48/0.64 inference(monotonicity,[status(thm)],[910])).
% 0.48/0.64 tff(912,plain,
% 0.48/0.64 (multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2) = multiply(identity, sk_c2)),
% 0.48/0.64 inference(symmetry,[status(thm)],[911])).
% 0.48/0.64 tff(913,plain,
% 0.48/0.64 (multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2) = sk_c2),
% 0.48/0.64 inference(transitivity,[status(thm)],[912, 909])).
% 0.48/0.64 tff(914,plain,
% 0.48/0.64 (inverse(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2)) = inverse(sk_c2)),
% 0.48/0.64 inference(monotonicity,[status(thm)],[913])).
% 0.48/0.64 tff(915,plain,
% 0.48/0.64 (inverse(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2)) = sk_c8),
% 0.48/0.64 inference(transitivity,[status(thm)],[914, 907, 622, 827, 830, 836, 840, 843, 849, 857, 906, 878, 884, 887, 899, 797, 189, 312, 749, 49, 670, 31, 29, 747, 198, 745, 743, 739, 730, 729, 501, 498, 497, 492, 490, 489, 486, 61])).
% 0.48/0.64 tff(916,plain,
% 0.48/0.64 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8)) | (~(multiply(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))), sk_c8) = sk_c7)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))) = sk_c7)) | (~(inverse(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2)) = sk_c8)) | (~(multiply(sk_c8, multiply(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2), sk_c8)) = sk_c7)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8)) | (~(multiply(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))), sk_c8) = sk_c7)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))) = sk_c7)) | (~(inverse(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2)) = sk_c8)) | (~(multiply(sk_c8, multiply(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2), sk_c8)) = sk_c7)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(917,plain,
% 0.48/0.64 (((~(inverse(sk_c8) = sk_c7)) | (~(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8)) | (~(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8)) | (~(multiply(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))), sk_c8) = sk_c7)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))) = sk_c7)) | (~(inverse(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2)) = sk_c8)) | (~(multiply(sk_c8, multiply(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2), sk_c8)) = sk_c7)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8))) <=> ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8)) | (~(multiply(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))), sk_c8) = sk_c7)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))) = sk_c7)) | (~(inverse(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2)) = sk_c8)) | (~(multiply(sk_c8, multiply(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2), sk_c8)) = sk_c7)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(918,plain,
% 0.48/0.64 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8)) | (~(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8)) | (~(multiply(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))), sk_c8) = sk_c7)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))) = sk_c7)) | (~(inverse(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2)) = sk_c8)) | (~(multiply(sk_c8, multiply(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2), sk_c8)) = sk_c7)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8)) | (~(multiply(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))), sk_c8) = sk_c7)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))) = sk_c7)) | (~(inverse(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2)) = sk_c8)) | (~(multiply(sk_c8, multiply(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2), sk_c8)) = sk_c7))))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[917])).
% 0.48/0.64 tff(919,plain,
% 0.48/0.64 (((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8)) | (~(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8)) | (~(multiply(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))), sk_c8) = sk_c7)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))) = sk_c7)) | (~(inverse(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2)) = sk_c8)) | (~(multiply(sk_c8, multiply(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2), sk_c8)) = sk_c7)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8)))) <=> ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8)) | (~(multiply(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))), sk_c8) = sk_c7)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))) = sk_c7)) | (~(inverse(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2)) = sk_c8)) | (~(multiply(sk_c8, multiply(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2), sk_c8)) = sk_c7)))),
% 0.48/0.65 inference(transitivity,[status(thm)],[918, 916])).
% 0.48/0.65 tff(920,plain,
% 0.48/0.65 ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8)) | (~(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8)) | (~(multiply(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))), sk_c8) = sk_c7)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))) = sk_c7)) | (~(inverse(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2)) = sk_c8)) | (~(multiply(sk_c8, multiply(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2), sk_c8)) = sk_c7)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8)))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(921,plain,
% 0.48/0.65 ((~![X4: $i, X3: $i, X5: $i, X1: $i] : ((~(inverse(sk_c8) = sk_c7)) | (~(inverse(X4) = sk_c8)) | (~(multiply(X1, sk_c7) = sk_c8)) | (~(inverse(X1) = sk_c8)) | (~(multiply(inverse(X5), sk_c8) = sk_c7)) | (~(multiply(X5, inverse(X5)) = sk_c7)) | (~(inverse(X3) = sk_c8)) | (~(multiply(sk_c8, multiply(X3, sk_c8)) = sk_c7)) | (~(multiply(X4, sk_c7) = sk_c8)))) | (~(inverse(sk_c8) = sk_c7)) | (~(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8)) | (~(multiply(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))), sk_c8) = sk_c7)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))) = sk_c7)) | (~(inverse(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2)) = sk_c8)) | (~(multiply(sk_c8, multiply(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2), sk_c8)) = sk_c7))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[920, 919])).
% 0.48/0.65 tff(922,plain,
% 0.48/0.65 ((~(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8)) | (~(multiply(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))), sk_c8) = sk_c7)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))) = sk_c7)) | (~(inverse(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2)) = sk_c8)) | (~(multiply(sk_c8, multiply(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c2), sk_c8)) = sk_c7))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[921, 38, 143])).
% 0.48/0.65 tff(923,plain,
% 0.48/0.65 ($false),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[922, 759, 760, 756, 753, 915, 905])).
% 0.48/0.65 tff(924,plain,(~(inverse(sk_c2) = sk_c3)), inference(lemma,lemma(discharge,[]))).
% 0.48/0.65 tff(925,plain,
% 0.48/0.65 (((inverse(sk_c2) = sk_c3) | (multiply(sk_c4, sk_c7) = sk_c8)) <=> ((inverse(sk_c2) = sk_c3) | (multiply(sk_c4, sk_c7) = sk_c8))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(926,axiom,((inverse(sk_c2) = sk_c3) | (multiply(sk_c4, sk_c7) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_18')).
% 0.48/0.65 tff(927,plain,
% 0.48/0.65 ((inverse(sk_c2) = sk_c3) | (multiply(sk_c4, sk_c7) = sk_c8)),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[926, 925])).
% 0.48/0.65 tff(928,plain,
% 0.48/0.65 (multiply(sk_c4, sk_c7) = sk_c8),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[927, 924])).
% 0.48/0.65 tff(929,plain,
% 0.48/0.65 (multiply(sk_c4, sk_c8) = multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))),
% 0.48/0.65 inference(transitivity,[status(thm)],[779, 928, 87, 444, 447, 450, 453, 461, 159, 463, 471, 474])).
% 0.48/0.65 tff(930,plain,
% 0.48/0.65 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))),
% 0.48/0.65 inference(monotonicity,[status(thm)],[754, 929])).
% 0.48/0.65 tff(931,plain,
% 0.48/0.65 (multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7),
% 0.48/0.65 inference(transitivity,[status(thm)],[930, 477, 428, 207, 313, 9])).
% 0.48/0.65 tff(932,plain,
% 0.48/0.65 (((inverse(sk_c2) = sk_c3) | (inverse(sk_c4) = sk_c8)) <=> ((inverse(sk_c2) = sk_c3) | (inverse(sk_c4) = sk_c8))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(933,axiom,((inverse(sk_c2) = sk_c3) | (inverse(sk_c4) = sk_c8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this_17')).
% 0.48/0.65 tff(934,plain,
% 0.48/0.65 ((inverse(sk_c2) = sk_c3) | (inverse(sk_c4) = sk_c8)),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[933, 932])).
% 0.48/0.65 tff(935,plain,
% 0.48/0.65 (inverse(sk_c4) = sk_c8),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[934, 924])).
% 0.48/0.65 tff(936,plain,
% 0.48/0.65 ((~(multiply(sk_c8, multiply(sk_c4, sk_c8)) = sk_c7)) | (~(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))) = sk_c8)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), sk_c7) = sk_c8)) | (~(multiply(inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1))), sk_c8) = sk_c7)) | (~(multiply(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)), inverse(multiply(multiply(sk_c3, sk_c1), multiply(sk_c7, sk_c1)))) = sk_c7))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[794, 38, 935, 143])).
% 0.48/0.65 tff(937,plain,
% 0.48/0.65 ($false),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[936, 759, 760, 931, 756, 753])).
% 0.48/0.65 % SZS output end Proof
% 0.48/0.65 % E exiting
%------------------------------------------------------------------------------